0.002 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.277 * * * [progress]: [2/2] Setting up program.
0.283 * [progress]: [Phase 2 of 3] Improving.
0.283 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.284 * [simplify]: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.284 * * [simplify]: iteration 1: (13 enodes)
0.293 * * [simplify]: iteration 2: (57 enodes)
0.314 * * [simplify]: iteration 3: (102 enodes)
0.351 * * [simplify]: iteration 4: (189 enodes)
0.430 * * [simplify]: iteration 5: (375 enodes)
0.596 * * [simplify]: iteration 6: (937 enodes)
1.546 * * [simplify]: Extracting #0: cost 1 inf + 0
1.546 * * [simplify]: Extracting #1: cost 60 inf + 0
1.548 * * [simplify]: Extracting #2: cost 219 inf + 1
1.551 * * [simplify]: Extracting #3: cost 277 inf + 210
1.555 * * [simplify]: Extracting #4: cost 283 inf + 2300
1.568 * * [simplify]: Extracting #5: cost 183 inf + 26485
1.609 * * [simplify]: Extracting #6: cost 74 inf + 97550
1.658 * * [simplify]: Extracting #7: cost 0 inf + 165315
1.710 * * [simplify]: Extracting #8: cost 0 inf + 165195
1.754 * [simplify]: Simplified to (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))
1.761 * * [progress]: iteration 1 / 4
1.761 * * * [progress]: picking best candidate
1.767 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))>
1.767 * * * [progress]: localizing error
1.790 * * * [progress]: generating rewritten candidates
1.790 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
1.806 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
1.819 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
1.836 * * * [progress]: generating series expansions
1.836 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
1.837 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
1.837 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
1.838 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
1.838 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
1.838 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
1.838 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
1.838 * [taylor]: Taking taylor expansion of 1/2 in k
1.838 * [backup-simplify]: Simplify 1/2 into 1/2
1.838 * [taylor]: Taking taylor expansion of (- 1 k) in k
1.838 * [taylor]: Taking taylor expansion of 1 in k
1.838 * [backup-simplify]: Simplify 1 into 1
1.838 * [taylor]: Taking taylor expansion of k in k
1.838 * [backup-simplify]: Simplify 0 into 0
1.838 * [backup-simplify]: Simplify 1 into 1
1.838 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
1.838 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
1.838 * [taylor]: Taking taylor expansion of 2 in k
1.838 * [backup-simplify]: Simplify 2 into 2
1.838 * [taylor]: Taking taylor expansion of (* n PI) in k
1.838 * [taylor]: Taking taylor expansion of n in k
1.838 * [backup-simplify]: Simplify n into n
1.838 * [taylor]: Taking taylor expansion of PI in k
1.838 * [backup-simplify]: Simplify PI into PI
1.838 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.838 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
1.838 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
1.839 * [backup-simplify]: Simplify (- 0) into 0
1.839 * [backup-simplify]: Simplify (+ 1 0) into 1
1.840 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.840 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
1.840 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
1.840 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
1.840 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
1.840 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
1.840 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
1.840 * [taylor]: Taking taylor expansion of 1/2 in n
1.840 * [backup-simplify]: Simplify 1/2 into 1/2
1.840 * [taylor]: Taking taylor expansion of (- 1 k) in n
1.840 * [taylor]: Taking taylor expansion of 1 in n
1.841 * [backup-simplify]: Simplify 1 into 1
1.841 * [taylor]: Taking taylor expansion of k in n
1.841 * [backup-simplify]: Simplify k into k
1.841 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.841 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.841 * [taylor]: Taking taylor expansion of 2 in n
1.841 * [backup-simplify]: Simplify 2 into 2
1.841 * [taylor]: Taking taylor expansion of (* n PI) in n
1.841 * [taylor]: Taking taylor expansion of n in n
1.841 * [backup-simplify]: Simplify 0 into 0
1.841 * [backup-simplify]: Simplify 1 into 1
1.841 * [taylor]: Taking taylor expansion of PI in n
1.841 * [backup-simplify]: Simplify PI into PI
1.841 * [backup-simplify]: Simplify (* 0 PI) into 0
1.842 * [backup-simplify]: Simplify (* 2 0) into 0
1.843 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.844 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.845 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.845 * [backup-simplify]: Simplify (- k) into (- k)
1.845 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
1.845 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
1.846 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.846 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
1.847 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
1.847 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
1.847 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
1.847 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
1.847 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
1.847 * [taylor]: Taking taylor expansion of 1/2 in n
1.847 * [backup-simplify]: Simplify 1/2 into 1/2
1.847 * [taylor]: Taking taylor expansion of (- 1 k) in n
1.847 * [taylor]: Taking taylor expansion of 1 in n
1.847 * [backup-simplify]: Simplify 1 into 1
1.847 * [taylor]: Taking taylor expansion of k in n
1.847 * [backup-simplify]: Simplify k into k
1.847 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.847 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.847 * [taylor]: Taking taylor expansion of 2 in n
1.847 * [backup-simplify]: Simplify 2 into 2
1.847 * [taylor]: Taking taylor expansion of (* n PI) in n
1.847 * [taylor]: Taking taylor expansion of n in n
1.847 * [backup-simplify]: Simplify 0 into 0
1.847 * [backup-simplify]: Simplify 1 into 1
1.847 * [taylor]: Taking taylor expansion of PI in n
1.847 * [backup-simplify]: Simplify PI into PI
1.848 * [backup-simplify]: Simplify (* 0 PI) into 0
1.848 * [backup-simplify]: Simplify (* 2 0) into 0
1.849 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.850 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.850 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.850 * [backup-simplify]: Simplify (- k) into (- k)
1.850 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
1.850 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
1.851 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.852 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
1.853 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
1.853 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
1.853 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
1.853 * [taylor]: Taking taylor expansion of 1/2 in k
1.853 * [backup-simplify]: Simplify 1/2 into 1/2
1.853 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
1.853 * [taylor]: Taking taylor expansion of (- 1 k) in k
1.853 * [taylor]: Taking taylor expansion of 1 in k
1.853 * [backup-simplify]: Simplify 1 into 1
1.853 * [taylor]: Taking taylor expansion of k in k
1.853 * [backup-simplify]: Simplify 0 into 0
1.853 * [backup-simplify]: Simplify 1 into 1
1.853 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
1.853 * [taylor]: Taking taylor expansion of (log n) in k
1.853 * [taylor]: Taking taylor expansion of n in k
1.853 * [backup-simplify]: Simplify n into n
1.853 * [backup-simplify]: Simplify (log n) into (log n)
1.853 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.853 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.853 * [taylor]: Taking taylor expansion of 2 in k
1.853 * [backup-simplify]: Simplify 2 into 2
1.853 * [taylor]: Taking taylor expansion of PI in k
1.853 * [backup-simplify]: Simplify PI into PI
1.854 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.854 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.855 * [backup-simplify]: Simplify (- 0) into 0
1.855 * [backup-simplify]: Simplify (+ 1 0) into 1
1.856 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.856 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
1.857 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
1.858 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.858 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.859 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.860 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.861 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.861 * [backup-simplify]: Simplify (- 0) into 0
1.862 * [backup-simplify]: Simplify (+ 0 0) into 0
1.862 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
1.863 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.863 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
1.865 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.865 * [taylor]: Taking taylor expansion of 0 in k
1.865 * [backup-simplify]: Simplify 0 into 0
1.865 * [backup-simplify]: Simplify 0 into 0
1.865 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
1.866 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.867 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.867 * [backup-simplify]: Simplify (+ 0 0) into 0
1.867 * [backup-simplify]: Simplify (- 1) into -1
1.868 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.868 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
1.870 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
1.871 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.873 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.874 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.875 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.878 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.879 * [backup-simplify]: Simplify (- 0) into 0
1.879 * [backup-simplify]: Simplify (+ 0 0) into 0
1.880 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
1.881 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.883 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.885 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.885 * [taylor]: Taking taylor expansion of 0 in k
1.885 * [backup-simplify]: Simplify 0 into 0
1.885 * [backup-simplify]: Simplify 0 into 0
1.885 * [backup-simplify]: Simplify 0 into 0
1.887 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
1.888 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.891 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.892 * [backup-simplify]: Simplify (+ 0 0) into 0
1.892 * [backup-simplify]: Simplify (- 0) into 0
1.893 * [backup-simplify]: Simplify (+ 0 0) into 0
1.895 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.898 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.901 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
1.906 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
1.916 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
1.917 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (* (- 1 (/ 1 k)) 1/2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
1.917 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
1.917 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
1.917 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
1.917 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
1.917 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
1.917 * [taylor]: Taking taylor expansion of 1/2 in k
1.918 * [backup-simplify]: Simplify 1/2 into 1/2
1.918 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
1.918 * [taylor]: Taking taylor expansion of 1 in k
1.918 * [backup-simplify]: Simplify 1 into 1
1.918 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.918 * [taylor]: Taking taylor expansion of k in k
1.918 * [backup-simplify]: Simplify 0 into 0
1.918 * [backup-simplify]: Simplify 1 into 1
1.918 * [backup-simplify]: Simplify (/ 1 1) into 1
1.918 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
1.918 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
1.918 * [taylor]: Taking taylor expansion of 2 in k
1.918 * [backup-simplify]: Simplify 2 into 2
1.918 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.918 * [taylor]: Taking taylor expansion of PI in k
1.918 * [backup-simplify]: Simplify PI into PI
1.918 * [taylor]: Taking taylor expansion of n in k
1.918 * [backup-simplify]: Simplify n into n
1.918 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.919 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
1.919 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
1.919 * [backup-simplify]: Simplify (- 1) into -1
1.919 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.920 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
1.920 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
1.920 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
1.920 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
1.920 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.920 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.920 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
1.920 * [taylor]: Taking taylor expansion of 1/2 in n
1.921 * [backup-simplify]: Simplify 1/2 into 1/2
1.921 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
1.921 * [taylor]: Taking taylor expansion of 1 in n
1.921 * [backup-simplify]: Simplify 1 into 1
1.921 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.921 * [taylor]: Taking taylor expansion of k in n
1.921 * [backup-simplify]: Simplify k into k
1.921 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.921 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.921 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.921 * [taylor]: Taking taylor expansion of 2 in n
1.921 * [backup-simplify]: Simplify 2 into 2
1.921 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.921 * [taylor]: Taking taylor expansion of PI in n
1.921 * [backup-simplify]: Simplify PI into PI
1.921 * [taylor]: Taking taylor expansion of n in n
1.921 * [backup-simplify]: Simplify 0 into 0
1.921 * [backup-simplify]: Simplify 1 into 1
1.921 * [backup-simplify]: Simplify (/ PI 1) into PI
1.922 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.923 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.923 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
1.923 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
1.923 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
1.925 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.926 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
1.927 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
1.927 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
1.927 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.927 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.927 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
1.927 * [taylor]: Taking taylor expansion of 1/2 in n
1.927 * [backup-simplify]: Simplify 1/2 into 1/2
1.927 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
1.927 * [taylor]: Taking taylor expansion of 1 in n
1.927 * [backup-simplify]: Simplify 1 into 1
1.927 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.927 * [taylor]: Taking taylor expansion of k in n
1.927 * [backup-simplify]: Simplify k into k
1.927 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.927 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.927 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.927 * [taylor]: Taking taylor expansion of 2 in n
1.927 * [backup-simplify]: Simplify 2 into 2
1.927 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.928 * [taylor]: Taking taylor expansion of PI in n
1.928 * [backup-simplify]: Simplify PI into PI
1.928 * [taylor]: Taking taylor expansion of n in n
1.928 * [backup-simplify]: Simplify 0 into 0
1.928 * [backup-simplify]: Simplify 1 into 1
1.932 * [backup-simplify]: Simplify (/ PI 1) into PI
1.932 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.933 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.933 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
1.933 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
1.933 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
1.934 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.934 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
1.935 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
1.935 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
1.935 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
1.935 * [taylor]: Taking taylor expansion of 1/2 in k
1.935 * [backup-simplify]: Simplify 1/2 into 1/2
1.935 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
1.935 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
1.935 * [taylor]: Taking taylor expansion of 1 in k
1.935 * [backup-simplify]: Simplify 1 into 1
1.935 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.935 * [taylor]: Taking taylor expansion of k in k
1.935 * [backup-simplify]: Simplify 0 into 0
1.935 * [backup-simplify]: Simplify 1 into 1
1.936 * [backup-simplify]: Simplify (/ 1 1) into 1
1.936 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
1.936 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.936 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.936 * [taylor]: Taking taylor expansion of 2 in k
1.936 * [backup-simplify]: Simplify 2 into 2
1.936 * [taylor]: Taking taylor expansion of PI in k
1.936 * [backup-simplify]: Simplify PI into PI
1.936 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.937 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.937 * [taylor]: Taking taylor expansion of (log n) in k
1.937 * [taylor]: Taking taylor expansion of n in k
1.937 * [backup-simplify]: Simplify n into n
1.937 * [backup-simplify]: Simplify (log n) into (log n)
1.937 * [backup-simplify]: Simplify (- 1) into -1
1.937 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.937 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.938 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
1.938 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
1.939 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
1.940 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
1.941 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
1.941 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.942 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.943 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.943 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.943 * [backup-simplify]: Simplify (- 0) into 0
1.943 * [backup-simplify]: Simplify (+ 0 0) into 0
1.943 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
1.944 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.945 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
1.946 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.946 * [taylor]: Taking taylor expansion of 0 in k
1.946 * [backup-simplify]: Simplify 0 into 0
1.946 * [backup-simplify]: Simplify 0 into 0
1.946 * [backup-simplify]: Simplify 0 into 0
1.947 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.947 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.949 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.949 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.949 * [backup-simplify]: Simplify (- 0) into 0
1.950 * [backup-simplify]: Simplify (+ 0 0) into 0
1.950 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
1.951 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.952 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
1.953 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.953 * [taylor]: Taking taylor expansion of 0 in k
1.953 * [backup-simplify]: Simplify 0 into 0
1.953 * [backup-simplify]: Simplify 0 into 0
1.953 * [backup-simplify]: Simplify 0 into 0
1.954 * [backup-simplify]: Simplify 0 into 0
1.954 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.955 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.958 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
1.958 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.959 * [backup-simplify]: Simplify (- 0) into 0
1.959 * [backup-simplify]: Simplify (+ 0 0) into 0
1.960 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
1.962 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.963 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
1.966 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
1.966 * [taylor]: Taking taylor expansion of 0 in k
1.966 * [backup-simplify]: Simplify 0 into 0
1.966 * [backup-simplify]: Simplify 0 into 0
1.968 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
1.968 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (* (- 1 (/ 1 (- k))) 1/2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
1.968 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
1.968 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
1.968 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
1.968 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
1.968 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
1.968 * [taylor]: Taking taylor expansion of 1/2 in k
1.968 * [backup-simplify]: Simplify 1/2 into 1/2
1.968 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
1.968 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.968 * [taylor]: Taking taylor expansion of k in k
1.969 * [backup-simplify]: Simplify 0 into 0
1.969 * [backup-simplify]: Simplify 1 into 1
1.969 * [backup-simplify]: Simplify (/ 1 1) into 1
1.969 * [taylor]: Taking taylor expansion of 1 in k
1.969 * [backup-simplify]: Simplify 1 into 1
1.969 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
1.969 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
1.969 * [taylor]: Taking taylor expansion of -2 in k
1.969 * [backup-simplify]: Simplify -2 into -2
1.969 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.969 * [taylor]: Taking taylor expansion of PI in k
1.969 * [backup-simplify]: Simplify PI into PI
1.969 * [taylor]: Taking taylor expansion of n in k
1.969 * [backup-simplify]: Simplify n into n
1.969 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.969 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
1.969 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
1.970 * [backup-simplify]: Simplify (+ 1 0) into 1
1.970 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.970 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
1.971 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
1.971 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
1.971 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
1.971 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
1.971 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
1.971 * [taylor]: Taking taylor expansion of 1/2 in n
1.971 * [backup-simplify]: Simplify 1/2 into 1/2
1.971 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
1.971 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.971 * [taylor]: Taking taylor expansion of k in n
1.971 * [backup-simplify]: Simplify k into k
1.971 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.971 * [taylor]: Taking taylor expansion of 1 in n
1.971 * [backup-simplify]: Simplify 1 into 1
1.971 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.971 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.971 * [taylor]: Taking taylor expansion of -2 in n
1.971 * [backup-simplify]: Simplify -2 into -2
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 PI) into (* -2 PI)
1.973 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.973 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
1.973 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
1.973 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.974 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
1.975 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
1.975 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
1.975 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
1.975 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
1.975 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
1.975 * [taylor]: Taking taylor expansion of 1/2 in n
1.975 * [backup-simplify]: Simplify 1/2 into 1/2
1.975 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
1.975 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.975 * [taylor]: Taking taylor expansion of k in n
1.975 * [backup-simplify]: Simplify k into k
1.975 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.975 * [taylor]: Taking taylor expansion of 1 in n
1.975 * [backup-simplify]: Simplify 1 into 1
1.975 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.975 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.975 * [taylor]: Taking taylor expansion of -2 in n
1.975 * [backup-simplify]: Simplify -2 into -2
1.975 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.975 * [taylor]: Taking taylor expansion of PI in n
1.975 * [backup-simplify]: Simplify PI into PI
1.975 * [taylor]: Taking taylor expansion of n in n
1.975 * [backup-simplify]: Simplify 0 into 0
1.975 * [backup-simplify]: Simplify 1 into 1
1.976 * [backup-simplify]: Simplify (/ PI 1) into PI
1.976 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.976 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.977 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
1.977 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
1.977 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.978 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
1.979 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
1.979 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
1.979 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
1.979 * [taylor]: Taking taylor expansion of 1/2 in k
1.979 * [backup-simplify]: Simplify 1/2 into 1/2
1.979 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
1.979 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
1.979 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.979 * [taylor]: Taking taylor expansion of k in k
1.979 * [backup-simplify]: Simplify 0 into 0
1.979 * [backup-simplify]: Simplify 1 into 1
1.979 * [backup-simplify]: Simplify (/ 1 1) into 1
1.979 * [taylor]: Taking taylor expansion of 1 in k
1.979 * [backup-simplify]: Simplify 1 into 1
1.979 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
1.979 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
1.979 * [taylor]: Taking taylor expansion of (* -2 PI) in k
1.979 * [taylor]: Taking taylor expansion of -2 in k
1.979 * [backup-simplify]: Simplify -2 into -2
1.979 * [taylor]: Taking taylor expansion of PI in k
1.979 * [backup-simplify]: Simplify PI into PI
1.980 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.980 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.980 * [taylor]: Taking taylor expansion of (log n) in k
1.980 * [taylor]: Taking taylor expansion of n in k
1.980 * [backup-simplify]: Simplify n into n
1.980 * [backup-simplify]: Simplify (log n) into (log n)
1.981 * [backup-simplify]: Simplify (+ 1 0) into 1
1.981 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.981 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
1.982 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
1.983 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
1.983 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
1.984 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
1.985 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.985 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
1.986 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
1.986 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.986 * [backup-simplify]: Simplify (+ 0 0) into 0
1.987 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
1.987 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.988 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
1.989 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.989 * [taylor]: Taking taylor expansion of 0 in k
1.989 * [backup-simplify]: Simplify 0 into 0
1.989 * [backup-simplify]: Simplify 0 into 0
1.989 * [backup-simplify]: Simplify 0 into 0
1.990 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.990 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
1.992 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
1.992 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.993 * [backup-simplify]: Simplify (+ 0 0) into 0
1.993 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
1.994 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.995 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
1.996 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.996 * [taylor]: Taking taylor expansion of 0 in k
1.996 * [backup-simplify]: Simplify 0 into 0
1.996 * [backup-simplify]: Simplify 0 into 0
1.996 * [backup-simplify]: Simplify 0 into 0
1.996 * [backup-simplify]: Simplify 0 into 0
1.997 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.998 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.001 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
2.001 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.001 * [backup-simplify]: Simplify (+ 0 0) into 0
2.002 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
2.003 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.004 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
2.006 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.006 * [taylor]: Taking taylor expansion of 0 in k
2.006 * [backup-simplify]: Simplify 0 into 0
2.006 * [backup-simplify]: Simplify 0 into 0
2.006 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
2.006 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
2.007 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
2.007 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
2.007 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.007 * [taylor]: Taking taylor expansion of 2 in n
2.007 * [backup-simplify]: Simplify 2 into 2
2.007 * [taylor]: Taking taylor expansion of (* n PI) in n
2.007 * [taylor]: Taking taylor expansion of n in n
2.007 * [backup-simplify]: Simplify 0 into 0
2.007 * [backup-simplify]: Simplify 1 into 1
2.007 * [taylor]: Taking taylor expansion of PI in n
2.007 * [backup-simplify]: Simplify PI into PI
2.007 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.007 * [taylor]: Taking taylor expansion of 2 in n
2.007 * [backup-simplify]: Simplify 2 into 2
2.007 * [taylor]: Taking taylor expansion of (* n PI) in n
2.007 * [taylor]: Taking taylor expansion of n in n
2.007 * [backup-simplify]: Simplify 0 into 0
2.007 * [backup-simplify]: Simplify 1 into 1
2.007 * [taylor]: Taking taylor expansion of PI in n
2.007 * [backup-simplify]: Simplify PI into PI
2.007 * [backup-simplify]: Simplify (* 0 PI) into 0
2.008 * [backup-simplify]: Simplify (* 2 0) into 0
2.008 * [backup-simplify]: Simplify 0 into 0
2.009 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.009 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.010 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.010 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.011 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.011 * [backup-simplify]: Simplify 0 into 0
2.012 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.012 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.012 * [backup-simplify]: Simplify 0 into 0
2.013 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.014 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.014 * [backup-simplify]: Simplify 0 into 0
2.015 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.016 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
2.016 * [backup-simplify]: Simplify 0 into 0
2.017 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.018 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
2.018 * [backup-simplify]: Simplify 0 into 0
2.019 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
2.023 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
2.023 * [backup-simplify]: Simplify 0 into 0
2.024 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
2.024 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
2.024 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
2.024 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.024 * [taylor]: Taking taylor expansion of 2 in n
2.024 * [backup-simplify]: Simplify 2 into 2
2.024 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.024 * [taylor]: Taking taylor expansion of PI in n
2.024 * [backup-simplify]: Simplify PI into PI
2.025 * [taylor]: Taking taylor expansion of n in n
2.025 * [backup-simplify]: Simplify 0 into 0
2.025 * [backup-simplify]: Simplify 1 into 1
2.025 * [backup-simplify]: Simplify (/ PI 1) into PI
2.025 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.025 * [taylor]: Taking taylor expansion of 2 in n
2.025 * [backup-simplify]: Simplify 2 into 2
2.025 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.025 * [taylor]: Taking taylor expansion of PI in n
2.025 * [backup-simplify]: Simplify PI into PI
2.025 * [taylor]: Taking taylor expansion of n in n
2.025 * [backup-simplify]: Simplify 0 into 0
2.025 * [backup-simplify]: Simplify 1 into 1
2.025 * [backup-simplify]: Simplify (/ PI 1) into PI
2.026 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.026 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.026 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.027 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.027 * [backup-simplify]: Simplify 0 into 0
2.027 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.028 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.028 * [backup-simplify]: Simplify 0 into 0
2.029 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.029 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.029 * [backup-simplify]: Simplify 0 into 0
2.030 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.031 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.031 * [backup-simplify]: Simplify 0 into 0
2.031 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.032 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.032 * [backup-simplify]: Simplify 0 into 0
2.033 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.034 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.034 * [backup-simplify]: Simplify 0 into 0
2.034 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
2.034 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
2.035 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
2.035 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.035 * [taylor]: Taking taylor expansion of -2 in n
2.035 * [backup-simplify]: Simplify -2 into -2
2.035 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.035 * [taylor]: Taking taylor expansion of PI in n
2.035 * [backup-simplify]: Simplify PI into PI
2.035 * [taylor]: Taking taylor expansion of n in n
2.035 * [backup-simplify]: Simplify 0 into 0
2.035 * [backup-simplify]: Simplify 1 into 1
2.035 * [backup-simplify]: Simplify (/ PI 1) into PI
2.035 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.035 * [taylor]: Taking taylor expansion of -2 in n
2.035 * [backup-simplify]: Simplify -2 into -2
2.035 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.035 * [taylor]: Taking taylor expansion of PI in n
2.035 * [backup-simplify]: Simplify PI into PI
2.035 * [taylor]: Taking taylor expansion of n in n
2.035 * [backup-simplify]: Simplify 0 into 0
2.035 * [backup-simplify]: Simplify 1 into 1
2.035 * [backup-simplify]: Simplify (/ PI 1) into PI
2.036 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.036 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.037 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.037 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.037 * [backup-simplify]: Simplify 0 into 0
2.038 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.038 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.038 * [backup-simplify]: Simplify 0 into 0
2.039 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.040 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.040 * [backup-simplify]: Simplify 0 into 0
2.040 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.041 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.041 * [backup-simplify]: Simplify 0 into 0
2.042 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.042 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.043 * [backup-simplify]: Simplify 0 into 0
2.043 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.045 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.045 * [backup-simplify]: Simplify 0 into 0
2.045 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
2.045 * * * * [progress]: [ 3 / 3 ] generating series at (2)
2.046 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
2.046 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (n k) around 0
2.046 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
2.046 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
2.046 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
2.046 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
2.046 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
2.046 * [taylor]: Taking taylor expansion of 1/2 in k
2.046 * [backup-simplify]: Simplify 1/2 into 1/2
2.046 * [taylor]: Taking taylor expansion of (- 1 k) in k
2.046 * [taylor]: Taking taylor expansion of 1 in k
2.046 * [backup-simplify]: Simplify 1 into 1
2.046 * [taylor]: Taking taylor expansion of k in k
2.046 * [backup-simplify]: Simplify 0 into 0
2.046 * [backup-simplify]: Simplify 1 into 1
2.046 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
2.046 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
2.046 * [taylor]: Taking taylor expansion of 2 in k
2.046 * [backup-simplify]: Simplify 2 into 2
2.046 * [taylor]: Taking taylor expansion of (* n PI) in k
2.046 * [taylor]: Taking taylor expansion of n in k
2.046 * [backup-simplify]: Simplify n into n
2.046 * [taylor]: Taking taylor expansion of PI in k
2.046 * [backup-simplify]: Simplify PI into PI
2.046 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.047 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
2.047 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
2.047 * [backup-simplify]: Simplify (- 0) into 0
2.047 * [backup-simplify]: Simplify (+ 1 0) into 1
2.048 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.048 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
2.048 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
2.048 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.048 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.048 * [taylor]: Taking taylor expansion of k in k
2.048 * [backup-simplify]: Simplify 0 into 0
2.048 * [backup-simplify]: Simplify 1 into 1
2.048 * [backup-simplify]: Simplify (/ 1 1) into 1
2.049 * [backup-simplify]: Simplify (sqrt 0) into 0
2.050 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.050 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
2.050 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
2.050 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
2.050 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
2.051 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
2.051 * [taylor]: Taking taylor expansion of 1/2 in n
2.051 * [backup-simplify]: Simplify 1/2 into 1/2
2.051 * [taylor]: Taking taylor expansion of (- 1 k) in n
2.051 * [taylor]: Taking taylor expansion of 1 in n
2.051 * [backup-simplify]: Simplify 1 into 1
2.051 * [taylor]: Taking taylor expansion of k in n
2.051 * [backup-simplify]: Simplify k into k
2.051 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.051 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.051 * [taylor]: Taking taylor expansion of 2 in n
2.051 * [backup-simplify]: Simplify 2 into 2
2.051 * [taylor]: Taking taylor expansion of (* n PI) in n
2.051 * [taylor]: Taking taylor expansion of n in n
2.051 * [backup-simplify]: Simplify 0 into 0
2.051 * [backup-simplify]: Simplify 1 into 1
2.051 * [taylor]: Taking taylor expansion of PI in n
2.051 * [backup-simplify]: Simplify PI into PI
2.051 * [backup-simplify]: Simplify (* 0 PI) into 0
2.052 * [backup-simplify]: Simplify (* 2 0) into 0
2.053 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.054 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.055 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.055 * [backup-simplify]: Simplify (- k) into (- k)
2.055 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
2.055 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
2.057 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.058 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
2.059 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
2.059 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.059 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.059 * [taylor]: Taking taylor expansion of k in n
2.059 * [backup-simplify]: Simplify k into k
2.059 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.059 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.059 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.059 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.059 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
2.059 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
2.059 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
2.059 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
2.059 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
2.059 * [taylor]: Taking taylor expansion of 1/2 in n
2.059 * [backup-simplify]: Simplify 1/2 into 1/2
2.059 * [taylor]: Taking taylor expansion of (- 1 k) in n
2.059 * [taylor]: Taking taylor expansion of 1 in n
2.059 * [backup-simplify]: Simplify 1 into 1
2.059 * [taylor]: Taking taylor expansion of k in n
2.059 * [backup-simplify]: Simplify k into k
2.059 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.059 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.059 * [taylor]: Taking taylor expansion of 2 in n
2.059 * [backup-simplify]: Simplify 2 into 2
2.059 * [taylor]: Taking taylor expansion of (* n PI) in n
2.059 * [taylor]: Taking taylor expansion of n in n
2.059 * [backup-simplify]: Simplify 0 into 0
2.060 * [backup-simplify]: Simplify 1 into 1
2.060 * [taylor]: Taking taylor expansion of PI in n
2.060 * [backup-simplify]: Simplify PI into PI
2.060 * [backup-simplify]: Simplify (* 0 PI) into 0
2.060 * [backup-simplify]: Simplify (* 2 0) into 0
2.062 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.063 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.064 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.064 * [backup-simplify]: Simplify (- k) into (- k)
2.064 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
2.065 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
2.066 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.067 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
2.068 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
2.068 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.068 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.068 * [taylor]: Taking taylor expansion of k in n
2.068 * [backup-simplify]: Simplify k into k
2.068 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.068 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.068 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.068 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.069 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k)))
2.069 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
2.069 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
2.069 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
2.069 * [taylor]: Taking taylor expansion of 1/2 in k
2.069 * [backup-simplify]: Simplify 1/2 into 1/2
2.069 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
2.070 * [taylor]: Taking taylor expansion of (- 1 k) in k
2.070 * [taylor]: Taking taylor expansion of 1 in k
2.070 * [backup-simplify]: Simplify 1 into 1
2.070 * [taylor]: Taking taylor expansion of k in k
2.070 * [backup-simplify]: Simplify 0 into 0
2.070 * [backup-simplify]: Simplify 1 into 1
2.070 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
2.070 * [taylor]: Taking taylor expansion of (log n) in k
2.070 * [taylor]: Taking taylor expansion of n in k
2.070 * [backup-simplify]: Simplify n into n
2.070 * [backup-simplify]: Simplify (log n) into (log n)
2.070 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.070 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.070 * [taylor]: Taking taylor expansion of 2 in k
2.070 * [backup-simplify]: Simplify 2 into 2
2.070 * [taylor]: Taking taylor expansion of PI in k
2.070 * [backup-simplify]: Simplify PI into PI
2.070 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.071 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.072 * [backup-simplify]: Simplify (- 0) into 0
2.072 * [backup-simplify]: Simplify (+ 1 0) into 1
2.073 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.074 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
2.075 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
2.076 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
2.076 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.076 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.076 * [taylor]: Taking taylor expansion of k in k
2.076 * [backup-simplify]: Simplify 0 into 0
2.076 * [backup-simplify]: Simplify 1 into 1
2.076 * [backup-simplify]: Simplify (/ 1 1) into 1
2.077 * [backup-simplify]: Simplify (sqrt 0) into 0
2.078 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.079 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
2.079 * [backup-simplify]: Simplify 0 into 0
2.080 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.081 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.083 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.084 * [backup-simplify]: Simplify (- 0) into 0
2.084 * [backup-simplify]: Simplify (+ 0 0) into 0
2.084 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
2.086 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.087 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
2.089 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.090 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
2.090 * [taylor]: Taking taylor expansion of 0 in k
2.090 * [backup-simplify]: Simplify 0 into 0
2.090 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
2.091 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.093 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.093 * [backup-simplify]: Simplify (+ 0 0) into 0
2.094 * [backup-simplify]: Simplify (- 1) into -1
2.094 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.096 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
2.098 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
2.101 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.104 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.105 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.106 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.106 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
2.108 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.109 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.112 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.112 * [backup-simplify]: Simplify (- 0) into 0
2.113 * [backup-simplify]: Simplify (+ 0 0) into 0
2.114 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
2.115 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.116 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.119 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.120 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
2.120 * [taylor]: Taking taylor expansion of 0 in k
2.120 * [backup-simplify]: Simplify 0 into 0
2.120 * [backup-simplify]: Simplify 0 into 0
2.121 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
2.124 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.126 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
2.127 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.130 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.130 * [backup-simplify]: Simplify (+ 0 0) into 0
2.131 * [backup-simplify]: Simplify (- 0) into 0
2.131 * [backup-simplify]: Simplify (+ 0 0) into 0
2.133 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.135 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.139 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
2.153 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
2.158 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
2.159 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.159 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
2.161 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.162 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.168 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.168 * [backup-simplify]: Simplify (- 0) into 0
2.169 * [backup-simplify]: Simplify (+ 0 0) into 0
2.170 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
2.171 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.173 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.176 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.178 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
2.178 * [taylor]: Taking taylor expansion of 0 in k
2.178 * [backup-simplify]: Simplify 0 into 0
2.178 * [backup-simplify]: Simplify 0 into 0
2.178 * [backup-simplify]: Simplify 0 into 0
2.179 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.183 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.185 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
2.187 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.192 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.193 * [backup-simplify]: Simplify (+ 0 0) into 0
2.193 * [backup-simplify]: Simplify (- 0) into 0
2.194 * [backup-simplify]: Simplify (+ 0 0) into 0
2.196 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.198 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.205 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.221 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
2.233 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
2.252 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
2.253 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (* (- 1 (/ 1 k)) 1/2)) (sqrt (/ 1 k))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
2.253 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (n k) around 0
2.253 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
2.253 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
2.254 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
2.254 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
2.254 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
2.254 * [taylor]: Taking taylor expansion of 1/2 in k
2.254 * [backup-simplify]: Simplify 1/2 into 1/2
2.254 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
2.254 * [taylor]: Taking taylor expansion of 1 in k
2.254 * [backup-simplify]: Simplify 1 into 1
2.254 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.254 * [taylor]: Taking taylor expansion of k in k
2.254 * [backup-simplify]: Simplify 0 into 0
2.254 * [backup-simplify]: Simplify 1 into 1
2.254 * [backup-simplify]: Simplify (/ 1 1) into 1
2.254 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
2.254 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
2.254 * [taylor]: Taking taylor expansion of 2 in k
2.254 * [backup-simplify]: Simplify 2 into 2
2.254 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.254 * [taylor]: Taking taylor expansion of PI in k
2.255 * [backup-simplify]: Simplify PI into PI
2.255 * [taylor]: Taking taylor expansion of n in k
2.255 * [backup-simplify]: Simplify n into n
2.255 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.255 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
2.255 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
2.255 * [backup-simplify]: Simplify (- 1) into -1
2.256 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.256 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
2.256 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
2.256 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
2.257 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.257 * [taylor]: Taking taylor expansion of k in k
2.257 * [backup-simplify]: Simplify 0 into 0
2.257 * [backup-simplify]: Simplify 1 into 1
2.257 * [backup-simplify]: Simplify (sqrt 0) into 0
2.259 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.259 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
2.259 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
2.259 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.259 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.259 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
2.259 * [taylor]: Taking taylor expansion of 1/2 in n
2.259 * [backup-simplify]: Simplify 1/2 into 1/2
2.259 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
2.259 * [taylor]: Taking taylor expansion of 1 in n
2.259 * [backup-simplify]: Simplify 1 into 1
2.259 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.259 * [taylor]: Taking taylor expansion of k in n
2.259 * [backup-simplify]: Simplify k into k
2.259 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.259 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.259 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.259 * [taylor]: Taking taylor expansion of 2 in n
2.259 * [backup-simplify]: Simplify 2 into 2
2.259 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.259 * [taylor]: Taking taylor expansion of PI in n
2.259 * [backup-simplify]: Simplify PI into PI
2.259 * [taylor]: Taking taylor expansion of n in n
2.259 * [backup-simplify]: Simplify 0 into 0
2.259 * [backup-simplify]: Simplify 1 into 1
2.260 * [backup-simplify]: Simplify (/ PI 1) into PI
2.260 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.261 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.262 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.262 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
2.262 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
2.264 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.265 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
2.266 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
2.266 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.266 * [taylor]: Taking taylor expansion of k in n
2.266 * [backup-simplify]: Simplify k into k
2.266 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.266 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.266 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
2.266 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
2.266 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.266 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.266 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
2.266 * [taylor]: Taking taylor expansion of 1/2 in n
2.266 * [backup-simplify]: Simplify 1/2 into 1/2
2.266 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
2.267 * [taylor]: Taking taylor expansion of 1 in n
2.267 * [backup-simplify]: Simplify 1 into 1
2.267 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.267 * [taylor]: Taking taylor expansion of k in n
2.267 * [backup-simplify]: Simplify k into k
2.267 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.267 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.267 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.267 * [taylor]: Taking taylor expansion of 2 in n
2.267 * [backup-simplify]: Simplify 2 into 2
2.267 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.267 * [taylor]: Taking taylor expansion of PI in n
2.267 * [backup-simplify]: Simplify PI into PI
2.267 * [taylor]: Taking taylor expansion of n in n
2.267 * [backup-simplify]: Simplify 0 into 0
2.267 * [backup-simplify]: Simplify 1 into 1
2.267 * [backup-simplify]: Simplify (/ PI 1) into PI
2.268 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.269 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.269 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.269 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
2.269 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
2.271 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.272 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
2.273 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
2.273 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.273 * [taylor]: Taking taylor expansion of k in n
2.273 * [backup-simplify]: Simplify k into k
2.273 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.273 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.274 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
2.274 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
2.274 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
2.274 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
2.274 * [taylor]: Taking taylor expansion of 1/2 in k
2.274 * [backup-simplify]: Simplify 1/2 into 1/2
2.275 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
2.275 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
2.275 * [taylor]: Taking taylor expansion of 1 in k
2.275 * [backup-simplify]: Simplify 1 into 1
2.275 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.275 * [taylor]: Taking taylor expansion of k in k
2.275 * [backup-simplify]: Simplify 0 into 0
2.275 * [backup-simplify]: Simplify 1 into 1
2.275 * [backup-simplify]: Simplify (/ 1 1) into 1
2.275 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
2.275 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.275 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.275 * [taylor]: Taking taylor expansion of 2 in k
2.275 * [backup-simplify]: Simplify 2 into 2
2.275 * [taylor]: Taking taylor expansion of PI in k
2.275 * [backup-simplify]: Simplify PI into PI
2.276 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.277 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.277 * [taylor]: Taking taylor expansion of (log n) in k
2.277 * [taylor]: Taking taylor expansion of n in k
2.277 * [backup-simplify]: Simplify n into n
2.277 * [backup-simplify]: Simplify (log n) into (log n)
2.277 * [backup-simplify]: Simplify (- 1) into -1
2.278 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.278 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.279 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
2.280 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
2.281 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
2.282 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
2.282 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.283 * [taylor]: Taking taylor expansion of k in k
2.283 * [backup-simplify]: Simplify 0 into 0
2.283 * [backup-simplify]: Simplify 1 into 1
2.283 * [backup-simplify]: Simplify (sqrt 0) into 0
2.285 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.286 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0
2.286 * [backup-simplify]: Simplify 0 into 0
2.287 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.288 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.296 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.296 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.297 * [backup-simplify]: Simplify (- 0) into 0
2.297 * [backup-simplify]: Simplify (+ 0 0) into 0
2.298 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
2.299 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.300 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
2.302 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.304 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
2.304 * [taylor]: Taking taylor expansion of 0 in k
2.304 * [backup-simplify]: Simplify 0 into 0
2.304 * [backup-simplify]: Simplify 0 into 0
2.306 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.307 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.308 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
2.309 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.310 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.313 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.313 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.314 * [backup-simplify]: Simplify (- 0) into 0
2.314 * [backup-simplify]: Simplify (+ 0 0) into 0
2.315 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
2.317 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.318 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
2.321 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.322 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
2.322 * [taylor]: Taking taylor expansion of 0 in k
2.322 * [backup-simplify]: Simplify 0 into 0
2.322 * [backup-simplify]: Simplify 0 into 0
2.322 * [backup-simplify]: Simplify 0 into 0
2.326 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.328 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.329 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.330 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
2.331 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.332 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.338 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.338 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.339 * [backup-simplify]: Simplify (- 0) into 0
2.339 * [backup-simplify]: Simplify (+ 0 0) into 0
2.341 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
2.342 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.344 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
2.347 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.349 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
2.349 * [taylor]: Taking taylor expansion of 0 in k
2.349 * [backup-simplify]: Simplify 0 into 0
2.349 * [backup-simplify]: Simplify 0 into 0
2.349 * [backup-simplify]: Simplify 0 into 0
2.349 * [backup-simplify]: Simplify 0 into 0
2.353 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.355 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.356 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.361 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
2.362 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (* (- 1 (/ 1 (- k))) 1/2)) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
2.362 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (n k) around 0
2.362 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
2.362 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
2.362 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
2.362 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
2.362 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
2.362 * [taylor]: Taking taylor expansion of 1/2 in k
2.362 * [backup-simplify]: Simplify 1/2 into 1/2
2.362 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
2.362 * [taylor]: Taking taylor expansion of (/ 1 k) in k
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
2.363 * [backup-simplify]: Simplify (/ 1 1) into 1
2.363 * [taylor]: Taking taylor expansion of 1 in k
2.363 * [backup-simplify]: Simplify 1 into 1
2.363 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
2.363 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
2.363 * [taylor]: Taking taylor expansion of -2 in k
2.363 * [backup-simplify]: Simplify -2 into -2
2.363 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.363 * [taylor]: Taking taylor expansion of PI in k
2.363 * [backup-simplify]: Simplify PI into PI
2.363 * [taylor]: Taking taylor expansion of n in k
2.363 * [backup-simplify]: Simplify n into n
2.363 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.363 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
2.363 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
2.364 * [backup-simplify]: Simplify (+ 1 0) into 1
2.364 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.364 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
2.364 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
2.364 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.364 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.364 * [taylor]: Taking taylor expansion of -1 in k
2.364 * [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
2.367 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.367 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
2.367 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
2.367 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
2.367 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
2.367 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
2.367 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
2.367 * [taylor]: Taking taylor expansion of 1/2 in n
2.367 * [backup-simplify]: Simplify 1/2 into 1/2
2.367 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
2.367 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.367 * [taylor]: Taking taylor expansion of k in n
2.367 * [backup-simplify]: Simplify k into k
2.367 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.367 * [taylor]: Taking taylor expansion of 1 in n
2.367 * [backup-simplify]: Simplify 1 into 1
2.367 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.368 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.368 * [taylor]: Taking taylor expansion of -2 in n
2.368 * [backup-simplify]: Simplify -2 into -2
2.368 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.368 * [taylor]: Taking taylor expansion of PI in n
2.368 * [backup-simplify]: Simplify PI into PI
2.368 * [taylor]: Taking taylor expansion of n in n
2.368 * [backup-simplify]: Simplify 0 into 0
2.368 * [backup-simplify]: Simplify 1 into 1
2.368 * [backup-simplify]: Simplify (/ PI 1) into PI
2.369 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.370 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.370 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
2.370 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
2.371 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.372 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
2.373 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
2.373 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.373 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.373 * [taylor]: Taking taylor expansion of -1 in n
2.373 * [backup-simplify]: Simplify -1 into -1
2.373 * [taylor]: Taking taylor expansion of k in n
2.374 * [backup-simplify]: Simplify k into k
2.374 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.374 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.374 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.374 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.375 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
2.375 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
2.375 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
2.375 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
2.375 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
2.375 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
2.375 * [taylor]: Taking taylor expansion of 1/2 in n
2.375 * [backup-simplify]: Simplify 1/2 into 1/2
2.375 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
2.375 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.375 * [taylor]: Taking taylor expansion of k in n
2.375 * [backup-simplify]: Simplify k into k
2.375 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.376 * [taylor]: Taking taylor expansion of 1 in n
2.376 * [backup-simplify]: Simplify 1 into 1
2.376 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.376 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.376 * [taylor]: Taking taylor expansion of -2 in n
2.376 * [backup-simplify]: Simplify -2 into -2
2.376 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.376 * [taylor]: Taking taylor expansion of PI in n
2.376 * [backup-simplify]: Simplify PI into PI
2.376 * [taylor]: Taking taylor expansion of n in n
2.376 * [backup-simplify]: Simplify 0 into 0
2.376 * [backup-simplify]: Simplify 1 into 1
2.376 * [backup-simplify]: Simplify (/ PI 1) into PI
2.377 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.378 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.378 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
2.378 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
2.379 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.381 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
2.382 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
2.382 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.382 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.382 * [taylor]: Taking taylor expansion of -1 in n
2.382 * [backup-simplify]: Simplify -1 into -1
2.382 * [taylor]: Taking taylor expansion of k in n
2.382 * [backup-simplify]: Simplify k into k
2.382 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.382 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.382 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.382 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.384 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
2.384 * [taylor]: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k
2.384 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
2.384 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
2.384 * [taylor]: Taking taylor expansion of 1/2 in k
2.384 * [backup-simplify]: Simplify 1/2 into 1/2
2.384 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
2.384 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
2.384 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.384 * [taylor]: Taking taylor expansion of k in k
2.384 * [backup-simplify]: Simplify 0 into 0
2.384 * [backup-simplify]: Simplify 1 into 1
2.385 * [backup-simplify]: Simplify (/ 1 1) into 1
2.385 * [taylor]: Taking taylor expansion of 1 in k
2.385 * [backup-simplify]: Simplify 1 into 1
2.385 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
2.385 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
2.385 * [taylor]: Taking taylor expansion of (* -2 PI) in k
2.385 * [taylor]: Taking taylor expansion of -2 in k
2.385 * [backup-simplify]: Simplify -2 into -2
2.385 * [taylor]: Taking taylor expansion of PI in k
2.385 * [backup-simplify]: Simplify PI into PI
2.385 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.386 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.386 * [taylor]: Taking taylor expansion of (log n) in k
2.387 * [taylor]: Taking taylor expansion of n in k
2.387 * [backup-simplify]: Simplify n into n
2.387 * [backup-simplify]: Simplify (log n) into (log n)
2.387 * [backup-simplify]: Simplify (+ 1 0) into 1
2.387 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.388 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
2.389 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
2.390 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
2.391 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
2.391 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.391 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.391 * [taylor]: Taking taylor expansion of -1 in k
2.391 * [backup-simplify]: Simplify -1 into -1
2.392 * [taylor]: Taking taylor expansion of k in k
2.392 * [backup-simplify]: Simplify 0 into 0
2.392 * [backup-simplify]: Simplify 1 into 1
2.392 * [backup-simplify]: Simplify (/ -1 1) into -1
2.392 * [backup-simplify]: Simplify (sqrt 0) into 0
2.393 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.394 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
2.394 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
2.395 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.395 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.397 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
2.397 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.397 * [backup-simplify]: Simplify (+ 0 0) into 0
2.397 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
2.398 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.399 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
2.400 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.401 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
2.401 * [taylor]: Taking taylor expansion of 0 in k
2.401 * [backup-simplify]: Simplify 0 into 0
2.401 * [backup-simplify]: Simplify 0 into 0
2.401 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
2.403 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.404 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.405 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.406 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.408 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
2.408 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.409 * [backup-simplify]: Simplify (+ 0 0) into 0
2.409 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
2.410 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.411 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
2.412 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.413 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.413 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
2.414 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
2.414 * [taylor]: Taking taylor expansion of 0 in k
2.414 * [backup-simplify]: Simplify 0 into 0
2.414 * [backup-simplify]: Simplify 0 into 0
2.414 * [backup-simplify]: Simplify 0 into 0
2.415 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.417 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.419 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.423 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.426 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
2.426 * * * [progress]: simplifying candidates
2.426 * * * * [progress]: [ 1 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (* (- 1 k) 1/2))) (sqrt k)))>
2.426 * * * * [progress]: [ 2 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (* (- 1 k) 1/2))) (sqrt k)))>
2.426 * * * * [progress]: [ 3 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))) (sqrt k)))>
2.426 * * * * [progress]: [ 4 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (* (- 1 k) 1/2))) (sqrt k)))>
2.426 * * * * [progress]: [ 5 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (* (- 1 k) 1/2))) (sqrt k)))>
2.426 * * * * [progress]: [ 6 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (* (- 1 k) 1/2))) (sqrt k)))>
2.426 * * * * [progress]: [ 7 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (* (- 1 k) 1/2))) (sqrt k)))>
2.426 * * * * [progress]: [ 8 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1 k)) 1/2) (sqrt k)))>
2.427 * * * * [progress]: [ 9 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (* (- 1 k) 1/2)) (pow (* 2 PI) (* (- 1 k) 1/2))) (sqrt k)))>
2.427 * * * * [progress]: [ 10 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) 1) (sqrt k)))>
2.427 * * * * [progress]: [ 11 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))>
2.427 * * * * [progress]: [ 12 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))>
2.427 * * * * [progress]: [ 13 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))>
2.427 * * * * [progress]: [ 14 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))>
2.427 * * * * [progress]: [ 15 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))>
2.427 * * * * [progress]: [ 16 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)))>
2.427 * * * * [progress]: [ 17 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2))) (sqrt k)))>
2.427 * * * * [progress]: [ 18 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt k)))>
2.427 * * * * [progress]: [ 19 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 20 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 21 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 22 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 23 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 24 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 25 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 26 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 27 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 28 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 29 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 30 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 31 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 32 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 33 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))>
2.427 * * * * [progress]: [ 34 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))>
2.428 * * * * [progress]: [ 35 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (* (- 1 k) 1/2)) (sqrt k)))>
2.428 * * * * [progress]: [ 36 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (* (- 1 k) 1/2)) (sqrt k)))>
2.428 * * * * [progress]: [ 37 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (* (- 1 k) 1/2)) (sqrt k)))>
2.428 * * * * [progress]: [ 38 / 104 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)) 1))>
2.428 * * * * [progress]: [ 39 / 104 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (* (- 1 k) 1/2)) (log (sqrt k)))))>
2.428 * * * * [progress]: [ 40 / 104 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (log (* 2 PI))) (* (- 1 k) 1/2)) (log (sqrt k)))))>
2.428 * * * * [progress]: [ 41 / 104 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (* (- 1 k) 1/2)) (log (sqrt k)))))>
2.428 * * * * [progress]: [ 42 / 104 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (* (- 1 k) 1/2)) (log (sqrt k)))))>
2.428 * * * * [progress]: [ 43 / 104 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (log (sqrt k)))))>
2.428 * * * * [progress]: [ 44 / 104 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
2.428 * * * * [progress]: [ 45 / 104 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
2.428 * * * * [progress]: [ 46 / 104 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
2.428 * * * * [progress]: [ 47 / 104 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
2.428 * * * * [progress]: [ 48 / 104 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
2.428 * * * * [progress]: [ 49 / 104 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
2.428 * * * * [progress]: [ 50 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (- (sqrt k))))>
2.428 * * * * [progress]: [ 51 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (cbrt (sqrt k)))))>
2.428 * * * * [progress]: [ 52 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (cbrt k)))))>
2.428 * * * * [progress]: [ 53 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
2.428 * * * * [progress]: [ 54 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (sqrt 1)) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
2.428 * * * * [progress]: [ 55 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
2.428 * * * * [progress]: [ 56 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (* (- 1 k) 1/2)) 1) (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k))))>
2.428 * * * * [progress]: [ 57 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (sqrt k)))))>
2.428 * * * * [progress]: [ 58 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (cbrt k)))))>
2.428 * * * * [progress]: [ 59 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))))>
2.429 * * * * [progress]: [ 60 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt 1)) (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))>
2.429 * * * * [progress]: [ 61 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))))>
2.429 * * * * [progress]: [ 62 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) 1) (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))>
2.429 * * * * [progress]: [ 63 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (sqrt k)))))>
2.429 * * * * [progress]: [ 64 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (cbrt k)))))>
2.429 * * * * [progress]: [ 65 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))))>
2.429 * * * * [progress]: [ 66 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))>
2.429 * * * * [progress]: [ 67 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k)))))>
2.429 * * * * [progress]: [ 68 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) 1) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k))))>
2.429 * * * * [progress]: [ 69 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (cbrt (sqrt k)))))>
2.429 * * * * [progress]: [ 70 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (cbrt k)))))>
2.429 * * * * [progress]: [ 71 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
2.429 * * * * [progress]: [ 72 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))))>
2.429 * * * * [progress]: [ 73 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k)))))>
2.429 * * * * [progress]: [ 74 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))))>
2.429 * * * * [progress]: [ 75 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (cbrt (sqrt k)))))>
2.429 * * * * [progress]: [ 76 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (cbrt k)))))>
2.429 * * * * [progress]: [ 77 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))))>
2.429 * * * * [progress]: [ 78 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt k))))>
2.429 * * * * [progress]: [ 79 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k)))))>
2.429 * * * * [progress]: [ 80 / 104 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt k))))>
2.429 * * * * [progress]: [ 81 / 104 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))))>
2.429 * * * * [progress]: [ 82 / 104 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (/ 1 (sqrt k))))>
2.429 * * * * [progress]: [ 83 / 104 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))))>
2.430 * * * * [progress]: [ 84 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
2.430 * * * * [progress]: [ 85 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
2.430 * * * * [progress]: [ 86 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.430 * * * * [progress]: [ 87 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt 1)) (sqrt k)))>
2.430 * * * * [progress]: [ 88 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.430 * * * * [progress]: [ 89 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) 1) (sqrt k)))>
2.430 * * * * [progress]: [ 90 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow n (* (- 1 k) 1/2)) (/ (sqrt k) (pow (* 2 PI) (* (- 1 k) 1/2)))))>
2.430 * * * * [progress]: [ 91 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))))))>
2.430 * * * * [progress]: [ 92 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))))))>
2.430 * * * * [progress]: [ 93 / 104 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))))>
2.430 * * * * [progress]: [ 94 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)))))>
2.430 * * * * [progress]: [ 95 / 104 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))))>
2.430 * * * * [progress]: [ 96 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
2.430 * * * * [progress]: [ 97 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))>
2.430 * * * * [progress]: [ 98 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))>
2.430 * * * * [progress]: [ 99 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k)))>
2.430 * * * * [progress]: [ 100 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k)))>
2.430 * * * * [progress]: [ 101 / 104 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k)))>
2.430 * * * * [progress]: [ 102 / 104 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
2.430 * * * * [progress]: [ 103 / 104 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
2.430 * * * * [progress]: [ 104 / 104 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
2.432 * [simplify]: Simplifying (* (+ (log n) (+ (log 2) (log PI))) (* (- 1 k) 1/2)), (* (+ (log n) (log (* 2 PI))) (* (- 1 k) 1/2)), (* (log (* n (* 2 PI))) (* (- 1 k) 1/2)), (* (log (* n (* 2 PI))) (* (- 1 k) 1/2)), (* 1 (* (- 1 k) 1/2)), (* 1 (* (- 1 k) 1/2)), (* 1 (* (- 1 k) 1/2)), (pow (* n (* 2 PI)) (- 1 k)), (pow n (* (- 1 k) 1/2)), (pow (* 2 PI) (* (- 1 k) 1/2)), (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2))), (exp (pow (* n (* 2 PI)) (* (- 1 k) 1/2))), (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))), (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))), (* (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))), (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))), (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))), (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)), (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)), (real->posit16 (pow (* n (* 2 PI)) (* (- 1 k) 1/2))), (* n (* 2 PI)), (* n (* 2 PI)), (+ (log n) (+ (log 2) (log PI))), (+ (log n) (log (* 2 PI))), (log (* n (* 2 PI))), (exp (* n (* 2 PI))), (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI))), (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI))), (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))), (cbrt (* n (* 2 PI))), (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI))), (sqrt (* n (* 2 PI))), (sqrt (* n (* 2 PI))), (* n 2), (* (cbrt n) (* 2 PI)), (* (sqrt n) (* 2 PI)), (* n (* 2 PI)), (real->posit16 (* n (* 2 PI))), (- (* (+ (log n) (+ (log 2) (log PI))) (* (- 1 k) 1/2)) (log (sqrt k))), (- (* (+ (log n) (log (* 2 PI))) (* (- 1 k) 1/2)) (log (sqrt k))), (- (* (log (* n (* 2 PI))) (* (- 1 k) 1/2)) (log (sqrt k))), (- (* (log (* n (* 2 PI))) (* (- 1 k) 1/2)) (log (sqrt k))), (- (log (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (log (sqrt k))), (log (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))), (exp (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))), (/ (* (* (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (* (* (sqrt k) (sqrt k)) (sqrt k))), (* (cbrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)))), (cbrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))), (* (* (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))), (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))), (sqrt (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))), (- (pow (* n (* 2 PI)) (* (- 1 k) 1/2))), (- (sqrt k)), (/ (pow n (* (- 1 k) 1/2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (cbrt (sqrt k))), (/ (pow n (* (- 1 k) 1/2)) (sqrt (* (cbrt k) (cbrt k)))), (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (cbrt k))), (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k))), (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k))), (/ (pow n (* (- 1 k) 1/2)) (sqrt 1)), (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)), (/ (pow n (* (- 1 k) 1/2)) (sqrt (sqrt k))), (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt (sqrt k))), (/ (pow n (* (- 1 k) 1/2)) 1), (/ (pow (* 2 PI) (* (- 1 k) 1/2)) (sqrt k)), (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (sqrt k))), (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (* (cbrt k) (cbrt k)))), (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (cbrt k))), (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))), (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k))), (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt 1)), (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)), (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) (sqrt (sqrt k))), (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k))), (/ (* (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2)))) 1), (/ (cbrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)), (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (cbrt (sqrt k))), (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (* (cbrt k) (cbrt k)))), (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (cbrt k))), (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt 1)), (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)), (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) 1), (/ (sqrt (pow (* n (* 2 PI)) (* (- 1 k) 1/2))) (sqrt k)), (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (cbrt (sqrt k))), (/ 1 (sqrt (* (cbrt k) (cbrt k)))), (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (cbrt k))), (/ 1 (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k))), (/ 1 (sqrt 1)), (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)), (/ 1 (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt (sqrt k))), (/ 1 1), (/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k)), (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (cbrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (* (cbrt k) (cbrt k)))), (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (cbrt k))), (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 1/2) 2)) (sqrt 1)), (/ (pow (* n (* 2 PI)) (/ (* (- 1 k) 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1/2)) (sqrt k))), (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))), (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))), (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))), (* 2 (* n PI)), (* 2 (* n PI)), (* 2 (* n PI)), (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))), (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))), (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
2.437 * * [simplify]: iteration 1: (239 enodes)
2.527 * * [simplify]: iteration 2: (1017 enodes)
2.869 * * [simplify]: Extracting #0: cost 82 inf + 0
2.870 * * [simplify]: Extracting #1: cost 369 inf + 1
2.872 * * [simplify]: Extracting #2: cost 598 inf + 10298
2.884 * * [simplify]: Extracting #3: cost 482 inf + 86599
2.908 * * [simplify]: Extracting #4: cost 275 inf + 195662
2.960 * * [simplify]: Extracting #5: cost 169 inf + 249507
3.020 * * [simplify]: Extracting #6: cost 134 inf + 284603
3.092 * * [simplify]: Extracting #7: cost 54 inf + 339415
3.174 * * [simplify]: Extracting #8: cost 10 inf + 374683
3.284 * * [simplify]: Extracting #9: cost 2 inf + 379546
3.404 * * [simplify]: Extracting #10: cost 0 inf + 380902
3.535 * * [simplify]: Extracting #11: cost 0 inf + 380822
3.636 * [simplify]: Simplified to (* (log (* n (* PI 2))) (* (- 1 k) 1/2)), (* (log (* n (* PI 2))) (* (- 1 k) 1/2)), (* (log (* n (* PI 2))) (* (- 1 k) 1/2)), (* (log (* n (* PI 2))) (* (- 1 k) 1/2)), (* (- 1 k) 1/2), (* (- 1 k) 1/2), (* (- 1 k) 1/2), (pow (* n (* PI 2)) (- 1 k)), (pow n (* (- 1 k) 1/2)), (pow (* PI 2) (* (- 1 k) 1/2)), (* (log (* n (* PI 2))) (* (- 1 k) 1/2)), (exp (pow (* n (* PI 2)) (/ (- 1 k) 2))), (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))), (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))), (pow (pow (* n (* PI 2)) (/ (- 1 k) 2)) 3), (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))), (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))), (pow (* n (* PI 2)) (/ (- 1 k) 4)), (pow (* n (* PI 2)) (/ (- 1 k) 4)), (real->posit16 (pow (* n (* PI 2)) (/ (- 1 k) 2))), (* n (* PI 2)), (* n (* PI 2)), (log (* n (* PI 2))), (log (* n (* PI 2))), (log (* n (* PI 2))), (* (exp (* PI n)) (exp (* PI n))), (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))), (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))), (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))), (cbrt (* n (* PI 2))), (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))), (sqrt (* n (* PI 2))), (sqrt (* n (* PI 2))), (* n 2), (* 2 (* PI (cbrt n))), (* (sqrt n) (* PI 2)), (* n (* PI 2)), (real->posit16 (* n (* PI 2))), (- (* (log (* n (* PI 2))) (* (- 1 k) 1/2)) (log (sqrt k))), (- (* (log (* n (* PI 2))) (* (- 1 k) 1/2)) (log (sqrt k))), (- (* (log (* n (* PI 2))) (* (- 1 k) 1/2)) (log (sqrt k))), (- (* (log (* n (* PI 2))) (* (- 1 k) 1/2)) (log (sqrt k))), (- (* (log (* n (* PI 2))) (* (- 1 k) 1/2)) (log (sqrt k))), (- (* (log (* n (* PI 2))) (* (- 1 k) 1/2)) (log (sqrt k))), (exp (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))), (/ (/ (pow (pow (* n (* PI 2)) (/ (- 1 k) 2)) 3) k) (sqrt k)), (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))), (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))), (/ (* (/ (pow (* n 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PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))), (* (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (fabs (cbrt k))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))), (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt k))), (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k))), (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))), (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)), (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k))), (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))), (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (fabs (cbrt k))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt k))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)), (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k))), (/ 1 (fabs (cbrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (cbrt k))), (/ 1 (sqrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))), 1, (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)), (/ 1 (sqrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))), 1, (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)), (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (cbrt (sqrt k))) (cbrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (cbrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (fabs (cbrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt (cbrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt (sqrt k))), (pow (* n (* PI 2)) (/ (- 1 k) 4)), (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt k)), (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt (sqrt k))), (pow (* n (* PI 2)) (/ (- 1 k) 4)), (/ (pow (* n (* PI 2)) (/ (- 1 k) 4)) (sqrt k)), (/ 1 (sqrt k)), (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2))), (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k))) (cbrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (fabs (cbrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (pow (* n (* PI 2)) (/ (- 1 k) 2)), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (pow (* n (* PI 2)) (/ (- 1 k) 2)), (/ (sqrt k) (pow (* PI 2) (* (- 1 k) 1/2))), (/ (sqrt k) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))), (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))), (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2))), (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 4))), (real->posit16 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))), (- (+ (+ (* (* (* (log (* PI 2)) 1/4) (* (exp (* 1/2 (log (* n (* PI 2))))) (log n))) (* k k)) (* (* (exp (* 1/2 (log (* n (* PI 2))))) 1/8) (* (* (log n) k) (* (log n) k)))) (+ (exp (* 1/2 (log (* n (* PI 2))))) (* (* (log (* PI 2)) (log (* PI 2))) (* (* (exp (* 1/2 (log (* n (* PI 2))))) (* k k)) 1/8)))) (* (* k (+ (* (exp (* 1/2 (log (* n (* PI 2))))) (log n)) (* (exp (* 1/2 (log (* n (* PI 2))))) (log (* PI 2))))) 1/2)), (exp (* (log (* n (* PI 2))) (* (- 1 k) 1/2))), (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* (- 1 k) 1/2))), (* n (* PI 2)), (* n (* PI 2)), (* n (* PI 2)), (- (* (- +nan.0) (* (* (log (* PI 2)) (* (* k k) (log n))) (exp (* 1/2 (log (* n (* PI 2))))))) (+ (* (* (log (* PI 2)) (* (exp (* 1/2 (log (* n (* PI 2))))) (* k k))) (- +nan.0)) (+ (- (* +nan.0 (* (* (* (log n) k) (* (log n) k)) (exp (* 1/2 (log (* n (* PI 2))))))) (* +nan.0 (* (exp (* 1/2 (log (* n (* PI 2))))) k))) (+ (- (* (exp (* 1/2 (log (* n (* PI 2))))) +nan.0) (* (* (* (log (* PI 2)) (log (* PI 2))) (* (exp (* 1/2 (log (* n (* PI 2))))) (* k k))) +nan.0)) (- (* (* (exp (* 1/2 (log (* n (* PI 2))))) (log n)) (* (* k k) +nan.0)) (- (* (exp (* 1/2 (log (* n (* PI 2))))) (* (* k k) +nan.0)) (- (* (* (log (* PI 2)) +nan.0) (* (exp (* 1/2 (log (* n (* PI 2))))) k)) (* +nan.0 (* (* (exp (* 1/2 (log (* n (* PI 2))))) (log n)) k))))))))), (+ (* +nan.0 (- (/ (exp (* (log (* n (* PI 2))) (* (- 1 k) 1/2))) (* k k)) (/ (/ (exp (* (log (* n (* PI 2))) (* (- 1 k) 1/2))) k) (* k k)))) (* (- +nan.0) (/ (exp (* (log (* n (* PI 2))) (* (- 1 k) 1/2))) k))), (+ (- (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* (- 1 k) 1/2))) (/ k +nan.0))) (* +nan.0 (- (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* (- 1 k) 1/2))) (* k k)) (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* (- 1 k) 1/2))))))
3.648 * * * [progress]: adding candidates to table
4.701 * * [progress]: iteration 2 / 4
4.701 * * * [progress]: picking best candidate
4.791 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))>
4.791 * * * [progress]: localizing error
4.833 * * * [progress]: generating rewritten candidates
4.833 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
4.865 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
4.879 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
4.891 * * * [progress]: generating series expansions
4.891 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
4.892 * [backup-simplify]: Simplify (pow (* n (* PI 2)) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
4.893 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
4.893 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
4.893 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
4.893 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
4.893 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
4.893 * [taylor]: Taking taylor expansion of 1/2 in k
4.893 * [backup-simplify]: Simplify 1/2 into 1/2
4.893 * [taylor]: Taking taylor expansion of (- 1 k) in k
4.893 * [taylor]: Taking taylor expansion of 1 in k
4.893 * [backup-simplify]: Simplify 1 into 1
4.893 * [taylor]: Taking taylor expansion of k in k
4.893 * [backup-simplify]: Simplify 0 into 0
4.893 * [backup-simplify]: Simplify 1 into 1
4.893 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
4.893 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
4.893 * [taylor]: Taking taylor expansion of 2 in k
4.893 * [backup-simplify]: Simplify 2 into 2
4.893 * [taylor]: Taking taylor expansion of (* n PI) in k
4.893 * [taylor]: Taking taylor expansion of n in k
4.893 * [backup-simplify]: Simplify n into n
4.893 * [taylor]: Taking taylor expansion of PI in k
4.893 * [backup-simplify]: Simplify PI into PI
4.893 * [backup-simplify]: Simplify (* n PI) into (* n PI)
4.893 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
4.893 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
4.893 * [backup-simplify]: Simplify (- 0) into 0
4.894 * [backup-simplify]: Simplify (+ 1 0) into 1
4.894 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
4.894 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
4.894 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
4.894 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
4.894 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
4.894 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
4.894 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
4.894 * [taylor]: Taking taylor expansion of 1/2 in n
4.894 * [backup-simplify]: Simplify 1/2 into 1/2
4.894 * [taylor]: Taking taylor expansion of (- 1 k) in n
4.894 * [taylor]: Taking taylor expansion of 1 in n
4.894 * [backup-simplify]: Simplify 1 into 1
4.894 * [taylor]: Taking taylor expansion of k in n
4.894 * [backup-simplify]: Simplify k into k
4.894 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
4.894 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
4.894 * [taylor]: Taking taylor expansion of 2 in n
4.894 * [backup-simplify]: Simplify 2 into 2
4.894 * [taylor]: Taking taylor expansion of (* n PI) in n
4.894 * [taylor]: Taking taylor expansion of n in n
4.894 * [backup-simplify]: Simplify 0 into 0
4.894 * [backup-simplify]: Simplify 1 into 1
4.894 * [taylor]: Taking taylor expansion of PI in n
4.894 * [backup-simplify]: Simplify PI into PI
4.895 * [backup-simplify]: Simplify (* 0 PI) into 0
4.895 * [backup-simplify]: Simplify (* 2 0) into 0
4.896 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.897 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
4.897 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.897 * [backup-simplify]: Simplify (- k) into (- k)
4.897 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
4.898 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
4.898 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.899 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
4.900 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
4.900 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
4.900 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
4.900 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
4.900 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
4.900 * [taylor]: Taking taylor expansion of 1/2 in n
4.900 * [backup-simplify]: Simplify 1/2 into 1/2
4.900 * [taylor]: Taking taylor expansion of (- 1 k) in n
4.900 * [taylor]: Taking taylor expansion of 1 in n
4.900 * [backup-simplify]: Simplify 1 into 1
4.900 * [taylor]: Taking taylor expansion of k in n
4.900 * [backup-simplify]: Simplify k into k
4.900 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
4.900 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
4.900 * [taylor]: Taking taylor expansion of 2 in n
4.900 * [backup-simplify]: Simplify 2 into 2
4.900 * [taylor]: Taking taylor expansion of (* n PI) in n
4.900 * [taylor]: Taking taylor expansion of n in n
4.900 * [backup-simplify]: Simplify 0 into 0
4.900 * [backup-simplify]: Simplify 1 into 1
4.900 * [taylor]: Taking taylor expansion of PI in n
4.900 * [backup-simplify]: Simplify PI into PI
4.900 * [backup-simplify]: Simplify (* 0 PI) into 0
4.901 * [backup-simplify]: Simplify (* 2 0) into 0
4.902 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.902 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
4.903 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.903 * [backup-simplify]: Simplify (- k) into (- k)
4.903 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
4.903 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
4.904 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.905 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
4.907 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
4.907 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
4.907 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
4.907 * [taylor]: Taking taylor expansion of 1/2 in k
4.907 * [backup-simplify]: Simplify 1/2 into 1/2
4.907 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
4.907 * [taylor]: Taking taylor expansion of (- 1 k) in k
4.907 * [taylor]: Taking taylor expansion of 1 in k
4.907 * [backup-simplify]: Simplify 1 into 1
4.907 * [taylor]: Taking taylor expansion of k in k
4.907 * [backup-simplify]: Simplify 0 into 0
4.907 * [backup-simplify]: Simplify 1 into 1
4.907 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
4.907 * [taylor]: Taking taylor expansion of (log n) in k
4.907 * [taylor]: Taking taylor expansion of n in k
4.907 * [backup-simplify]: Simplify n into n
4.908 * [backup-simplify]: Simplify (log n) into (log n)
4.908 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
4.908 * [taylor]: Taking taylor expansion of (* 2 PI) in k
4.908 * [taylor]: Taking taylor expansion of 2 in k
4.908 * [backup-simplify]: Simplify 2 into 2
4.908 * [taylor]: Taking taylor expansion of PI in k
4.908 * [backup-simplify]: Simplify PI into PI
4.908 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.909 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.909 * [backup-simplify]: Simplify (- 0) into 0
4.910 * [backup-simplify]: Simplify (+ 1 0) into 1
4.911 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.912 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
4.913 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
4.914 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
4.915 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
4.916 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
4.917 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
4.919 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
4.919 * [backup-simplify]: Simplify (- 0) into 0
4.920 * [backup-simplify]: Simplify (+ 0 0) into 0
4.920 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
4.922 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.923 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
4.924 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
4.924 * [taylor]: Taking taylor expansion of 0 in k
4.924 * [backup-simplify]: Simplify 0 into 0
4.924 * [backup-simplify]: Simplify 0 into 0
4.925 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
4.926 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
4.928 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
4.928 * [backup-simplify]: Simplify (+ 0 0) into 0
4.929 * [backup-simplify]: Simplify (- 1) into -1
4.929 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.931 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
4.933 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
4.936 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
4.939 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
4.940 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
4.941 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
4.945 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
4.945 * [backup-simplify]: Simplify (- 0) into 0
4.945 * [backup-simplify]: Simplify (+ 0 0) into 0
4.946 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
4.948 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.949 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
4.952 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
4.952 * [taylor]: Taking taylor expansion of 0 in k
4.952 * [backup-simplify]: Simplify 0 into 0
4.952 * [backup-simplify]: Simplify 0 into 0
4.952 * [backup-simplify]: Simplify 0 into 0
4.954 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
4.955 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
4.958 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
4.959 * [backup-simplify]: Simplify (+ 0 0) into 0
4.959 * [backup-simplify]: Simplify (- 0) into 0
4.960 * [backup-simplify]: Simplify (+ 0 0) into 0
4.961 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
4.964 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
4.973 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
4.977 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
4.983 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
4.984 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
4.984 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
4.984 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
4.984 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
4.984 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
4.984 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
4.984 * [taylor]: Taking taylor expansion of 1/2 in k
4.984 * [backup-simplify]: Simplify 1/2 into 1/2
4.984 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
4.984 * [taylor]: Taking taylor expansion of 1 in k
4.984 * [backup-simplify]: Simplify 1 into 1
4.984 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.984 * [taylor]: Taking taylor expansion of k in k
4.984 * [backup-simplify]: Simplify 0 into 0
4.984 * [backup-simplify]: Simplify 1 into 1
4.984 * [backup-simplify]: Simplify (/ 1 1) into 1
4.984 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
4.984 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
4.984 * [taylor]: Taking taylor expansion of 2 in k
4.984 * [backup-simplify]: Simplify 2 into 2
4.984 * [taylor]: Taking taylor expansion of (/ PI n) in k
4.984 * [taylor]: Taking taylor expansion of PI in k
4.984 * [backup-simplify]: Simplify PI into PI
4.984 * [taylor]: Taking taylor expansion of n in k
4.984 * [backup-simplify]: Simplify n into n
4.984 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
4.984 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
4.984 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
4.985 * [backup-simplify]: Simplify (- 1) into -1
4.985 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.985 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
4.985 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
4.985 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
4.985 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
4.986 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
4.986 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
4.986 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
4.986 * [taylor]: Taking taylor expansion of 1/2 in n
4.986 * [backup-simplify]: Simplify 1/2 into 1/2
4.986 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
4.986 * [taylor]: Taking taylor expansion of 1 in n
4.986 * [backup-simplify]: Simplify 1 into 1
4.986 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.986 * [taylor]: Taking taylor expansion of k in n
4.986 * [backup-simplify]: Simplify k into k
4.986 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.986 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
4.986 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
4.986 * [taylor]: Taking taylor expansion of 2 in n
4.986 * [backup-simplify]: Simplify 2 into 2
4.986 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.986 * [taylor]: Taking taylor expansion of PI in n
4.986 * [backup-simplify]: Simplify PI into PI
4.986 * [taylor]: Taking taylor expansion of n in n
4.986 * [backup-simplify]: Simplify 0 into 0
4.986 * [backup-simplify]: Simplify 1 into 1
4.986 * [backup-simplify]: Simplify (/ PI 1) into PI
4.986 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.987 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.987 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
4.987 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
4.987 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
4.988 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
4.989 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
4.990 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
4.990 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
4.990 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
4.990 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
4.990 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
4.990 * [taylor]: Taking taylor expansion of 1/2 in n
4.990 * [backup-simplify]: Simplify 1/2 into 1/2
4.990 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
4.990 * [taylor]: Taking taylor expansion of 1 in n
4.990 * [backup-simplify]: Simplify 1 into 1
4.990 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.990 * [taylor]: Taking taylor expansion of k in n
4.990 * [backup-simplify]: Simplify k into k
4.990 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.990 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
4.990 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
4.990 * [taylor]: Taking taylor expansion of 2 in n
4.990 * [backup-simplify]: Simplify 2 into 2
4.990 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.990 * [taylor]: Taking taylor expansion of PI in n
4.990 * [backup-simplify]: Simplify PI into PI
4.990 * [taylor]: Taking taylor expansion of n in n
4.990 * [backup-simplify]: Simplify 0 into 0
4.990 * [backup-simplify]: Simplify 1 into 1
4.990 * [backup-simplify]: Simplify (/ PI 1) into PI
4.991 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.991 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.991 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
4.991 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
4.991 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
4.992 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
4.993 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
4.994 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
4.994 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
4.994 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
4.994 * [taylor]: Taking taylor expansion of 1/2 in k
4.994 * [backup-simplify]: Simplify 1/2 into 1/2
4.994 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
4.994 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
4.994 * [taylor]: Taking taylor expansion of 1 in k
4.994 * [backup-simplify]: Simplify 1 into 1
4.994 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.994 * [taylor]: Taking taylor expansion of k in k
4.994 * [backup-simplify]: Simplify 0 into 0
4.994 * [backup-simplify]: Simplify 1 into 1
4.994 * [backup-simplify]: Simplify (/ 1 1) into 1
4.994 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
4.994 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
4.994 * [taylor]: Taking taylor expansion of (* 2 PI) in k
4.994 * [taylor]: Taking taylor expansion of 2 in k
4.994 * [backup-simplify]: Simplify 2 into 2
4.994 * [taylor]: Taking taylor expansion of PI in k
4.994 * [backup-simplify]: Simplify PI into PI
4.995 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.995 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.995 * [taylor]: Taking taylor expansion of (log n) in k
4.995 * [taylor]: Taking taylor expansion of n in k
4.995 * [backup-simplify]: Simplify n into n
4.995 * [backup-simplify]: Simplify (log n) into (log n)
4.996 * [backup-simplify]: Simplify (- 1) into -1
4.996 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.996 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
4.997 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
4.997 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
4.998 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
4.999 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.000 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.000 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.001 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.002 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.002 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.002 * [backup-simplify]: Simplify (- 0) into 0
5.002 * [backup-simplify]: Simplify (+ 0 0) into 0
5.003 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
5.004 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.005 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.006 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.006 * [taylor]: Taking taylor expansion of 0 in k
5.006 * [backup-simplify]: Simplify 0 into 0
5.006 * [backup-simplify]: Simplify 0 into 0
5.006 * [backup-simplify]: Simplify 0 into 0
5.007 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.008 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.011 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.012 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.012 * [backup-simplify]: Simplify (- 0) into 0
5.012 * [backup-simplify]: Simplify (+ 0 0) into 0
5.013 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
5.014 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.016 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
5.018 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.018 * [taylor]: Taking taylor expansion of 0 in k
5.018 * [backup-simplify]: Simplify 0 into 0
5.018 * [backup-simplify]: Simplify 0 into 0
5.018 * [backup-simplify]: Simplify 0 into 0
5.018 * [backup-simplify]: Simplify 0 into 0
5.019 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.020 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.026 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
5.027 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.027 * [backup-simplify]: Simplify (- 0) into 0
5.028 * [backup-simplify]: Simplify (+ 0 0) into 0
5.029 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
5.030 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.032 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
5.035 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.035 * [taylor]: Taking taylor expansion of 0 in k
5.035 * [backup-simplify]: Simplify 0 into 0
5.035 * [backup-simplify]: Simplify 0 into 0
5.037 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
5.038 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
5.038 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
5.038 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.038 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.038 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.038 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.038 * [taylor]: Taking taylor expansion of 1/2 in k
5.038 * [backup-simplify]: Simplify 1/2 into 1/2
5.038 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.038 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.038 * [taylor]: Taking taylor expansion of k in k
5.038 * [backup-simplify]: Simplify 0 into 0
5.038 * [backup-simplify]: Simplify 1 into 1
5.039 * [backup-simplify]: Simplify (/ 1 1) into 1
5.039 * [taylor]: Taking taylor expansion of 1 in k
5.039 * [backup-simplify]: Simplify 1 into 1
5.039 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.039 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.039 * [taylor]: Taking taylor expansion of -2 in k
5.039 * [backup-simplify]: Simplify -2 into -2
5.039 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.039 * [taylor]: Taking taylor expansion of PI in k
5.039 * [backup-simplify]: Simplify PI into PI
5.039 * [taylor]: Taking taylor expansion of n in k
5.039 * [backup-simplify]: Simplify n into n
5.039 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.039 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.039 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.040 * [backup-simplify]: Simplify (+ 1 0) into 1
5.040 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.040 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.041 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.041 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.041 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.041 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.041 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.041 * [taylor]: Taking taylor expansion of 1/2 in n
5.041 * [backup-simplify]: Simplify 1/2 into 1/2
5.041 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.041 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.041 * [taylor]: Taking taylor expansion of k in n
5.041 * [backup-simplify]: Simplify k into k
5.041 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.041 * [taylor]: Taking taylor expansion of 1 in n
5.041 * [backup-simplify]: Simplify 1 into 1
5.041 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.041 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.041 * [taylor]: Taking taylor expansion of -2 in n
5.041 * [backup-simplify]: Simplify -2 into -2
5.041 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.041 * [taylor]: Taking taylor expansion of PI in n
5.041 * [backup-simplify]: Simplify PI into PI
5.041 * [taylor]: Taking taylor expansion of n in n
5.041 * [backup-simplify]: Simplify 0 into 0
5.041 * [backup-simplify]: Simplify 1 into 1
5.042 * [backup-simplify]: Simplify (/ PI 1) into PI
5.042 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.043 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.043 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.043 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.045 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.046 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.047 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.047 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.047 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.047 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.047 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.047 * [taylor]: Taking taylor expansion of 1/2 in n
5.047 * [backup-simplify]: Simplify 1/2 into 1/2
5.047 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.047 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.047 * [taylor]: Taking taylor expansion of k in n
5.047 * [backup-simplify]: Simplify k into k
5.047 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.047 * [taylor]: Taking taylor expansion of 1 in n
5.048 * [backup-simplify]: Simplify 1 into 1
5.048 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.048 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.048 * [taylor]: Taking taylor expansion of -2 in n
5.048 * [backup-simplify]: Simplify -2 into -2
5.048 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.048 * [taylor]: Taking taylor expansion of PI in n
5.048 * [backup-simplify]: Simplify PI into PI
5.048 * [taylor]: Taking taylor expansion of n in n
5.048 * [backup-simplify]: Simplify 0 into 0
5.048 * [backup-simplify]: Simplify 1 into 1
5.048 * [backup-simplify]: Simplify (/ PI 1) into PI
5.049 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.050 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.050 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.050 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.051 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.053 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.054 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.054 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
5.054 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
5.054 * [taylor]: Taking taylor expansion of 1/2 in k
5.054 * [backup-simplify]: Simplify 1/2 into 1/2
5.054 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
5.054 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.054 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.054 * [taylor]: Taking taylor expansion of k in k
5.054 * [backup-simplify]: Simplify 0 into 0
5.054 * [backup-simplify]: Simplify 1 into 1
5.055 * [backup-simplify]: Simplify (/ 1 1) into 1
5.055 * [taylor]: Taking taylor expansion of 1 in k
5.055 * [backup-simplify]: Simplify 1 into 1
5.055 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
5.055 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
5.055 * [taylor]: Taking taylor expansion of (* -2 PI) in k
5.055 * [taylor]: Taking taylor expansion of -2 in k
5.055 * [backup-simplify]: Simplify -2 into -2
5.055 * [taylor]: Taking taylor expansion of PI in k
5.055 * [backup-simplify]: Simplify PI into PI
5.055 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.056 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.056 * [taylor]: Taking taylor expansion of (log n) in k
5.056 * [taylor]: Taking taylor expansion of n in k
5.057 * [backup-simplify]: Simplify n into n
5.057 * [backup-simplify]: Simplify (log n) into (log n)
5.057 * [backup-simplify]: Simplify (+ 1 0) into 1
5.057 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.058 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
5.059 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
5.060 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
5.061 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.063 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.064 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.064 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.066 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
5.066 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.067 * [backup-simplify]: Simplify (+ 0 0) into 0
5.067 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
5.069 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.070 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
5.071 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.072 * [taylor]: Taking taylor expansion of 0 in k
5.072 * [backup-simplify]: Simplify 0 into 0
5.072 * [backup-simplify]: Simplify 0 into 0
5.072 * [backup-simplify]: Simplify 0 into 0
5.073 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.074 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.077 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
5.078 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.078 * [backup-simplify]: Simplify (+ 0 0) into 0
5.079 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
5.080 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.081 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
5.083 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.083 * [taylor]: Taking taylor expansion of 0 in k
5.083 * [backup-simplify]: Simplify 0 into 0
5.083 * [backup-simplify]: Simplify 0 into 0
5.083 * [backup-simplify]: Simplify 0 into 0
5.083 * [backup-simplify]: Simplify 0 into 0
5.083 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.084 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.087 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
5.088 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.088 * [backup-simplify]: Simplify (+ 0 0) into 0
5.089 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
5.093 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.094 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
5.096 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.096 * [taylor]: Taking taylor expansion of 0 in k
5.096 * [backup-simplify]: Simplify 0 into 0
5.096 * [backup-simplify]: Simplify 0 into 0
5.097 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
5.097 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
5.097 * [backup-simplify]: Simplify (* n (* PI 2)) into (* 2 (* n PI))
5.097 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
5.097 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.097 * [taylor]: Taking taylor expansion of 2 in n
5.097 * [backup-simplify]: Simplify 2 into 2
5.097 * [taylor]: Taking taylor expansion of (* n PI) in n
5.097 * [taylor]: Taking taylor expansion of n in n
5.097 * [backup-simplify]: Simplify 0 into 0
5.097 * [backup-simplify]: Simplify 1 into 1
5.097 * [taylor]: Taking taylor expansion of PI in n
5.097 * [backup-simplify]: Simplify PI into PI
5.097 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.097 * [taylor]: Taking taylor expansion of 2 in n
5.097 * [backup-simplify]: Simplify 2 into 2
5.097 * [taylor]: Taking taylor expansion of (* n PI) in n
5.097 * [taylor]: Taking taylor expansion of n in n
5.097 * [backup-simplify]: Simplify 0 into 0
5.097 * [backup-simplify]: Simplify 1 into 1
5.097 * [taylor]: Taking taylor expansion of PI in n
5.097 * [backup-simplify]: Simplify PI into PI
5.098 * [backup-simplify]: Simplify (* 0 PI) into 0
5.098 * [backup-simplify]: Simplify (* 2 0) into 0
5.098 * [backup-simplify]: Simplify 0 into 0
5.099 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.100 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.100 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.101 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.101 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.101 * [backup-simplify]: Simplify 0 into 0
5.102 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.103 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.103 * [backup-simplify]: Simplify 0 into 0
5.104 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.104 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
5.104 * [backup-simplify]: Simplify 0 into 0
5.105 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.106 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
5.106 * [backup-simplify]: Simplify 0 into 0
5.107 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.108 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
5.108 * [backup-simplify]: Simplify 0 into 0
5.109 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
5.110 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
5.110 * [backup-simplify]: Simplify 0 into 0
5.110 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
5.111 * [backup-simplify]: Simplify (* (/ 1 n) (* PI 2)) into (* 2 (/ PI n))
5.111 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
5.111 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.111 * [taylor]: Taking taylor expansion of 2 in n
5.111 * [backup-simplify]: Simplify 2 into 2
5.111 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.111 * [taylor]: Taking taylor expansion of PI in n
5.111 * [backup-simplify]: Simplify PI into PI
5.111 * [taylor]: Taking taylor expansion of n in n
5.111 * [backup-simplify]: Simplify 0 into 0
5.111 * [backup-simplify]: Simplify 1 into 1
5.111 * [backup-simplify]: Simplify (/ PI 1) into PI
5.111 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.111 * [taylor]: Taking taylor expansion of 2 in n
5.111 * [backup-simplify]: Simplify 2 into 2
5.111 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.111 * [taylor]: Taking taylor expansion of PI in n
5.111 * [backup-simplify]: Simplify PI into PI
5.111 * [taylor]: Taking taylor expansion of n in n
5.111 * [backup-simplify]: Simplify 0 into 0
5.111 * [backup-simplify]: Simplify 1 into 1
5.112 * [backup-simplify]: Simplify (/ PI 1) into PI
5.112 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.113 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.114 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.114 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.114 * [backup-simplify]: Simplify 0 into 0
5.116 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.117 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.117 * [backup-simplify]: Simplify 0 into 0
5.118 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.119 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.119 * [backup-simplify]: Simplify 0 into 0
5.120 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.121 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.121 * [backup-simplify]: Simplify 0 into 0
5.122 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.124 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.124 * [backup-simplify]: Simplify 0 into 0
5.124 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.125 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.125 * [backup-simplify]: Simplify 0 into 0
5.126 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
5.126 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* PI 2)) into (* -2 (/ PI n))
5.126 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
5.126 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.126 * [taylor]: Taking taylor expansion of -2 in n
5.126 * [backup-simplify]: Simplify -2 into -2
5.126 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.126 * [taylor]: Taking taylor expansion of PI in n
5.126 * [backup-simplify]: Simplify PI into PI
5.126 * [taylor]: Taking taylor expansion of n in n
5.126 * [backup-simplify]: Simplify 0 into 0
5.126 * [backup-simplify]: Simplify 1 into 1
5.127 * [backup-simplify]: Simplify (/ PI 1) into PI
5.127 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.127 * [taylor]: Taking taylor expansion of -2 in n
5.127 * [backup-simplify]: Simplify -2 into -2
5.127 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.127 * [taylor]: Taking taylor expansion of PI in n
5.127 * [backup-simplify]: Simplify PI into PI
5.127 * [taylor]: Taking taylor expansion of n in n
5.127 * [backup-simplify]: Simplify 0 into 0
5.127 * [backup-simplify]: Simplify 1 into 1
5.127 * [backup-simplify]: Simplify (/ PI 1) into PI
5.127 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.128 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.128 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.129 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.129 * [backup-simplify]: Simplify 0 into 0
5.129 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.130 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.130 * [backup-simplify]: Simplify 0 into 0
5.130 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.131 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.131 * [backup-simplify]: Simplify 0 into 0
5.132 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.133 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.133 * [backup-simplify]: Simplify 0 into 0
5.133 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.134 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.134 * [backup-simplify]: Simplify 0 into 0
5.135 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.136 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.136 * [backup-simplify]: Simplify 0 into 0
5.136 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
5.136 * * * * [progress]: [ 3 / 3 ] generating series at (2)
5.137 * [backup-simplify]: Simplify (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
5.137 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (n k) around 0
5.137 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
5.137 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
5.137 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
5.137 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
5.137 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
5.137 * [taylor]: Taking taylor expansion of 1/2 in k
5.137 * [backup-simplify]: Simplify 1/2 into 1/2
5.137 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.137 * [taylor]: Taking taylor expansion of 1 in k
5.137 * [backup-simplify]: Simplify 1 into 1
5.137 * [taylor]: Taking taylor expansion of k in k
5.137 * [backup-simplify]: Simplify 0 into 0
5.137 * [backup-simplify]: Simplify 1 into 1
5.137 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.137 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.137 * [taylor]: Taking taylor expansion of 2 in k
5.137 * [backup-simplify]: Simplify 2 into 2
5.137 * [taylor]: Taking taylor expansion of (* n PI) in k
5.137 * [taylor]: Taking taylor expansion of n in k
5.137 * [backup-simplify]: Simplify n into n
5.137 * [taylor]: Taking taylor expansion of PI in k
5.137 * [backup-simplify]: Simplify PI into PI
5.137 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.137 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.137 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.137 * [backup-simplify]: Simplify (- 0) into 0
5.138 * [backup-simplify]: Simplify (+ 1 0) into 1
5.138 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.138 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.138 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.138 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.138 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.138 * [taylor]: Taking taylor expansion of k in k
5.138 * [backup-simplify]: Simplify 0 into 0
5.138 * [backup-simplify]: Simplify 1 into 1
5.138 * [backup-simplify]: Simplify (/ 1 1) into 1
5.139 * [backup-simplify]: Simplify (sqrt 0) into 0
5.140 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.140 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
5.140 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.140 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.140 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.140 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.140 * [taylor]: Taking taylor expansion of 1/2 in n
5.140 * [backup-simplify]: Simplify 1/2 into 1/2
5.140 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.140 * [taylor]: Taking taylor expansion of 1 in n
5.140 * [backup-simplify]: Simplify 1 into 1
5.140 * [taylor]: Taking taylor expansion of k in n
5.140 * [backup-simplify]: Simplify k into k
5.140 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.140 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.140 * [taylor]: Taking taylor expansion of 2 in n
5.140 * [backup-simplify]: Simplify 2 into 2
5.140 * [taylor]: Taking taylor expansion of (* n PI) in n
5.140 * [taylor]: Taking taylor expansion of n in n
5.140 * [backup-simplify]: Simplify 0 into 0
5.140 * [backup-simplify]: Simplify 1 into 1
5.140 * [taylor]: Taking taylor expansion of PI in n
5.140 * [backup-simplify]: Simplify PI into PI
5.140 * [backup-simplify]: Simplify (* 0 PI) into 0
5.140 * [backup-simplify]: Simplify (* 2 0) into 0
5.141 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.142 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.143 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.143 * [backup-simplify]: Simplify (- k) into (- k)
5.143 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.143 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.144 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.145 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.145 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.145 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
5.145 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.145 * [taylor]: Taking taylor expansion of k in n
5.145 * [backup-simplify]: Simplify k into k
5.145 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.145 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
5.145 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.146 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
5.146 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
5.146 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.146 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.146 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.146 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.146 * [taylor]: Taking taylor expansion of 1/2 in n
5.146 * [backup-simplify]: Simplify 1/2 into 1/2
5.146 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.146 * [taylor]: Taking taylor expansion of 1 in n
5.146 * [backup-simplify]: Simplify 1 into 1
5.146 * [taylor]: Taking taylor expansion of k in n
5.146 * [backup-simplify]: Simplify k into k
5.146 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.146 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.146 * [taylor]: Taking taylor expansion of 2 in n
5.146 * [backup-simplify]: Simplify 2 into 2
5.146 * [taylor]: Taking taylor expansion of (* n PI) in n
5.146 * [taylor]: Taking taylor expansion of n in n
5.146 * [backup-simplify]: Simplify 0 into 0
5.146 * [backup-simplify]: Simplify 1 into 1
5.146 * [taylor]: Taking taylor expansion of PI in n
5.146 * [backup-simplify]: Simplify PI into PI
5.146 * [backup-simplify]: Simplify (* 0 PI) into 0
5.147 * [backup-simplify]: Simplify (* 2 0) into 0
5.147 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.148 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.149 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.149 * [backup-simplify]: Simplify (- k) into (- k)
5.149 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.149 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.150 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.151 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.151 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.151 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
5.151 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.151 * [taylor]: Taking taylor expansion of k in n
5.151 * [backup-simplify]: Simplify k into k
5.151 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.152 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
5.152 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.152 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
5.152 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k)))
5.152 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
5.152 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
5.152 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
5.153 * [taylor]: Taking taylor expansion of 1/2 in k
5.153 * [backup-simplify]: Simplify 1/2 into 1/2
5.153 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
5.153 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.153 * [taylor]: Taking taylor expansion of 1 in k
5.153 * [backup-simplify]: Simplify 1 into 1
5.153 * [taylor]: Taking taylor expansion of k in k
5.153 * [backup-simplify]: Simplify 0 into 0
5.153 * [backup-simplify]: Simplify 1 into 1
5.153 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
5.153 * [taylor]: Taking taylor expansion of (log n) in k
5.153 * [taylor]: Taking taylor expansion of n in k
5.153 * [backup-simplify]: Simplify n into n
5.153 * [backup-simplify]: Simplify (log n) into (log n)
5.153 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.153 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.153 * [taylor]: Taking taylor expansion of 2 in k
5.153 * [backup-simplify]: Simplify 2 into 2
5.153 * [taylor]: Taking taylor expansion of PI in k
5.153 * [backup-simplify]: Simplify PI into PI
5.153 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.154 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.154 * [backup-simplify]: Simplify (- 0) into 0
5.154 * [backup-simplify]: Simplify (+ 1 0) into 1
5.155 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.155 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
5.156 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
5.157 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.158 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.158 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.158 * [taylor]: Taking taylor expansion of k in k
5.158 * [backup-simplify]: Simplify 0 into 0
5.158 * [backup-simplify]: Simplify 1 into 1
5.158 * [backup-simplify]: Simplify (/ 1 1) into 1
5.158 * [backup-simplify]: Simplify (sqrt 0) into 0
5.160 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.161 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
5.161 * [backup-simplify]: Simplify 0 into 0
5.162 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.163 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.165 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.165 * [backup-simplify]: Simplify (- 0) into 0
5.166 * [backup-simplify]: Simplify (+ 0 0) into 0
5.166 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
5.167 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.168 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
5.170 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.171 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
5.172 * [taylor]: Taking taylor expansion of 0 in k
5.172 * [backup-simplify]: Simplify 0 into 0
5.172 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
5.173 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.175 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.175 * [backup-simplify]: Simplify (+ 0 0) into 0
5.176 * [backup-simplify]: Simplify (- 1) into -1
5.176 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.178 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
5.180 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
5.183 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
5.187 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
5.189 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
5.189 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.190 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
5.191 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.192 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.196 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.196 * [backup-simplify]: Simplify (- 0) into 0
5.196 * [backup-simplify]: Simplify (+ 0 0) into 0
5.197 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
5.198 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.199 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.204 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.205 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
5.205 * [taylor]: Taking taylor expansion of 0 in k
5.205 * [backup-simplify]: Simplify 0 into 0
5.205 * [backup-simplify]: Simplify 0 into 0
5.206 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.208 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.209 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
5.209 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.211 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.212 * [backup-simplify]: Simplify (+ 0 0) into 0
5.212 * [backup-simplify]: Simplify (- 0) into 0
5.212 * [backup-simplify]: Simplify (+ 0 0) into 0
5.213 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.215 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.217 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
5.222 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
5.225 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
5.225 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.226 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
5.227 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.227 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
5.230 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
5.231 * [backup-simplify]: Simplify (- 0) into 0
5.231 * [backup-simplify]: Simplify (+ 0 0) into 0
5.232 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
5.233 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.234 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
5.236 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.238 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
5.238 * [taylor]: Taking taylor expansion of 0 in k
5.238 * [backup-simplify]: Simplify 0 into 0
5.238 * [backup-simplify]: Simplify 0 into 0
5.238 * [backup-simplify]: Simplify 0 into 0
5.239 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.243 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.246 * [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
5.247 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.252 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
5.253 * [backup-simplify]: Simplify (+ 0 0) into 0
5.253 * [backup-simplify]: Simplify (- 0) into 0
5.253 * [backup-simplify]: Simplify (+ 0 0) into 0
5.255 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
5.256 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
5.260 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
5.270 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
5.277 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
5.294 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
5.295 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
5.295 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (n k) around 0
5.295 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
5.295 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
5.295 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.295 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.295 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
5.295 * [taylor]: Taking taylor expansion of 1/2 in k
5.295 * [backup-simplify]: Simplify 1/2 into 1/2
5.295 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.295 * [taylor]: Taking taylor expansion of 1 in k
5.295 * [backup-simplify]: Simplify 1 into 1
5.295 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.295 * [taylor]: Taking taylor expansion of k in k
5.295 * [backup-simplify]: Simplify 0 into 0
5.295 * [backup-simplify]: Simplify 1 into 1
5.301 * [backup-simplify]: Simplify (/ 1 1) into 1
5.301 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.301 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.301 * [taylor]: Taking taylor expansion of 2 in k
5.302 * [backup-simplify]: Simplify 2 into 2
5.302 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.302 * [taylor]: Taking taylor expansion of PI in k
5.302 * [backup-simplify]: Simplify PI into PI
5.302 * [taylor]: Taking taylor expansion of n in k
5.302 * [backup-simplify]: Simplify n into n
5.302 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.302 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.302 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.303 * [backup-simplify]: Simplify (- 1) into -1
5.303 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.304 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
5.304 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.304 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
5.304 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.304 * [taylor]: Taking taylor expansion of k in k
5.304 * [backup-simplify]: Simplify 0 into 0
5.304 * [backup-simplify]: Simplify 1 into 1
5.305 * [backup-simplify]: Simplify (sqrt 0) into 0
5.306 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.306 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
5.306 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.306 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.306 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.306 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.306 * [taylor]: Taking taylor expansion of 1/2 in n
5.306 * [backup-simplify]: Simplify 1/2 into 1/2
5.306 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.306 * [taylor]: Taking taylor expansion of 1 in n
5.306 * [backup-simplify]: Simplify 1 into 1
5.306 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.306 * [taylor]: Taking taylor expansion of k in n
5.306 * [backup-simplify]: Simplify k into k
5.307 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.307 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.307 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.307 * [taylor]: Taking taylor expansion of 2 in n
5.307 * [backup-simplify]: Simplify 2 into 2
5.307 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.307 * [taylor]: Taking taylor expansion of PI in n
5.307 * [backup-simplify]: Simplify PI into PI
5.307 * [taylor]: Taking taylor expansion of n in n
5.307 * [backup-simplify]: Simplify 0 into 0
5.307 * [backup-simplify]: Simplify 1 into 1
5.307 * [backup-simplify]: Simplify (/ PI 1) into PI
5.308 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.308 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.308 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.308 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.308 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.309 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.310 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.311 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.311 * [taylor]: Taking taylor expansion of (sqrt k) in n
5.311 * [taylor]: Taking taylor expansion of k in n
5.311 * [backup-simplify]: Simplify k into k
5.311 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
5.311 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
5.311 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
5.311 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.311 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.311 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.311 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.311 * [taylor]: Taking taylor expansion of 1/2 in n
5.311 * [backup-simplify]: Simplify 1/2 into 1/2
5.311 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.311 * [taylor]: Taking taylor expansion of 1 in n
5.311 * [backup-simplify]: Simplify 1 into 1
5.311 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.311 * [taylor]: Taking taylor expansion of k in n
5.311 * [backup-simplify]: Simplify k into k
5.311 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.311 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.311 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.311 * [taylor]: Taking taylor expansion of 2 in n
5.311 * [backup-simplify]: Simplify 2 into 2
5.311 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.311 * [taylor]: Taking taylor expansion of PI in n
5.311 * [backup-simplify]: Simplify PI into PI
5.311 * [taylor]: Taking taylor expansion of n in n
5.311 * [backup-simplify]: Simplify 0 into 0
5.311 * [backup-simplify]: Simplify 1 into 1
5.312 * [backup-simplify]: Simplify (/ PI 1) into PI
5.312 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.313 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.313 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.313 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.313 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.314 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.314 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.315 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.315 * [taylor]: Taking taylor expansion of (sqrt k) in n
5.315 * [taylor]: Taking taylor expansion of k in n
5.315 * [backup-simplify]: Simplify k into k
5.315 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
5.315 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
5.316 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
5.316 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
5.316 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
5.316 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
5.316 * [taylor]: Taking taylor expansion of 1/2 in k
5.316 * [backup-simplify]: Simplify 1/2 into 1/2
5.316 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
5.316 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.316 * [taylor]: Taking taylor expansion of 1 in k
5.316 * [backup-simplify]: Simplify 1 into 1
5.316 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.316 * [taylor]: Taking taylor expansion of k in k
5.316 * [backup-simplify]: Simplify 0 into 0
5.316 * [backup-simplify]: Simplify 1 into 1
5.316 * [backup-simplify]: Simplify (/ 1 1) into 1
5.316 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
5.316 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.316 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.316 * [taylor]: Taking taylor expansion of 2 in k
5.316 * [backup-simplify]: Simplify 2 into 2
5.316 * [taylor]: Taking taylor expansion of PI in k
5.316 * [backup-simplify]: Simplify PI into PI
5.317 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.317 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.317 * [taylor]: Taking taylor expansion of (log n) in k
5.317 * [taylor]: Taking taylor expansion of n in k
5.317 * [backup-simplify]: Simplify n into n
5.317 * [backup-simplify]: Simplify (log n) into (log n)
5.318 * [backup-simplify]: Simplify (- 1) into -1
5.318 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.318 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.319 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
5.319 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
5.320 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
5.321 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.321 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.321 * [taylor]: Taking taylor expansion of k in k
5.321 * [backup-simplify]: Simplify 0 into 0
5.321 * [backup-simplify]: Simplify 1 into 1
5.321 * [backup-simplify]: Simplify (sqrt 0) into 0
5.322 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.322 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0
5.322 * [backup-simplify]: Simplify 0 into 0
5.323 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.323 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.324 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.325 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.325 * [backup-simplify]: Simplify (- 0) into 0
5.325 * [backup-simplify]: Simplify (+ 0 0) into 0
5.325 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
5.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.328 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.329 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.330 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
5.330 * [taylor]: Taking taylor expansion of 0 in k
5.330 * [backup-simplify]: Simplify 0 into 0
5.330 * [backup-simplify]: Simplify 0 into 0
5.331 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
5.332 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
5.332 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
5.333 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.334 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.335 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.335 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.336 * [backup-simplify]: Simplify (- 0) into 0
5.336 * [backup-simplify]: Simplify (+ 0 0) into 0
5.336 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
5.337 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.338 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
5.340 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.341 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
5.341 * [taylor]: Taking taylor expansion of 0 in k
5.341 * [backup-simplify]: Simplify 0 into 0
5.341 * [backup-simplify]: Simplify 0 into 0
5.342 * [backup-simplify]: Simplify 0 into 0
5.344 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.346 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
5.348 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
5.348 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
5.350 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.351 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.354 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
5.354 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.355 * [backup-simplify]: Simplify (- 0) into 0
5.355 * [backup-simplify]: Simplify (+ 0 0) into 0
5.356 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
5.357 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.358 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
5.359 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.361 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
5.361 * [taylor]: Taking taylor expansion of 0 in k
5.361 * [backup-simplify]: Simplify 0 into 0
5.361 * [backup-simplify]: Simplify 0 into 0
5.361 * [backup-simplify]: Simplify 0 into 0
5.361 * [backup-simplify]: Simplify 0 into 0
5.363 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.364 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
5.365 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
5.367 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
5.368 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
5.368 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (n k) around 0
5.368 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
5.368 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.368 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.368 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.368 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.368 * [taylor]: Taking taylor expansion of 1/2 in k
5.368 * [backup-simplify]: Simplify 1/2 into 1/2
5.368 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.368 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.368 * [taylor]: Taking taylor expansion of k in k
5.368 * [backup-simplify]: Simplify 0 into 0
5.368 * [backup-simplify]: Simplify 1 into 1
5.368 * [backup-simplify]: Simplify (/ 1 1) into 1
5.368 * [taylor]: Taking taylor expansion of 1 in k
5.368 * [backup-simplify]: Simplify 1 into 1
5.368 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.369 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.369 * [taylor]: Taking taylor expansion of -2 in k
5.369 * [backup-simplify]: Simplify -2 into -2
5.369 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.369 * [taylor]: Taking taylor expansion of PI in k
5.369 * [backup-simplify]: Simplify PI into PI
5.369 * [taylor]: Taking taylor expansion of n in k
5.369 * [backup-simplify]: Simplify n into n
5.369 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.369 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.369 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.369 * [backup-simplify]: Simplify (+ 1 0) into 1
5.369 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.369 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.369 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.370 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.370 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.370 * [taylor]: Taking taylor expansion of -1 in k
5.370 * [backup-simplify]: Simplify -1 into -1
5.370 * [taylor]: Taking taylor expansion of k in k
5.370 * [backup-simplify]: Simplify 0 into 0
5.370 * [backup-simplify]: Simplify 1 into 1
5.370 * [backup-simplify]: Simplify (/ -1 1) into -1
5.370 * [backup-simplify]: Simplify (sqrt 0) into 0
5.371 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.371 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
5.371 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
5.371 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.371 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.371 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.371 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.371 * [taylor]: Taking taylor expansion of 1/2 in n
5.371 * [backup-simplify]: Simplify 1/2 into 1/2
5.371 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.371 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.371 * [taylor]: Taking taylor expansion of k in n
5.371 * [backup-simplify]: Simplify k into k
5.371 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.371 * [taylor]: Taking taylor expansion of 1 in n
5.371 * [backup-simplify]: Simplify 1 into 1
5.371 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.371 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.371 * [taylor]: Taking taylor expansion of -2 in n
5.372 * [backup-simplify]: Simplify -2 into -2
5.372 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.372 * [taylor]: Taking taylor expansion of PI in n
5.372 * [backup-simplify]: Simplify PI into PI
5.372 * [taylor]: Taking taylor expansion of n in n
5.372 * [backup-simplify]: Simplify 0 into 0
5.372 * [backup-simplify]: Simplify 1 into 1
5.372 * [backup-simplify]: Simplify (/ PI 1) into PI
5.372 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.373 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.373 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.373 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.374 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.375 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.375 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.375 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
5.375 * [taylor]: Taking taylor expansion of (/ -1 k) in n
5.375 * [taylor]: Taking taylor expansion of -1 in n
5.375 * [backup-simplify]: Simplify -1 into -1
5.375 * [taylor]: Taking taylor expansion of k in n
5.375 * [backup-simplify]: Simplify k into k
5.375 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
5.376 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
5.376 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
5.376 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
5.376 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
5.376 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
5.376 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.376 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.376 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.376 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.377 * [taylor]: Taking taylor expansion of 1/2 in n
5.377 * [backup-simplify]: Simplify 1/2 into 1/2
5.377 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.377 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.377 * [taylor]: Taking taylor expansion of k in n
5.377 * [backup-simplify]: Simplify k into k
5.377 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.377 * [taylor]: Taking taylor expansion of 1 in n
5.377 * [backup-simplify]: Simplify 1 into 1
5.377 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.377 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.377 * [taylor]: Taking taylor expansion of -2 in n
5.377 * [backup-simplify]: Simplify -2 into -2
5.377 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.377 * [taylor]: Taking taylor expansion of PI in n
5.377 * [backup-simplify]: Simplify PI into PI
5.377 * [taylor]: Taking taylor expansion of n in n
5.377 * [backup-simplify]: Simplify 0 into 0
5.377 * [backup-simplify]: Simplify 1 into 1
5.377 * [backup-simplify]: Simplify (/ PI 1) into PI
5.377 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.378 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.378 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.378 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.379 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.380 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.380 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.380 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
5.380 * [taylor]: Taking taylor expansion of (/ -1 k) in n
5.380 * [taylor]: Taking taylor expansion of -1 in n
5.380 * [backup-simplify]: Simplify -1 into -1
5.380 * [taylor]: Taking taylor expansion of k in n
5.380 * [backup-simplify]: Simplify k into k
5.380 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
5.381 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
5.381 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
5.381 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
5.381 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
5.381 * [taylor]: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k
5.381 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
5.382 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
5.382 * [taylor]: Taking taylor expansion of 1/2 in k
5.382 * [backup-simplify]: Simplify 1/2 into 1/2
5.382 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
5.382 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.382 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.382 * [taylor]: Taking taylor expansion of k in k
5.382 * [backup-simplify]: Simplify 0 into 0
5.382 * [backup-simplify]: Simplify 1 into 1
5.382 * [backup-simplify]: Simplify (/ 1 1) into 1
5.382 * [taylor]: Taking taylor expansion of 1 in k
5.382 * [backup-simplify]: Simplify 1 into 1
5.382 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
5.382 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
5.382 * [taylor]: Taking taylor expansion of (* -2 PI) in k
5.382 * [taylor]: Taking taylor expansion of -2 in k
5.382 * [backup-simplify]: Simplify -2 into -2
5.382 * [taylor]: Taking taylor expansion of PI in k
5.382 * [backup-simplify]: Simplify PI into PI
5.382 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.383 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.383 * [taylor]: Taking taylor expansion of (log n) in k
5.383 * [taylor]: Taking taylor expansion of n in k
5.383 * [backup-simplify]: Simplify n into n
5.383 * [backup-simplify]: Simplify (log n) into (log n)
5.384 * [backup-simplify]: Simplify (+ 1 0) into 1
5.384 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.384 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
5.385 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
5.386 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
5.386 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.386 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.386 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.386 * [taylor]: Taking taylor expansion of -1 in k
5.386 * [backup-simplify]: Simplify -1 into -1
5.386 * [taylor]: Taking taylor expansion of k in k
5.386 * [backup-simplify]: Simplify 0 into 0
5.386 * [backup-simplify]: Simplify 1 into 1
5.387 * [backup-simplify]: Simplify (/ -1 1) into -1
5.387 * [backup-simplify]: Simplify (sqrt 0) into 0
5.388 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.389 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
5.389 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
5.390 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.390 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.391 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
5.392 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.392 * [backup-simplify]: Simplify (+ 0 0) into 0
5.393 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
5.394 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.395 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
5.397 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.398 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
5.398 * [taylor]: Taking taylor expansion of 0 in k
5.398 * [backup-simplify]: Simplify 0 into 0
5.399 * [backup-simplify]: Simplify 0 into 0
5.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
5.409 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.411 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
5.412 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
5.413 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.413 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.415 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
5.415 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.416 * [backup-simplify]: Simplify (+ 0 0) into 0
5.416 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
5.417 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.418 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
5.420 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.420 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.420 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
5.421 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
5.421 * [taylor]: Taking taylor expansion of 0 in k
5.421 * [backup-simplify]: Simplify 0 into 0
5.421 * [backup-simplify]: Simplify 0 into 0
5.421 * [backup-simplify]: Simplify 0 into 0
5.422 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.424 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.426 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
5.427 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
5.429 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
5.429 * * * [progress]: simplifying candidates
5.429 * * * * [progress]: [ 1 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log PI) (log 2))) (/ (- 1 k) 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 2 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* PI 2))) (/ (- 1 k) 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 3 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* PI 2))) (/ (- 1 k) 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 4 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* PI 2))) (/ (- 1 k) 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 5 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* PI 2)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 6 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* PI 2)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 7 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* PI 2)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 8 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 9 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 10 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 11 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 12 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 13 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2)) (sqrt k)))>
5.430 * * * * [progress]: [ 14 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 15 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 16 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2)) (sqrt k)))>
5.430 * * * * [progress]: [ 17 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 18 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 19 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k)))>
5.430 * * * * [progress]: [ 20 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 21 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 22 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2)) (sqrt k)))>
5.430 * * * * [progress]: [ 23 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2))) (sqrt k)))>
5.430 * * * * [progress]: [ 24 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2))) (sqrt k)))>
5.431 * * * * [progress]: [ 25 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k)))>
5.431 * * * * [progress]: [ 26 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k)))>
5.431 * * * * [progress]: [ 27 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k)))>
5.431 * * * * [progress]: [ 28 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k)))>
5.431 * * * * [progress]: [ 29 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) 1) (/ (- 1 k) 2)) (sqrt k)))>
5.431 * * * * [progress]: [ 30 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (- 1 k)) (/ 1 2)) (sqrt k)))>
5.431 * * * * [progress]: [ 31 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (sqrt k)))>
5.431 * * * * [progress]: [ 32 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (- 1 k) 2)) 1) (sqrt k)))>
5.431 * * * * [progress]: [ 33 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
5.431 * * * * [progress]: [ 34 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
5.431 * * * * [progress]: [ 35 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
5.431 * * * * [progress]: [ 36 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
5.431 * * * * [progress]: [ 37 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
5.431 * * * * [progress]: [ 38 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))>
5.431 * * * * [progress]: [ 39 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
5.431 * * * * [progress]: [ 40 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
5.431 * * * * [progress]: [ 41 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) 1) (/ (- 1 k) 2)) (sqrt k)))>
5.431 * * * * [progress]: [ 42 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) 1) (/ (- 1 k) 2)) (sqrt k)))>
5.431 * * * * [progress]: [ 43 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* PI 2)) 1) (/ (- 1 k) 2)) (sqrt k)))>
5.431 * * * * [progress]: [ 44 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log PI) (log 2)))) (/ (- 1 k) 2)) (sqrt k)))>
5.431 * * * * [progress]: [ 45 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
5.431 * * * * [progress]: [ 46 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
5.431 * * * * [progress]: [ 47 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
5.431 * * * * [progress]: [ 48 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* PI PI) PI) (* (* 2 2) 2)))) (/ (- 1 k) 2)) (sqrt k)))>
5.431 * * * * [progress]: [ 49 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* PI 2) (* PI 2)) (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
5.432 * * * * [progress]: [ 50 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
5.432 * * * * [progress]: [ 51 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
5.432 * * * * [progress]: [ 52 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* PI 2))) (sqrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
5.432 * * * * [progress]: [ 53 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* PI 2))) (/ (- 1 k) 2)) (sqrt k)))>
5.432 * * * * [progress]: [ 54 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))>
5.432 * * * * [progress]: [ 55 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* PI 2))) (/ (- 1 k) 2)) (sqrt k)))>
5.432 * * * * [progress]: [ 56 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* PI 2))) (/ (- 1 k) 2)) (sqrt k)))>
5.432 * * * * [progress]: [ 57 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* PI 2))) (/ (- 1 k) 2)) (sqrt k)))>
5.432 * * * * [progress]: [ 58 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
5.432 * * * * [progress]: [ 59 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))>
5.432 * * * * [progress]: [ 60 / 127 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) 1))>
5.432 * * * * [progress]: [ 61 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (+ (log PI) (log 2))) (/ (- 1 k) 2)) (log (sqrt k)))))>
5.432 * * * * [progress]: [ 62 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (log (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k)))))>
5.432 * * * * [progress]: [ 63 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k)))))>
5.432 * * * * [progress]: [ 64 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k)))))>
5.432 * * * * [progress]: [ 65 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) (log (sqrt k)))))>
5.432 * * * * [progress]: [ 66 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
5.432 * * * * [progress]: [ 67 / 127 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
5.432 * * * * [progress]: [ 68 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
5.432 * * * * [progress]: [ 69 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
5.432 * * * * [progress]: [ 70 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
5.432 * * * * [progress]: [ 71 / 127 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
5.432 * * * * [progress]: [ 72 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* n (* PI 2)) (/ (- 1 k) 2))) (- (sqrt k))))>
5.432 * * * * [progress]: [ 73 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
5.432 * * * * [progress]: [ 74 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (cbrt k)))))>
5.433 * * * * [progress]: [ 75 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
5.433 * * * * [progress]: [ 76 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt 1)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
5.433 * * * * [progress]: [ 77 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
5.433 * * * * [progress]: [ 78 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) 1) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
5.433 * * * * [progress]: [ 79 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
5.433 * * * * [progress]: [ 80 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))>
5.433 * * * * [progress]: [ 81 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
5.433 * * * * [progress]: [ 82 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt 1)) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))))>
5.433 * * * * [progress]: [ 83 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
5.433 * * * * [progress]: [ 84 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))))>
5.433 * * * * [progress]: [ 85 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
5.433 * * * * [progress]: [ 86 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))>
5.433 * * * * [progress]: [ 87 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
5.433 * * * * [progress]: [ 88 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))))>
5.433 * * * * [progress]: [ 89 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
5.433 * * * * [progress]: [ 90 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))))>
5.433 * * * * [progress]: [ 91 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
5.433 * * * * [progress]: [ 92 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (cbrt k)))))>
5.433 * * * * [progress]: [ 93 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
5.433 * * * * [progress]: [ 94 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))>
5.434 * * * * [progress]: [ 95 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
5.434 * * * * [progress]: [ 96 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))>
5.434 * * * * [progress]: [ 97 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))))>
5.434 * * * * [progress]: [ 98 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))>
5.434 * * * * [progress]: [ 99 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))>
5.434 * * * * [progress]: [ 100 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt 1)) (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))>
5.434 * * * * [progress]: [ 101 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))>
5.434 * * * * [progress]: [ 102 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) 1) (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))>
5.434 * * * * [progress]: [ 103 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))>
5.434 * * * * [progress]: [ 104 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
5.434 * * * * [progress]: [ 105 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))>
5.434 * * * * [progress]: [ 106 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
5.434 * * * * [progress]: [ 107 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
5.434 * * * * [progress]: [ 108 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
5.434 * * * * [progress]: [ 109 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt 1)) (sqrt k)))>
5.434 * * * * [progress]: [ 110 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
5.434 * * * * [progress]: [ 111 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) 1) (sqrt k)))>
5.434 * * * * [progress]: [ 112 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))))>
5.434 * * * * [progress]: [ 113 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))))>
5.434 * * * * [progress]: [ 114 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))))>
5.434 * * * * [progress]: [ 115 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))>
5.434 * * * * [progress]: [ 116 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt k) (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)))))>
5.434 * * * * [progress]: [ 117 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
5.434 * * * * [progress]: [ 118 / 127 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
5.435 * * * * [progress]: [ 119 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
5.435 * * * * [progress]: [ 120 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))>
5.435 * * * * [progress]: [ 121 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))>
5.435 * * * * [progress]: [ 122 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
5.435 * * * * [progress]: [ 123 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
5.435 * * * * [progress]: [ 124 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
5.435 * * * * [progress]: [ 125 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
5.435 * * * * [progress]: [ 126 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
5.435 * * * * [progress]: [ 127 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
5.436 * [simplify]: Simplifying (* (+ (log n) (+ (log PI) (log 2))) (/ (- 1 k) 2)), (* (+ (log n) (log (* PI 2))) (/ (- 1 k) 2)), (* (log (* n (* PI 2))) (/ (- 1 k) 2)), (* (log (* n (* PI 2))) (/ (- 1 k) 2)), (* 1 (/ (- 1 k) 2)), (* 1 (/ (- 1 k) 2)), (* 1 (/ (- 1 k) 2)), (pow (* n (* PI 2)) (/ 1 2)), (pow (* n (* PI 2)) (/ k 2)), (pow (* n (* PI 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))), (pow (* n (* PI 2)) (sqrt (/ (- 1 k) 2))), (pow (* n (* PI 2)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))), (pow (* n (* PI 2)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))), (pow (* n (* PI 2)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)), (pow (* n (* PI 2)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))), (pow (* n (* PI 2)) (/ (sqrt (- 1 k)) (sqrt 2))), (pow (* n (* PI 2)) (/ (sqrt (- 1 k)) 1)), (pow (* n (* PI 2)) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* n (* PI 2)) (/ 1 (sqrt 2))), (pow (* n (* PI 2)) (/ 1 1)), (pow (* n (* PI 2)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))), (pow (* n (* PI 2)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))), (pow (* n (* PI 2)) (/ (+ (sqrt 1) (sqrt k)) 1)), (pow (* n (* PI 2)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))), (pow (* n (* PI 2)) (/ (+ 1 (sqrt k)) (sqrt 2))), (pow (* n (* PI 2)) (/ (+ 1 (sqrt k)) 1)), (pow (* n (* PI 2)) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* n (* PI 2)) (/ 1 (sqrt 2))), (pow (* n (* PI 2)) (/ 1 1)), (pow (* n (* PI 2)) 1), (pow (* n (* PI 2)) (- 1 k)), (pow n (/ (- 1 k) 2)), (pow (* PI 2) (/ (- 1 k) 2)), (log (pow (* n (* PI 2)) (/ (- 1 k) 2))), (exp (pow (* n (* PI 2)) (/ (- 1 k) 2))), (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))), (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))), (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))), (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))), (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))), (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)), (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)), (real->posit16 (pow (* n (* PI 2)) (/ (- 1 k) 2))), (* n (* PI 2)), (* n (* PI 2)), (+ (log n) (+ (log PI) (log 2))), (+ (log n) (log (* PI 2))), (log (* n (* PI 2))), (exp (* n (* PI 2))), (* (* (* n n) n) (* (* (* PI PI) PI) (* (* 2 2) 2))), (* (* (* n n) n) (* (* (* PI 2) (* PI 2)) (* PI 2))), (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))), (cbrt (* n (* PI 2))), (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))), (sqrt (* n (* PI 2))), (sqrt (* n (* PI 2))), (* n PI), (* (cbrt n) (* PI 2)), (* (sqrt n) (* PI 2)), (* n (* PI 2)), (real->posit16 (* n (* PI 2))), (- (* (+ (log n) (+ (log PI) (log 2))) (/ (- 1 k) 2)) (log (sqrt k))), (- (* (+ (log n) (log (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k))), (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k))), (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k))), (- (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) (log (sqrt k))), (log (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))), (exp (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))), (/ (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))), (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))), (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))), (* (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))), (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))), (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))), (- (pow (* n (* PI 2)) (/ (- 1 k) 2))), (- (sqrt k)), (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k))), (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))), (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (cbrt k))), (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow n (/ (- 1 k) 2)) (sqrt 1)), (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)), (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow n (/ (- 1 k) 2)) 1), (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)), (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))), (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k)))), (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt k))), (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k))), (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt 1)), (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)), (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k))), (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) 1), (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k)))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt k))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt 1)), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1), (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)), (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k))), (/ 1 (sqrt (* (cbrt k) (cbrt k)))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (cbrt k))), (/ 1 (sqrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ 1 (sqrt 1)), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)), (/ 1 (sqrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ 1 1), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))), (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k))), (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt 1)), (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt k)), (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) 1), (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt k)), (/ 1 (sqrt k)), (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt 1)), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) 1), (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))), (/ (sqrt k) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))), (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))), (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2))), (/ (sqrt k) (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2))), (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))), (real->posit16 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))), (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))), (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))), (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))), (* 2 (* n PI)), (* 2 (* n PI)), (* 2 (* n PI)), (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))), (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))), (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
5.439 * * [simplify]: iteration 1: (289 enodes)
5.590 * * [simplify]: iteration 2: (1252 enodes)
5.933 * * [simplify]: Extracting #0: cost 98 inf + 0
5.934 * * [simplify]: Extracting #1: cost 519 inf + 1
5.938 * * [simplify]: Extracting #2: cost 934 inf + 9368
5.955 * * [simplify]: Extracting #3: cost 896 inf + 82302
6.000 * * [simplify]: Extracting #4: cost 471 inf + 277036
6.077 * * [simplify]: Extracting #5: cost 192 inf + 430812
6.155 * * [simplify]: Extracting #6: cost 130 inf + 467701
6.274 * * [simplify]: Extracting #7: cost 60 inf + 502829
6.393 * * [simplify]: Extracting #8: cost 8 inf + 548335
6.505 * * [simplify]: Extracting #9: cost 1 inf + 549300
6.654 * * [simplify]: Extracting #10: cost 0 inf + 549558
6.807 * * [simplify]: Extracting #11: cost 0 inf + 549518
6.934 * [simplify]: Simplified to (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))), (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))), (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))), (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))), (/ (- 1 k) 2), (/ (- 1 k) 2), (/ (- 1 k) 2), (sqrt (* (* n PI) 2)), (pow (* (* n PI) 2) (/ k 2)), (pow (* (* n PI) 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))), (pow (* (* n PI) 2) (sqrt (/ (- 1 k) 2))), (pow (* (* n PI) 2) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2)))), (pow (* (* n PI) 2) (* (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt (- 1 k)))), (pow (* (* n PI) 2) (* (cbrt (- 1 k)) (cbrt (- 1 k)))), (pow (* (* n PI) 2) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2))), (pow (* (* n PI) 2) (/ (sqrt (- 1 k)) (sqrt 2))), (pow (* (* n PI) 2) (sqrt (- 1 k))), (pow (* (* n PI) 2) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* (* n PI) 2) (/ 1 (sqrt 2))), (* (* n PI) 2), (pow (* (* n PI) 2) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2))), (pow (* (* n PI) 2) (/ (+ (sqrt k) 1) (sqrt 2))), (pow (* (* n PI) 2) (+ (sqrt k) 1)), (pow (* (* n PI) 2) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2))), (pow (* (* n PI) 2) (/ (+ (sqrt k) 1) (sqrt 2))), (pow (* (* n PI) 2) (+ (sqrt k) 1)), (pow (* (* n PI) 2) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* (* n PI) 2) (/ 1 (sqrt 2))), (* (* n PI) 2), (* (* n PI) 2), (pow (* (* n PI) 2) (- 1 k)), (pow n (/ (- 1 k) 2)), (pow (* 2 PI) (/ (- 1 k) 2)), (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))), (exp (pow (* (* n PI) 2) (/ (- 1 k) 2))), (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))), (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))), (pow (pow (* (* n PI) 2) (/ (- 1 k) 2)) 3), (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))), (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))), (pow (* (* n PI) 2) (- 1/4 (/ k 4))), (pow (* (* n PI) 2) (- 1/4 (/ k 4))), (real->posit16 (pow (* (* n PI) 2) (/ (- 1 k) 2))), (* (* n PI) 2), (* (* n PI) 2), (log (* (* n PI) 2)), (log (* (* n PI) 2)), (log (* (* n PI) 2)), (* (exp (* n PI)) (exp (* n PI))), (* (* (* (* n PI) 2) (* (* n PI) 2)) (* (* n PI) 2)), (* (* (* (* n PI) 2) (* (* n PI) 2)) (* (* n PI) 2)), (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2))), (cbrt (* (* n PI) 2)), (* (* (* (* n PI) 2) (* (* n PI) 2)) (* (* n PI) 2)), (sqrt (* (* n PI) 2)), (sqrt (* (* n PI) 2)), (* n PI), (* (* 2 PI) (cbrt n)), (* (* 2 PI) (sqrt n)), (* (* n PI) 2), (real->posit16 (* (* n PI) 2)), (- (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))) (log (sqrt k))), (- (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))) (log (sqrt k))), (- (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))) (log (sqrt k))), (- (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))) (log (sqrt k))), (- (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))) (log (sqrt k))), (- (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))) (log (sqrt k))), (exp (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))), (/ (pow (pow (* (* n PI) 2) (/ (- 1 k) 2)) 3) (* (sqrt k) k)), (* (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))), (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))), (* (* (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))), (sqrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))), (sqrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))), (- (pow (* (* n PI) 2) (/ (- 1 k) 2))), (- (sqrt k)), (/ (/ (pow n (/ (- 1 k) 2)) (cbrt (sqrt k))) (cbrt (sqrt k))), (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k))), (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt k))), (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k))), (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))), (pow n (/ (- 1 k) 2)), (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)), (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))), (pow n (/ (- 1 k) 2)), (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)), (* (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))), (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))), (* (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (fabs (cbrt k))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))), (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (cbrt k))), (* (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))), (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))), (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))), (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k)), (* (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))), (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))), (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))), (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k)), (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))), (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (fabs (cbrt k))), (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (cbrt k))), (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))), (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))), (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k)), (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))), (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))), (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k)), (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))), (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (cbrt (sqrt k))), (/ 1 (fabs (cbrt k))), (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt (cbrt k))), (/ 1 (sqrt (sqrt k))), (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))), 1, (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)), (/ 1 (sqrt (sqrt k))), (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))), 1, (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)), (/ (/ (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (cbrt (sqrt k))) (cbrt (sqrt k))), (/ (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (cbrt (sqrt k))), (/ (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (fabs (cbrt k))), (/ (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (sqrt (cbrt k))), (/ (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (sqrt (sqrt k))), (/ (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (sqrt (sqrt k))), (pow (* (* n PI) 2) (- 1/4 (/ k 4))), (/ (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (sqrt k)), (/ (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (sqrt (sqrt k))), (/ (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (sqrt (sqrt k))), (pow (* (* n PI) 2) (- 1/4 (/ k 4))), (/ (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (sqrt k)), (/ 1 (sqrt k)), (/ (sqrt k) (pow (* (* n PI) 2) (/ (- 1 k) 2))), (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (fabs (cbrt k))), (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))), (pow (* (* n PI) 2) (/ (- 1 k) 2)), (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))), (pow (* (* n PI) 2) (/ (- 1 k) 2)), (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))), (/ (sqrt k) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))), (/ (sqrt k) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))), (/ (sqrt k) (pow (* (* n PI) 2) (/ (- 1 k) 2))), (/ (sqrt k) (pow (* (* n PI) 2) (- 1/4 (/ k 4)))), (* (sqrt k) (pow (* (* n PI) 2) (/ k 2))), (real->posit16 (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))), (+ (+ (* (* (exp (* 1/2 (log (* (* n PI) 2)))) (log (* 2 PI))) (* (* (* k k) (log n)) 1/4)) (* (* 1/8 (* (* (log n) k) (* (log n) k))) (exp (* 1/2 (log (* (* n PI) 2)))))) (- (+ (* 1/8 (* (exp (* 1/2 (log (* (* n PI) 2)))) (* (* k k) (* (log (* 2 PI)) (log (* 2 PI)))))) (exp (* 1/2 (log (* (* n PI) 2))))) (* 1/2 (* k (+ (* (exp (* 1/2 (log (* (* n PI) 2)))) (log n)) (* (exp (* 1/2 (log (* (* n PI) 2)))) (log (* 2 PI)))))))), (exp (* (* (- 1 k) (log (* (* n PI) 2))) 1/2)), (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* 1/2 (- 1 k)))), (* (* n PI) 2), (* (* n PI) 2), (* (* n PI) 2), (+ (* (- (* (log (* 2 PI)) +nan.0)) (* (exp (* 1/2 (log (* (* n PI) 2)))) (* (* k k) (log n)))) (- (- (* (* (* (log (* 2 PI)) +nan.0) (* k k)) (exp (* 1/2 (log (* (* n PI) 2))))) (* (exp (* 1/2 (log (* (* n PI) 2)))) (* (* (* (log n) k) (* (log n) k)) +nan.0))) (- (* (* k (exp (* 1/2 (log (* (* n PI) 2))))) (- +nan.0)) (- (* (- +nan.0) (exp (* 1/2 (log (* (* n PI) 2))))) (+ (* (- +nan.0) (* (exp (* 1/2 (log (* (* n PI) 2)))) (* (* k k) (* (log (* 2 PI)) (log (* 2 PI)))))) (+ (- (* (exp (* 1/2 (log (* (* n PI) 2)))) (* (* (* k k) (log n)) +nan.0)) (* (* +nan.0 (* k k)) (exp (* 1/2 (log (* (* n PI) 2)))))) (* +nan.0 (- (* (* (log (* 2 PI)) k) (exp (* 1/2 (log (* (* n PI) 2))))) (* (* k (exp (* 1/2 (log (* (* n PI) 2))))) (log n)))))))))), (- (- (/ +nan.0 (/ k (exp (* (* (- 1 k) (log (* (* n PI) 2))) 1/2)))) (* +nan.0 (- (/ (exp (* (* (- 1 k) (log (* (* n PI) 2))) 1/2)) (* k k)) (/ (/ (exp (* (* (- 1 k) (log (* (* n PI) 2))) 1/2)) (* k k)) k))))), (+ (* (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* 1/2 (- 1 k)))) k) (- +nan.0)) (* +nan.0 (- (/ (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* 1/2 (- 1 k)))) k) k) (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* 1/2 (- 1 k)))))))
6.943 * * * [progress]: adding candidates to table
8.703 * * [progress]: iteration 3 / 4
8.703 * * * [progress]: picking best candidate
8.759 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.759 * * * [progress]: localizing error
8.782 * * * [progress]: generating rewritten candidates
8.783 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
8.797 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
8.815 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1)
8.820 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
8.860 * * * [progress]: generating series expansions
8.860 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
8.861 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
8.861 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
8.861 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
8.861 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
8.861 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
8.861 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
8.861 * [taylor]: Taking taylor expansion of 1/2 in k
8.861 * [backup-simplify]: Simplify 1/2 into 1/2
8.861 * [taylor]: Taking taylor expansion of (- 1 k) in k
8.861 * [taylor]: Taking taylor expansion of 1 in k
8.861 * [backup-simplify]: Simplify 1 into 1
8.861 * [taylor]: Taking taylor expansion of k in k
8.861 * [backup-simplify]: Simplify 0 into 0
8.862 * [backup-simplify]: Simplify 1 into 1
8.862 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
8.862 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
8.862 * [taylor]: Taking taylor expansion of 2 in k
8.862 * [backup-simplify]: Simplify 2 into 2
8.862 * [taylor]: Taking taylor expansion of (* n PI) in k
8.862 * [taylor]: Taking taylor expansion of n in k
8.862 * [backup-simplify]: Simplify n into n
8.862 * [taylor]: Taking taylor expansion of PI in k
8.862 * [backup-simplify]: Simplify PI into PI
8.862 * [backup-simplify]: Simplify (* n PI) into (* n PI)
8.862 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
8.862 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
8.862 * [backup-simplify]: Simplify (- 0) into 0
8.863 * [backup-simplify]: Simplify (+ 1 0) into 1
8.863 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
8.864 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
8.864 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
8.864 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
8.864 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
8.864 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
8.864 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
8.864 * [taylor]: Taking taylor expansion of 1/2 in n
8.864 * [backup-simplify]: Simplify 1/2 into 1/2
8.864 * [taylor]: Taking taylor expansion of (- 1 k) in n
8.864 * [taylor]: Taking taylor expansion of 1 in n
8.864 * [backup-simplify]: Simplify 1 into 1
8.864 * [taylor]: Taking taylor expansion of k in n
8.864 * [backup-simplify]: Simplify k into k
8.864 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
8.864 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.864 * [taylor]: Taking taylor expansion of 2 in n
8.864 * [backup-simplify]: Simplify 2 into 2
8.864 * [taylor]: Taking taylor expansion of (* n PI) in n
8.864 * [taylor]: Taking taylor expansion of n in n
8.864 * [backup-simplify]: Simplify 0 into 0
8.864 * [backup-simplify]: Simplify 1 into 1
8.864 * [taylor]: Taking taylor expansion of PI in n
8.864 * [backup-simplify]: Simplify PI into PI
8.865 * [backup-simplify]: Simplify (* 0 PI) into 0
8.865 * [backup-simplify]: Simplify (* 2 0) into 0
8.867 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.869 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
8.870 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.870 * [backup-simplify]: Simplify (- k) into (- k)
8.870 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
8.870 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
8.872 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.873 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
8.874 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
8.874 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
8.874 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
8.875 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
8.875 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
8.875 * [taylor]: Taking taylor expansion of 1/2 in n
8.875 * [backup-simplify]: Simplify 1/2 into 1/2
8.875 * [taylor]: Taking taylor expansion of (- 1 k) in n
8.875 * [taylor]: Taking taylor expansion of 1 in n
8.875 * [backup-simplify]: Simplify 1 into 1
8.875 * [taylor]: Taking taylor expansion of k in n
8.875 * [backup-simplify]: Simplify k into k
8.875 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
8.875 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.875 * [taylor]: Taking taylor expansion of 2 in n
8.875 * [backup-simplify]: Simplify 2 into 2
8.875 * [taylor]: Taking taylor expansion of (* n PI) in n
8.875 * [taylor]: Taking taylor expansion of n in n
8.875 * [backup-simplify]: Simplify 0 into 0
8.875 * [backup-simplify]: Simplify 1 into 1
8.875 * [taylor]: Taking taylor expansion of PI in n
8.875 * [backup-simplify]: Simplify PI into PI
8.876 * [backup-simplify]: Simplify (* 0 PI) into 0
8.876 * [backup-simplify]: Simplify (* 2 0) into 0
8.878 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.880 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
8.881 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.881 * [backup-simplify]: Simplify (- k) into (- k)
8.881 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
8.881 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
8.883 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.884 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
8.885 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
8.885 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
8.885 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
8.885 * [taylor]: Taking taylor expansion of 1/2 in k
8.885 * [backup-simplify]: Simplify 1/2 into 1/2
8.885 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
8.885 * [taylor]: Taking taylor expansion of (- 1 k) in k
8.885 * [taylor]: Taking taylor expansion of 1 in k
8.885 * [backup-simplify]: Simplify 1 into 1
8.885 * [taylor]: Taking taylor expansion of k in k
8.885 * [backup-simplify]: Simplify 0 into 0
8.886 * [backup-simplify]: Simplify 1 into 1
8.886 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
8.886 * [taylor]: Taking taylor expansion of (log n) in k
8.886 * [taylor]: Taking taylor expansion of n in k
8.886 * [backup-simplify]: Simplify n into n
8.886 * [backup-simplify]: Simplify (log n) into (log n)
8.886 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
8.886 * [taylor]: Taking taylor expansion of (* 2 PI) in k
8.886 * [taylor]: Taking taylor expansion of 2 in k
8.886 * [backup-simplify]: Simplify 2 into 2
8.886 * [taylor]: Taking taylor expansion of PI in k
8.886 * [backup-simplify]: Simplify PI into PI
8.886 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.887 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.888 * [backup-simplify]: Simplify (- 0) into 0
8.888 * [backup-simplify]: Simplify (+ 1 0) into 1
8.889 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.890 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
8.892 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
8.893 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
8.894 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
8.895 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.896 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
8.898 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
8.898 * [backup-simplify]: Simplify (- 0) into 0
8.899 * [backup-simplify]: Simplify (+ 0 0) into 0
8.899 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
8.901 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.902 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
8.904 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.904 * [taylor]: Taking taylor expansion of 0 in k
8.904 * [backup-simplify]: Simplify 0 into 0
8.904 * [backup-simplify]: Simplify 0 into 0
8.905 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
8.906 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
8.908 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
8.908 * [backup-simplify]: Simplify (+ 0 0) into 0
8.909 * [backup-simplify]: Simplify (- 1) into -1
8.909 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.911 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
8.917 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
8.921 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
8.924 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
8.926 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
8.927 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
8.930 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
8.930 * [backup-simplify]: Simplify (- 0) into 0
8.931 * [backup-simplify]: Simplify (+ 0 0) into 0
8.932 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
8.933 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.935 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
8.937 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.937 * [taylor]: Taking taylor expansion of 0 in k
8.937 * [backup-simplify]: Simplify 0 into 0
8.937 * [backup-simplify]: Simplify 0 into 0
8.937 * [backup-simplify]: Simplify 0 into 0
8.939 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
8.940 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
8.943 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
8.944 * [backup-simplify]: Simplify (+ 0 0) into 0
8.944 * [backup-simplify]: Simplify (- 0) into 0
8.944 * [backup-simplify]: Simplify (+ 0 0) into 0
8.946 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
8.949 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
8.953 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
8.958 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
8.967 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
8.967 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
8.967 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
8.967 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
8.968 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
8.968 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
8.968 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
8.968 * [taylor]: Taking taylor expansion of 1/2 in k
8.968 * [backup-simplify]: Simplify 1/2 into 1/2
8.968 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
8.968 * [taylor]: Taking taylor expansion of 1 in k
8.968 * [backup-simplify]: Simplify 1 into 1
8.968 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.968 * [taylor]: Taking taylor expansion of k in k
8.968 * [backup-simplify]: Simplify 0 into 0
8.968 * [backup-simplify]: Simplify 1 into 1
8.968 * [backup-simplify]: Simplify (/ 1 1) into 1
8.968 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
8.968 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
8.968 * [taylor]: Taking taylor expansion of 2 in k
8.968 * [backup-simplify]: Simplify 2 into 2
8.968 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.968 * [taylor]: Taking taylor expansion of PI in k
8.968 * [backup-simplify]: Simplify PI into PI
8.968 * [taylor]: Taking taylor expansion of n in k
8.968 * [backup-simplify]: Simplify n into n
8.968 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.969 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
8.969 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
8.969 * [backup-simplify]: Simplify (- 1) into -1
8.969 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.970 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
8.970 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
8.970 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
8.970 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
8.970 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
8.970 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
8.970 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
8.970 * [taylor]: Taking taylor expansion of 1/2 in n
8.970 * [backup-simplify]: Simplify 1/2 into 1/2
8.970 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
8.970 * [taylor]: Taking taylor expansion of 1 in n
8.970 * [backup-simplify]: Simplify 1 into 1
8.970 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.970 * [taylor]: Taking taylor expansion of k in n
8.971 * [backup-simplify]: Simplify k into k
8.971 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.971 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
8.971 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.971 * [taylor]: Taking taylor expansion of 2 in n
8.971 * [backup-simplify]: Simplify 2 into 2
8.971 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.971 * [taylor]: Taking taylor expansion of PI in n
8.971 * [backup-simplify]: Simplify PI into PI
8.971 * [taylor]: Taking taylor expansion of n in n
8.971 * [backup-simplify]: Simplify 0 into 0
8.971 * [backup-simplify]: Simplify 1 into 1
8.971 * [backup-simplify]: Simplify (/ PI 1) into PI
8.972 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.973 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.973 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.973 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
8.973 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
8.974 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.975 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
8.976 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
8.977 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
8.977 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
8.977 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
8.977 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
8.977 * [taylor]: Taking taylor expansion of 1/2 in n
8.977 * [backup-simplify]: Simplify 1/2 into 1/2
8.977 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
8.977 * [taylor]: Taking taylor expansion of 1 in n
8.977 * [backup-simplify]: Simplify 1 into 1
8.977 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.977 * [taylor]: Taking taylor expansion of k in n
8.977 * [backup-simplify]: Simplify k into k
8.977 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.977 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
8.977 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.977 * [taylor]: Taking taylor expansion of 2 in n
8.977 * [backup-simplify]: Simplify 2 into 2
8.977 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.977 * [taylor]: Taking taylor expansion of PI in n
8.977 * [backup-simplify]: Simplify PI into PI
8.977 * [taylor]: Taking taylor expansion of n in n
8.977 * [backup-simplify]: Simplify 0 into 0
8.977 * [backup-simplify]: Simplify 1 into 1
8.978 * [backup-simplify]: Simplify (/ PI 1) into PI
8.978 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.979 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.979 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.979 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
8.979 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
8.981 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.982 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
8.983 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
8.983 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
8.983 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
8.983 * [taylor]: Taking taylor expansion of 1/2 in k
8.983 * [backup-simplify]: Simplify 1/2 into 1/2
8.983 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
8.983 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
8.983 * [taylor]: Taking taylor expansion of 1 in k
8.983 * [backup-simplify]: Simplify 1 into 1
8.983 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.983 * [taylor]: Taking taylor expansion of k in k
8.983 * [backup-simplify]: Simplify 0 into 0
8.983 * [backup-simplify]: Simplify 1 into 1
8.984 * [backup-simplify]: Simplify (/ 1 1) into 1
8.984 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
8.984 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
8.984 * [taylor]: Taking taylor expansion of (* 2 PI) in k
8.984 * [taylor]: Taking taylor expansion of 2 in k
8.984 * [backup-simplify]: Simplify 2 into 2
8.984 * [taylor]: Taking taylor expansion of PI in k
8.984 * [backup-simplify]: Simplify PI into PI
8.984 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.985 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.985 * [taylor]: Taking taylor expansion of (log n) in k
8.985 * [taylor]: Taking taylor expansion of n in k
8.985 * [backup-simplify]: Simplify n into n
8.985 * [backup-simplify]: Simplify (log n) into (log n)
8.986 * [backup-simplify]: Simplify (- 1) into -1
8.986 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.986 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
8.987 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
8.988 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
8.989 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
8.991 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
8.992 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
8.993 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.993 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
8.995 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
8.996 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.996 * [backup-simplify]: Simplify (- 0) into 0
8.996 * [backup-simplify]: Simplify (+ 0 0) into 0
8.997 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
8.998 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.999 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
9.001 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.001 * [taylor]: Taking taylor expansion of 0 in k
9.001 * [backup-simplify]: Simplify 0 into 0
9.001 * [backup-simplify]: Simplify 0 into 0
9.001 * [backup-simplify]: Simplify 0 into 0
9.002 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.004 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.006 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.006 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.006 * [backup-simplify]: Simplify (- 0) into 0
9.006 * [backup-simplify]: Simplify (+ 0 0) into 0
9.007 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
9.008 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.009 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
9.010 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.010 * [taylor]: Taking taylor expansion of 0 in k
9.010 * [backup-simplify]: Simplify 0 into 0
9.010 * [backup-simplify]: Simplify 0 into 0
9.010 * [backup-simplify]: Simplify 0 into 0
9.010 * [backup-simplify]: Simplify 0 into 0
9.011 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.011 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.014 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.015 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.015 * [backup-simplify]: Simplify (- 0) into 0
9.015 * [backup-simplify]: Simplify (+ 0 0) into 0
9.016 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
9.017 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.018 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
9.020 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.020 * [taylor]: Taking taylor expansion of 0 in k
9.020 * [backup-simplify]: Simplify 0 into 0
9.020 * [backup-simplify]: Simplify 0 into 0
9.020 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
9.021 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
9.021 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
9.021 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
9.021 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
9.021 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
9.021 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
9.021 * [taylor]: Taking taylor expansion of 1/2 in k
9.021 * [backup-simplify]: Simplify 1/2 into 1/2
9.021 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.021 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.021 * [taylor]: Taking taylor expansion of k in k
9.021 * [backup-simplify]: Simplify 0 into 0
9.021 * [backup-simplify]: Simplify 1 into 1
9.021 * [backup-simplify]: Simplify (/ 1 1) into 1
9.021 * [taylor]: Taking taylor expansion of 1 in k
9.021 * [backup-simplify]: Simplify 1 into 1
9.021 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
9.021 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
9.021 * [taylor]: Taking taylor expansion of -2 in k
9.022 * [backup-simplify]: Simplify -2 into -2
9.022 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.022 * [taylor]: Taking taylor expansion of PI in k
9.022 * [backup-simplify]: Simplify PI into PI
9.022 * [taylor]: Taking taylor expansion of n in k
9.022 * [backup-simplify]: Simplify n into n
9.022 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.022 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
9.022 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
9.022 * [backup-simplify]: Simplify (+ 1 0) into 1
9.022 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.022 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
9.022 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
9.023 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
9.023 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
9.023 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
9.023 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
9.023 * [taylor]: Taking taylor expansion of 1/2 in n
9.023 * [backup-simplify]: Simplify 1/2 into 1/2
9.023 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.023 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.023 * [taylor]: Taking taylor expansion of k in n
9.023 * [backup-simplify]: Simplify k into k
9.023 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.023 * [taylor]: Taking taylor expansion of 1 in n
9.023 * [backup-simplify]: Simplify 1 into 1
9.023 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.023 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.023 * [taylor]: Taking taylor expansion of -2 in n
9.023 * [backup-simplify]: Simplify -2 into -2
9.023 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.023 * [taylor]: Taking taylor expansion of PI in n
9.023 * [backup-simplify]: Simplify PI into PI
9.023 * [taylor]: Taking taylor expansion of n in n
9.023 * [backup-simplify]: Simplify 0 into 0
9.023 * [backup-simplify]: Simplify 1 into 1
9.023 * [backup-simplify]: Simplify (/ PI 1) into PI
9.023 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.024 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.024 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.024 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
9.025 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.026 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
9.026 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
9.026 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
9.026 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
9.026 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
9.026 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
9.026 * [taylor]: Taking taylor expansion of 1/2 in n
9.026 * [backup-simplify]: Simplify 1/2 into 1/2
9.026 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.027 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.027 * [taylor]: Taking taylor expansion of k in n
9.027 * [backup-simplify]: Simplify k into k
9.027 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.027 * [taylor]: Taking taylor expansion of 1 in n
9.027 * [backup-simplify]: Simplify 1 into 1
9.027 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.027 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.027 * [taylor]: Taking taylor expansion of -2 in n
9.027 * [backup-simplify]: Simplify -2 into -2
9.027 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.027 * [taylor]: Taking taylor expansion of PI in n
9.027 * [backup-simplify]: Simplify PI into PI
9.027 * [taylor]: Taking taylor expansion of n in n
9.027 * [backup-simplify]: Simplify 0 into 0
9.027 * [backup-simplify]: Simplify 1 into 1
9.027 * [backup-simplify]: Simplify (/ PI 1) into PI
9.027 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.028 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.028 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.028 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
9.030 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.031 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
9.032 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
9.032 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
9.032 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
9.032 * [taylor]: Taking taylor expansion of 1/2 in k
9.032 * [backup-simplify]: Simplify 1/2 into 1/2
9.032 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
9.032 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.032 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.032 * [taylor]: Taking taylor expansion of k in k
9.032 * [backup-simplify]: Simplify 0 into 0
9.032 * [backup-simplify]: Simplify 1 into 1
9.033 * [backup-simplify]: Simplify (/ 1 1) into 1
9.033 * [taylor]: Taking taylor expansion of 1 in k
9.033 * [backup-simplify]: Simplify 1 into 1
9.033 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
9.033 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
9.033 * [taylor]: Taking taylor expansion of (* -2 PI) in k
9.033 * [taylor]: Taking taylor expansion of -2 in k
9.033 * [backup-simplify]: Simplify -2 into -2
9.033 * [taylor]: Taking taylor expansion of PI in k
9.033 * [backup-simplify]: Simplify PI into PI
9.033 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.034 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.034 * [taylor]: Taking taylor expansion of (log n) in k
9.034 * [taylor]: Taking taylor expansion of n in k
9.034 * [backup-simplify]: Simplify n into n
9.034 * [backup-simplify]: Simplify (log n) into (log n)
9.035 * [backup-simplify]: Simplify (+ 1 0) into 1
9.035 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.036 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
9.037 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
9.038 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
9.039 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
9.040 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
9.041 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.042 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.049 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
9.049 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.050 * [backup-simplify]: Simplify (+ 0 0) into 0
9.050 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
9.052 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.053 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
9.055 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.055 * [taylor]: Taking taylor expansion of 0 in k
9.055 * [backup-simplify]: Simplify 0 into 0
9.055 * [backup-simplify]: Simplify 0 into 0
9.055 * [backup-simplify]: Simplify 0 into 0
9.056 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.057 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.060 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
9.060 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.061 * [backup-simplify]: Simplify (+ 0 0) into 0
9.062 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
9.063 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.065 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
9.067 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.067 * [taylor]: Taking taylor expansion of 0 in k
9.067 * [backup-simplify]: Simplify 0 into 0
9.068 * [backup-simplify]: Simplify 0 into 0
9.068 * [backup-simplify]: Simplify 0 into 0
9.068 * [backup-simplify]: Simplify 0 into 0
9.069 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.070 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.076 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
9.077 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.077 * [backup-simplify]: Simplify (+ 0 0) into 0
9.078 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
9.080 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.081 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
9.084 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.084 * [taylor]: Taking taylor expansion of 0 in k
9.084 * [backup-simplify]: Simplify 0 into 0
9.084 * [backup-simplify]: Simplify 0 into 0
9.085 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
9.085 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
9.086 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
9.086 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
9.086 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.086 * [taylor]: Taking taylor expansion of 2 in n
9.086 * [backup-simplify]: Simplify 2 into 2
9.086 * [taylor]: Taking taylor expansion of (* n PI) in n
9.086 * [taylor]: Taking taylor expansion of n in n
9.086 * [backup-simplify]: Simplify 0 into 0
9.086 * [backup-simplify]: Simplify 1 into 1
9.086 * [taylor]: Taking taylor expansion of PI in n
9.086 * [backup-simplify]: Simplify PI into PI
9.086 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.086 * [taylor]: Taking taylor expansion of 2 in n
9.086 * [backup-simplify]: Simplify 2 into 2
9.086 * [taylor]: Taking taylor expansion of (* n PI) in n
9.086 * [taylor]: Taking taylor expansion of n in n
9.086 * [backup-simplify]: Simplify 0 into 0
9.086 * [backup-simplify]: Simplify 1 into 1
9.086 * [taylor]: Taking taylor expansion of PI in n
9.086 * [backup-simplify]: Simplify PI into PI
9.087 * [backup-simplify]: Simplify (* 0 PI) into 0
9.087 * [backup-simplify]: Simplify (* 2 0) into 0
9.087 * [backup-simplify]: Simplify 0 into 0
9.089 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.090 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.091 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.092 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.093 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.093 * [backup-simplify]: Simplify 0 into 0
9.094 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.095 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.095 * [backup-simplify]: Simplify 0 into 0
9.097 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.098 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
9.098 * [backup-simplify]: Simplify 0 into 0
9.099 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.101 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
9.101 * [backup-simplify]: Simplify 0 into 0
9.102 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.104 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
9.104 * [backup-simplify]: Simplify 0 into 0
9.106 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
9.108 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
9.108 * [backup-simplify]: Simplify 0 into 0
9.109 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
9.109 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
9.109 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
9.109 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.109 * [taylor]: Taking taylor expansion of 2 in n
9.109 * [backup-simplify]: Simplify 2 into 2
9.109 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.109 * [taylor]: Taking taylor expansion of PI in n
9.109 * [backup-simplify]: Simplify PI into PI
9.109 * [taylor]: Taking taylor expansion of n in n
9.109 * [backup-simplify]: Simplify 0 into 0
9.109 * [backup-simplify]: Simplify 1 into 1
9.110 * [backup-simplify]: Simplify (/ PI 1) into PI
9.110 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.110 * [taylor]: Taking taylor expansion of 2 in n
9.110 * [backup-simplify]: Simplify 2 into 2
9.110 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.110 * [taylor]: Taking taylor expansion of PI in n
9.110 * [backup-simplify]: Simplify PI into PI
9.110 * [taylor]: Taking taylor expansion of n in n
9.110 * [backup-simplify]: Simplify 0 into 0
9.110 * [backup-simplify]: Simplify 1 into 1
9.110 * [backup-simplify]: Simplify (/ PI 1) into PI
9.111 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.111 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.112 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.113 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.113 * [backup-simplify]: Simplify 0 into 0
9.114 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.115 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.115 * [backup-simplify]: Simplify 0 into 0
9.116 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.116 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.117 * [backup-simplify]: Simplify 0 into 0
9.117 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.118 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.118 * [backup-simplify]: Simplify 0 into 0
9.118 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.119 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.120 * [backup-simplify]: Simplify 0 into 0
9.120 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.121 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.121 * [backup-simplify]: Simplify 0 into 0
9.121 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
9.122 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n))
9.122 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
9.122 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.122 * [taylor]: Taking taylor expansion of -2 in n
9.122 * [backup-simplify]: Simplify -2 into -2
9.122 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.122 * [taylor]: Taking taylor expansion of PI in n
9.122 * [backup-simplify]: Simplify PI into PI
9.122 * [taylor]: Taking taylor expansion of n in n
9.122 * [backup-simplify]: Simplify 0 into 0
9.122 * [backup-simplify]: Simplify 1 into 1
9.122 * [backup-simplify]: Simplify (/ PI 1) into PI
9.122 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.122 * [taylor]: Taking taylor expansion of -2 in n
9.122 * [backup-simplify]: Simplify -2 into -2
9.122 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.122 * [taylor]: Taking taylor expansion of PI in n
9.122 * [backup-simplify]: Simplify PI into PI
9.122 * [taylor]: Taking taylor expansion of n in n
9.122 * [backup-simplify]: Simplify 0 into 0
9.122 * [backup-simplify]: Simplify 1 into 1
9.123 * [backup-simplify]: Simplify (/ PI 1) into PI
9.123 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.123 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.124 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.124 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.124 * [backup-simplify]: Simplify 0 into 0
9.125 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.125 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.125 * [backup-simplify]: Simplify 0 into 0
9.126 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.127 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.127 * [backup-simplify]: Simplify 0 into 0
9.127 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.128 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.128 * [backup-simplify]: Simplify 0 into 0
9.129 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.129 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.129 * [backup-simplify]: Simplify 0 into 0
9.130 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.131 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.131 * [backup-simplify]: Simplify 0 into 0
9.131 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
9.131 * * * * [progress]: [ 3 / 4 ] generating series at (2 1)
9.131 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
9.132 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0
9.132 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.132 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.132 * [taylor]: Taking taylor expansion of k in k
9.132 * [backup-simplify]: Simplify 0 into 0
9.132 * [backup-simplify]: Simplify 1 into 1
9.132 * [backup-simplify]: Simplify (/ 1 1) into 1
9.132 * [backup-simplify]: Simplify (sqrt 0) into 0
9.133 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.133 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.133 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.133 * [taylor]: Taking taylor expansion of k in k
9.133 * [backup-simplify]: Simplify 0 into 0
9.133 * [backup-simplify]: Simplify 1 into 1
9.133 * [backup-simplify]: Simplify (/ 1 1) into 1
9.134 * [backup-simplify]: Simplify (sqrt 0) into 0
9.134 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.134 * [backup-simplify]: Simplify 0 into 0
9.134 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.135 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
9.137 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.137 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.137 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.139 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.139 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.140 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
9.140 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
9.140 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0
9.140 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.140 * [taylor]: Taking taylor expansion of k in k
9.140 * [backup-simplify]: Simplify 0 into 0
9.140 * [backup-simplify]: Simplify 1 into 1
9.140 * [backup-simplify]: Simplify (sqrt 0) into 0
9.141 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.141 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.141 * [taylor]: Taking taylor expansion of k in k
9.141 * [backup-simplify]: Simplify 0 into 0
9.141 * [backup-simplify]: Simplify 1 into 1
9.141 * [backup-simplify]: Simplify (sqrt 0) into 0
9.142 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.142 * [backup-simplify]: Simplify 0 into 0
9.142 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.144 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.144 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.146 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.146 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.146 * [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))))))))
9.146 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k)))
9.146 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0
9.146 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
9.146 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.146 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.146 * [taylor]: Taking taylor expansion of -1 in k
9.146 * [backup-simplify]: Simplify -1 into -1
9.146 * [taylor]: Taking taylor expansion of k in k
9.146 * [backup-simplify]: Simplify 0 into 0
9.146 * [backup-simplify]: Simplify 1 into 1
9.147 * [backup-simplify]: Simplify (/ -1 1) into -1
9.147 * [backup-simplify]: Simplify (sqrt 0) into 0
9.148 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.148 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
9.148 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
9.148 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.148 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.148 * [taylor]: Taking taylor expansion of -1 in k
9.148 * [backup-simplify]: Simplify -1 into -1
9.148 * [taylor]: Taking taylor expansion of k in k
9.148 * [backup-simplify]: Simplify 0 into 0
9.148 * [backup-simplify]: Simplify 1 into 1
9.148 * [backup-simplify]: Simplify (/ -1 1) into -1
9.149 * [backup-simplify]: Simplify (sqrt 0) into 0
9.149 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.150 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
9.150 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.150 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
9.152 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.153 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
9.153 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
9.154 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.156 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.158 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
9.159 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
9.159 * [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)))))
9.159 * * * * [progress]: [ 4 / 4 ] generating series at (2)
9.166 * [backup-simplify]: Simplify (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
9.166 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0
9.166 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
9.166 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
9.166 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
9.166 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
9.166 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
9.166 * [taylor]: Taking taylor expansion of 1/2 in n
9.167 * [backup-simplify]: Simplify 1/2 into 1/2
9.167 * [taylor]: Taking taylor expansion of (- 1 k) in n
9.167 * [taylor]: Taking taylor expansion of 1 in n
9.167 * [backup-simplify]: Simplify 1 into 1
9.167 * [taylor]: Taking taylor expansion of k in n
9.167 * [backup-simplify]: Simplify k into k
9.167 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.167 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.167 * [taylor]: Taking taylor expansion of 2 in n
9.167 * [backup-simplify]: Simplify 2 into 2
9.167 * [taylor]: Taking taylor expansion of (* n PI) in n
9.167 * [taylor]: Taking taylor expansion of n in n
9.167 * [backup-simplify]: Simplify 0 into 0
9.167 * [backup-simplify]: Simplify 1 into 1
9.167 * [taylor]: Taking taylor expansion of PI in n
9.167 * [backup-simplify]: Simplify PI into PI
9.168 * [backup-simplify]: Simplify (* 0 PI) into 0
9.168 * [backup-simplify]: Simplify (* 2 0) into 0
9.170 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.171 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.172 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.172 * [backup-simplify]: Simplify (- k) into (- k)
9.172 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
9.173 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
9.174 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.175 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
9.176 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
9.176 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
9.176 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.176 * [taylor]: Taking taylor expansion of k in n
9.176 * [backup-simplify]: Simplify k into k
9.176 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.176 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
9.176 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.177 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
9.177 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
9.177 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
9.177 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
9.177 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
9.177 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
9.177 * [taylor]: Taking taylor expansion of 1/2 in k
9.177 * [backup-simplify]: Simplify 1/2 into 1/2
9.177 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.177 * [taylor]: Taking taylor expansion of 1 in k
9.177 * [backup-simplify]: Simplify 1 into 1
9.177 * [taylor]: Taking taylor expansion of k in k
9.177 * [backup-simplify]: Simplify 0 into 0
9.177 * [backup-simplify]: Simplify 1 into 1
9.177 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
9.177 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
9.177 * [taylor]: Taking taylor expansion of 2 in k
9.177 * [backup-simplify]: Simplify 2 into 2
9.177 * [taylor]: Taking taylor expansion of (* n PI) in k
9.177 * [taylor]: Taking taylor expansion of n in k
9.177 * [backup-simplify]: Simplify n into n
9.177 * [taylor]: Taking taylor expansion of PI in k
9.177 * [backup-simplify]: Simplify PI into PI
9.177 * [backup-simplify]: Simplify (* n PI) into (* n PI)
9.177 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
9.177 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
9.178 * [backup-simplify]: Simplify (- 0) into 0
9.178 * [backup-simplify]: Simplify (+ 1 0) into 1
9.179 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.179 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
9.179 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
9.179 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.179 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.179 * [taylor]: Taking taylor expansion of k in k
9.179 * [backup-simplify]: Simplify 0 into 0
9.179 * [backup-simplify]: Simplify 1 into 1
9.179 * [backup-simplify]: Simplify (/ 1 1) into 1
9.180 * [backup-simplify]: Simplify (sqrt 0) into 0
9.181 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.181 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
9.181 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
9.181 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
9.181 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
9.181 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
9.182 * [taylor]: Taking taylor expansion of 1/2 in k
9.182 * [backup-simplify]: Simplify 1/2 into 1/2
9.182 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.182 * [taylor]: Taking taylor expansion of 1 in k
9.182 * [backup-simplify]: Simplify 1 into 1
9.182 * [taylor]: Taking taylor expansion of k in k
9.182 * [backup-simplify]: Simplify 0 into 0
9.182 * [backup-simplify]: Simplify 1 into 1
9.182 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
9.182 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
9.182 * [taylor]: Taking taylor expansion of 2 in k
9.182 * [backup-simplify]: Simplify 2 into 2
9.182 * [taylor]: Taking taylor expansion of (* n PI) in k
9.182 * [taylor]: Taking taylor expansion of n in k
9.182 * [backup-simplify]: Simplify n into n
9.182 * [taylor]: Taking taylor expansion of PI in k
9.182 * [backup-simplify]: Simplify PI into PI
9.182 * [backup-simplify]: Simplify (* n PI) into (* n PI)
9.182 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
9.182 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
9.183 * [backup-simplify]: Simplify (- 0) into 0
9.183 * [backup-simplify]: Simplify (+ 1 0) into 1
9.184 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.184 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
9.184 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
9.184 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.184 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.184 * [taylor]: Taking taylor expansion of k in k
9.184 * [backup-simplify]: Simplify 0 into 0
9.184 * [backup-simplify]: Simplify 1 into 1
9.185 * [backup-simplify]: Simplify (/ 1 1) into 1
9.185 * [backup-simplify]: Simplify (sqrt 0) into 0
9.187 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.187 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0
9.187 * [taylor]: Taking taylor expansion of 0 in n
9.187 * [backup-simplify]: Simplify 0 into 0
9.187 * [backup-simplify]: Simplify 0 into 0
9.187 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
9.188 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
9.189 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
9.189 * [backup-simplify]: Simplify (- 1) into -1
9.189 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.190 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
9.191 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
9.191 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))
9.192 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
9.192 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
9.192 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
9.192 * [taylor]: Taking taylor expansion of +nan.0 in n
9.192 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.192 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
9.192 * [taylor]: Taking taylor expansion of (sqrt 2) in n
9.192 * [taylor]: Taking taylor expansion of 2 in n
9.192 * [backup-simplify]: Simplify 2 into 2
9.192 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
9.193 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
9.193 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
9.193 * [taylor]: Taking taylor expansion of (* n PI) in n
9.193 * [taylor]: Taking taylor expansion of n in n
9.193 * [backup-simplify]: Simplify 0 into 0
9.193 * [backup-simplify]: Simplify 1 into 1
9.193 * [taylor]: Taking taylor expansion of PI in n
9.193 * [backup-simplify]: Simplify PI into PI
9.193 * [backup-simplify]: Simplify (* 0 PI) into 0
9.195 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.195 * [backup-simplify]: Simplify (sqrt 0) into 0
9.197 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
9.197 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
9.198 * [backup-simplify]: Simplify (* +nan.0 0) into 0
9.198 * [backup-simplify]: Simplify (- 0) into 0
9.198 * [backup-simplify]: Simplify 0 into 0
9.198 * [backup-simplify]: Simplify 0 into 0
9.199 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
9.202 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.202 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
9.203 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
9.205 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
9.205 * [backup-simplify]: Simplify (- 0) into 0
9.206 * [backup-simplify]: Simplify (+ 0 0) into 0
9.207 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
9.208 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
9.209 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))
9.210 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))
9.210 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n
9.210 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n
9.210 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
9.210 * [taylor]: Taking taylor expansion of +nan.0 in n
9.210 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.210 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
9.210 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
9.210 * [taylor]: Taking taylor expansion of (sqrt 2) in n
9.210 * [taylor]: Taking taylor expansion of 2 in n
9.210 * [backup-simplify]: Simplify 2 into 2
9.210 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
9.211 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
9.211 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.211 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.211 * [taylor]: Taking taylor expansion of 2 in n
9.211 * [backup-simplify]: Simplify 2 into 2
9.211 * [taylor]: Taking taylor expansion of (* n PI) in n
9.211 * [taylor]: Taking taylor expansion of n in n
9.211 * [backup-simplify]: Simplify 0 into 0
9.211 * [backup-simplify]: Simplify 1 into 1
9.211 * [taylor]: Taking taylor expansion of PI in n
9.211 * [backup-simplify]: Simplify PI into PI
9.212 * [backup-simplify]: Simplify (* 0 PI) into 0
9.212 * [backup-simplify]: Simplify (* 2 0) into 0
9.214 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.215 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.216 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.216 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
9.216 * [taylor]: Taking taylor expansion of (* n PI) in n
9.216 * [taylor]: Taking taylor expansion of n in n
9.216 * [backup-simplify]: Simplify 0 into 0
9.216 * [backup-simplify]: Simplify 1 into 1
9.216 * [taylor]: Taking taylor expansion of PI in n
9.216 * [backup-simplify]: Simplify PI into PI
9.217 * [backup-simplify]: Simplify (* 0 PI) into 0
9.218 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.219 * [backup-simplify]: Simplify (sqrt 0) into 0
9.220 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
9.220 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
9.220 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
9.220 * [taylor]: Taking taylor expansion of +nan.0 in n
9.220 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.220 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
9.220 * [taylor]: Taking taylor expansion of (sqrt 2) in n
9.220 * [taylor]: Taking taylor expansion of 2 in n
9.220 * [backup-simplify]: Simplify 2 into 2
9.221 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
9.221 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
9.221 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
9.221 * [taylor]: Taking taylor expansion of (* n PI) in n
9.221 * [taylor]: Taking taylor expansion of n in n
9.221 * [backup-simplify]: Simplify 0 into 0
9.221 * [backup-simplify]: Simplify 1 into 1
9.221 * [taylor]: Taking taylor expansion of PI in n
9.221 * [backup-simplify]: Simplify PI into PI
9.222 * [backup-simplify]: Simplify (* 0 PI) into 0
9.223 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.224 * [backup-simplify]: Simplify (sqrt 0) into 0
9.225 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
9.227 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.228 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
9.229 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
9.230 * [backup-simplify]: Simplify (* +nan.0 0) into 0
9.230 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
9.231 * [backup-simplify]: Simplify (* +nan.0 0) into 0
9.231 * [backup-simplify]: Simplify (- 0) into 0
9.232 * [backup-simplify]: Simplify (+ 0 0) into 0
9.232 * [backup-simplify]: Simplify (- 0) into 0
9.232 * [backup-simplify]: Simplify 0 into 0
9.235 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
9.240 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
9.243 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
9.246 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
9.246 * [backup-simplify]: Simplify 0 into 0
9.247 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.251 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.252 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.253 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
9.256 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0
9.256 * [backup-simplify]: Simplify (- 0) into 0
9.256 * [backup-simplify]: Simplify (+ 0 0) into 0
9.258 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
9.259 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
9.261 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))
9.262 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))))
9.262 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n
9.262 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n
9.262 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
9.262 * [taylor]: Taking taylor expansion of +nan.0 in n
9.262 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.262 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
9.262 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
9.262 * [taylor]: Taking taylor expansion of (sqrt 2) in n
9.262 * [taylor]: Taking taylor expansion of 2 in n
9.262 * [backup-simplify]: Simplify 2 into 2
9.263 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
9.264 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
9.264 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.264 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.264 * [taylor]: Taking taylor expansion of 2 in n
9.264 * [backup-simplify]: Simplify 2 into 2
9.264 * [taylor]: Taking taylor expansion of (* n PI) in n
9.264 * [taylor]: Taking taylor expansion of n in n
9.264 * [backup-simplify]: Simplify 0 into 0
9.264 * [backup-simplify]: Simplify 1 into 1
9.264 * [taylor]: Taking taylor expansion of PI in n
9.264 * [backup-simplify]: Simplify PI into PI
9.264 * [backup-simplify]: Simplify (* 0 PI) into 0
9.265 * [backup-simplify]: Simplify (* 2 0) into 0
9.266 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.268 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.269 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.269 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
9.269 * [taylor]: Taking taylor expansion of (* n PI) in n
9.269 * [taylor]: Taking taylor expansion of n in n
9.269 * [backup-simplify]: Simplify 0 into 0
9.269 * [backup-simplify]: Simplify 1 into 1
9.269 * [taylor]: Taking taylor expansion of PI in n
9.269 * [backup-simplify]: Simplify PI into PI
9.269 * [backup-simplify]: Simplify (* 0 PI) into 0
9.271 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.271 * [backup-simplify]: Simplify (sqrt 0) into 0
9.273 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
9.273 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n
9.273 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n
9.273 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
9.273 * [taylor]: Taking taylor expansion of +nan.0 in n
9.273 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.273 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
9.273 * [taylor]: Taking taylor expansion of (sqrt 2) in n
9.273 * [taylor]: Taking taylor expansion of 2 in n
9.273 * [backup-simplify]: Simplify 2 into 2
9.273 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
9.274 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
9.274 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
9.274 * [taylor]: Taking taylor expansion of (* n PI) in n
9.274 * [taylor]: Taking taylor expansion of n in n
9.274 * [backup-simplify]: Simplify 0 into 0
9.274 * [backup-simplify]: Simplify 1 into 1
9.274 * [taylor]: Taking taylor expansion of PI in n
9.274 * [backup-simplify]: Simplify PI into PI
9.275 * [backup-simplify]: Simplify (* 0 PI) into 0
9.276 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.276 * [backup-simplify]: Simplify (sqrt 0) into 0
9.277 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
9.277 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n
9.277 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
9.277 * [taylor]: Taking taylor expansion of +nan.0 in n
9.277 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.277 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
9.277 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
9.277 * [taylor]: Taking taylor expansion of (sqrt 2) in n
9.277 * [taylor]: Taking taylor expansion of 2 in n
9.277 * [backup-simplify]: Simplify 2 into 2
9.278 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
9.278 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
9.278 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
9.278 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.278 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.278 * [taylor]: Taking taylor expansion of 2 in n
9.278 * [backup-simplify]: Simplify 2 into 2
9.278 * [taylor]: Taking taylor expansion of (* n PI) in n
9.278 * [taylor]: Taking taylor expansion of n in n
9.278 * [backup-simplify]: Simplify 0 into 0
9.278 * [backup-simplify]: Simplify 1 into 1
9.278 * [taylor]: Taking taylor expansion of PI in n
9.278 * [backup-simplify]: Simplify PI into PI
9.279 * [backup-simplify]: Simplify (* 0 PI) into 0
9.279 * [backup-simplify]: Simplify (* 2 0) into 0
9.280 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.281 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.281 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.282 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.282 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
9.282 * [taylor]: Taking taylor expansion of (* n PI) in n
9.282 * [taylor]: Taking taylor expansion of n in n
9.282 * [backup-simplify]: Simplify 0 into 0
9.282 * [backup-simplify]: Simplify 1 into 1
9.282 * [taylor]: Taking taylor expansion of PI in n
9.282 * [backup-simplify]: Simplify PI into PI
9.282 * [backup-simplify]: Simplify (* 0 PI) into 0
9.283 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.284 * [backup-simplify]: Simplify (sqrt 0) into 0
9.284 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
9.285 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.286 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
9.287 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
9.287 * [backup-simplify]: Simplify (* +nan.0 0) into 0
9.288 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
9.288 * [backup-simplify]: Simplify (* +nan.0 0) into 0
9.289 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.290 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.291 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
9.292 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
9.292 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
9.293 * [backup-simplify]: Simplify (* +nan.0 0) into 0
9.293 * [backup-simplify]: Simplify (- 0) into 0
9.293 * [backup-simplify]: Simplify (+ 0 0) into 0
9.293 * [backup-simplify]: Simplify (- 0) into 0
9.294 * [backup-simplify]: Simplify (+ 0 0) into 0
9.294 * [backup-simplify]: Simplify (- 0) into 0
9.294 * [backup-simplify]: Simplify 0 into 0
9.299 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.300 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.301 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.302 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.303 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
9.304 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
9.311 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
9.314 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
9.319 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
9.323 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
9.331 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))
9.338 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))))
9.346 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))))
9.347 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.351 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
9.352 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
9.357 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
9.365 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
9.369 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
9.372 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
9.380 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
9.381 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
9.381 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0
9.381 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
9.381 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
9.381 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.381 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.381 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
9.381 * [taylor]: Taking taylor expansion of 1/2 in n
9.381 * [backup-simplify]: Simplify 1/2 into 1/2
9.381 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.381 * [taylor]: Taking taylor expansion of 1 in n
9.381 * [backup-simplify]: Simplify 1 into 1
9.381 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.381 * [taylor]: Taking taylor expansion of k in n
9.381 * [backup-simplify]: Simplify k into k
9.381 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.381 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.381 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.381 * [taylor]: Taking taylor expansion of 2 in n
9.381 * [backup-simplify]: Simplify 2 into 2
9.381 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.381 * [taylor]: Taking taylor expansion of PI in n
9.381 * [backup-simplify]: Simplify PI into PI
9.381 * [taylor]: Taking taylor expansion of n in n
9.381 * [backup-simplify]: Simplify 0 into 0
9.381 * [backup-simplify]: Simplify 1 into 1
9.381 * [backup-simplify]: Simplify (/ PI 1) into PI
9.382 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.383 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.383 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.383 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.383 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
9.384 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.384 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
9.385 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
9.385 * [taylor]: Taking taylor expansion of (sqrt k) in n
9.385 * [taylor]: Taking taylor expansion of k in n
9.385 * [backup-simplify]: Simplify k into k
9.385 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
9.385 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
9.385 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
9.385 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
9.385 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
9.385 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
9.385 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
9.385 * [taylor]: Taking taylor expansion of 1/2 in k
9.385 * [backup-simplify]: Simplify 1/2 into 1/2
9.385 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.385 * [taylor]: Taking taylor expansion of 1 in k
9.385 * [backup-simplify]: Simplify 1 into 1
9.385 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.385 * [taylor]: Taking taylor expansion of k in k
9.385 * [backup-simplify]: Simplify 0 into 0
9.385 * [backup-simplify]: Simplify 1 into 1
9.386 * [backup-simplify]: Simplify (/ 1 1) into 1
9.386 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
9.386 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
9.386 * [taylor]: Taking taylor expansion of 2 in k
9.386 * [backup-simplify]: Simplify 2 into 2
9.386 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.386 * [taylor]: Taking taylor expansion of PI in k
9.386 * [backup-simplify]: Simplify PI into PI
9.386 * [taylor]: Taking taylor expansion of n in k
9.386 * [backup-simplify]: Simplify n into n
9.386 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.386 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
9.386 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
9.386 * [backup-simplify]: Simplify (- 1) into -1
9.386 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.387 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
9.387 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
9.387 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
9.387 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.387 * [taylor]: Taking taylor expansion of k in k
9.387 * [backup-simplify]: Simplify 0 into 0
9.387 * [backup-simplify]: Simplify 1 into 1
9.387 * [backup-simplify]: Simplify (sqrt 0) into 0
9.388 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.388 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
9.388 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
9.388 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
9.388 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
9.389 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
9.389 * [taylor]: Taking taylor expansion of 1/2 in k
9.389 * [backup-simplify]: Simplify 1/2 into 1/2
9.389 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.389 * [taylor]: Taking taylor expansion of 1 in k
9.389 * [backup-simplify]: Simplify 1 into 1
9.389 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.389 * [taylor]: Taking taylor expansion of k in k
9.389 * [backup-simplify]: Simplify 0 into 0
9.389 * [backup-simplify]: Simplify 1 into 1
9.389 * [backup-simplify]: Simplify (/ 1 1) into 1
9.389 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
9.389 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
9.389 * [taylor]: Taking taylor expansion of 2 in k
9.389 * [backup-simplify]: Simplify 2 into 2
9.389 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.389 * [taylor]: Taking taylor expansion of PI in k
9.389 * [backup-simplify]: Simplify PI into PI
9.389 * [taylor]: Taking taylor expansion of n in k
9.389 * [backup-simplify]: Simplify n into n
9.389 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.389 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
9.389 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
9.389 * [backup-simplify]: Simplify (- 1) into -1
9.390 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.390 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
9.390 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
9.390 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
9.390 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.390 * [taylor]: Taking taylor expansion of k in k
9.390 * [backup-simplify]: Simplify 0 into 0
9.390 * [backup-simplify]: Simplify 1 into 1
9.390 * [backup-simplify]: Simplify (sqrt 0) into 0
9.391 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.391 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0
9.391 * [taylor]: Taking taylor expansion of 0 in n
9.392 * [backup-simplify]: Simplify 0 into 0
9.392 * [backup-simplify]: Simplify 0 into 0
9.392 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
9.392 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
9.392 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
9.392 * [taylor]: Taking taylor expansion of +nan.0 in n
9.392 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.392 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
9.392 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
9.392 * [taylor]: Taking taylor expansion of 1/2 in n
9.392 * [backup-simplify]: Simplify 1/2 into 1/2
9.392 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
9.392 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.392 * [taylor]: Taking taylor expansion of 1 in n
9.392 * [backup-simplify]: Simplify 1 into 1
9.392 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.392 * [taylor]: Taking taylor expansion of k in n
9.392 * [backup-simplify]: Simplify k into k
9.392 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.392 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.392 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.392 * [taylor]: Taking taylor expansion of 2 in n
9.392 * [backup-simplify]: Simplify 2 into 2
9.392 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.392 * [taylor]: Taking taylor expansion of PI in n
9.392 * [backup-simplify]: Simplify PI into PI
9.392 * [taylor]: Taking taylor expansion of n in n
9.392 * [backup-simplify]: Simplify 0 into 0
9.392 * [backup-simplify]: Simplify 1 into 1
9.393 * [backup-simplify]: Simplify (/ PI 1) into PI
9.393 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.394 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.394 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.394 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.395 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.395 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
9.396 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
9.397 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
9.397 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
9.398 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
9.399 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
9.399 * [backup-simplify]: Simplify 0 into 0
9.400 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.401 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
9.401 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
9.401 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
9.401 * [taylor]: Taking taylor expansion of +nan.0 in n
9.401 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.401 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
9.401 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
9.401 * [taylor]: Taking taylor expansion of 1/2 in n
9.401 * [backup-simplify]: Simplify 1/2 into 1/2
9.401 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
9.401 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.401 * [taylor]: Taking taylor expansion of 1 in n
9.401 * [backup-simplify]: Simplify 1 into 1
9.401 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.401 * [taylor]: Taking taylor expansion of k in n
9.401 * [backup-simplify]: Simplify k into k
9.401 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.401 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.401 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.401 * [taylor]: Taking taylor expansion of 2 in n
9.401 * [backup-simplify]: Simplify 2 into 2
9.401 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.401 * [taylor]: Taking taylor expansion of PI in n
9.401 * [backup-simplify]: Simplify PI into PI
9.401 * [taylor]: Taking taylor expansion of n in n
9.401 * [backup-simplify]: Simplify 0 into 0
9.402 * [backup-simplify]: Simplify 1 into 1
9.402 * [backup-simplify]: Simplify (/ PI 1) into PI
9.402 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.403 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.403 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.403 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.404 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.405 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
9.406 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
9.407 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
9.408 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
9.409 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
9.416 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
9.417 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.418 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.420 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.420 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.420 * [backup-simplify]: Simplify (- 0) into 0
9.421 * [backup-simplify]: Simplify (+ 0 0) into 0
9.422 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.423 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
9.425 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
9.427 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.429 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
9.429 * [backup-simplify]: Simplify (- 0) into 0
9.429 * [backup-simplify]: Simplify 0 into 0
9.429 * [backup-simplify]: Simplify 0 into 0
9.433 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.434 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
9.434 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
9.434 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
9.434 * [taylor]: Taking taylor expansion of +nan.0 in n
9.434 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.434 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
9.434 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
9.435 * [taylor]: Taking taylor expansion of 1/2 in n
9.435 * [backup-simplify]: Simplify 1/2 into 1/2
9.435 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
9.435 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.435 * [taylor]: Taking taylor expansion of 1 in n
9.435 * [backup-simplify]: Simplify 1 into 1
9.435 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.435 * [taylor]: Taking taylor expansion of k in n
9.435 * [backup-simplify]: Simplify k into k
9.435 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.435 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.435 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.435 * [taylor]: Taking taylor expansion of 2 in n
9.435 * [backup-simplify]: Simplify 2 into 2
9.435 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.435 * [taylor]: Taking taylor expansion of PI in n
9.435 * [backup-simplify]: Simplify PI into PI
9.435 * [taylor]: Taking taylor expansion of n in n
9.435 * [backup-simplify]: Simplify 0 into 0
9.435 * [backup-simplify]: Simplify 1 into 1
9.436 * [backup-simplify]: Simplify (/ PI 1) into PI
9.436 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.437 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.438 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.438 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.439 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.440 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
9.441 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
9.443 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
9.444 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
9.445 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
9.446 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
9.450 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
9.451 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
9.451 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0
9.451 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
9.451 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
9.451 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
9.451 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
9.452 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
9.452 * [taylor]: Taking taylor expansion of 1/2 in n
9.452 * [backup-simplify]: Simplify 1/2 into 1/2
9.452 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.452 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.452 * [taylor]: Taking taylor expansion of k in n
9.452 * [backup-simplify]: Simplify k into k
9.452 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.452 * [taylor]: Taking taylor expansion of 1 in n
9.452 * [backup-simplify]: Simplify 1 into 1
9.452 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.452 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.452 * [taylor]: Taking taylor expansion of -2 in n
9.452 * [backup-simplify]: Simplify -2 into -2
9.452 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.452 * [taylor]: Taking taylor expansion of PI in n
9.452 * [backup-simplify]: Simplify PI into PI
9.452 * [taylor]: Taking taylor expansion of n in n
9.452 * [backup-simplify]: Simplify 0 into 0
9.452 * [backup-simplify]: Simplify 1 into 1
9.453 * [backup-simplify]: Simplify (/ PI 1) into PI
9.453 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.454 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.454 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.454 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
9.456 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.457 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
9.458 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
9.458 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
9.458 * [taylor]: Taking taylor expansion of (/ -1 k) in n
9.458 * [taylor]: Taking taylor expansion of -1 in n
9.458 * [backup-simplify]: Simplify -1 into -1
9.458 * [taylor]: Taking taylor expansion of k in n
9.458 * [backup-simplify]: Simplify k into k
9.458 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
9.458 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
9.459 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
9.459 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
9.460 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
9.460 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
9.460 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
9.460 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
9.460 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
9.460 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
9.460 * [taylor]: Taking taylor expansion of 1/2 in k
9.460 * [backup-simplify]: Simplify 1/2 into 1/2
9.460 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.460 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.460 * [taylor]: Taking taylor expansion of k in k
9.460 * [backup-simplify]: Simplify 0 into 0
9.460 * [backup-simplify]: Simplify 1 into 1
9.461 * [backup-simplify]: Simplify (/ 1 1) into 1
9.461 * [taylor]: Taking taylor expansion of 1 in k
9.461 * [backup-simplify]: Simplify 1 into 1
9.461 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
9.461 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
9.461 * [taylor]: Taking taylor expansion of -2 in k
9.461 * [backup-simplify]: Simplify -2 into -2
9.461 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.461 * [taylor]: Taking taylor expansion of PI in k
9.461 * [backup-simplify]: Simplify PI into PI
9.461 * [taylor]: Taking taylor expansion of n in k
9.461 * [backup-simplify]: Simplify n into n
9.461 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.461 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
9.461 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
9.462 * [backup-simplify]: Simplify (+ 1 0) into 1
9.462 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.462 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
9.463 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
9.463 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.463 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.463 * [taylor]: Taking taylor expansion of -1 in k
9.463 * [backup-simplify]: Simplify -1 into -1
9.463 * [taylor]: Taking taylor expansion of k in k
9.463 * [backup-simplify]: Simplify 0 into 0
9.463 * [backup-simplify]: Simplify 1 into 1
9.463 * [backup-simplify]: Simplify (/ -1 1) into -1
9.464 * [backup-simplify]: Simplify (sqrt 0) into 0
9.465 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.465 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
9.466 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
9.466 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
9.466 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
9.466 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
9.466 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
9.466 * [taylor]: Taking taylor expansion of 1/2 in k
9.466 * [backup-simplify]: Simplify 1/2 into 1/2
9.466 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.466 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.466 * [taylor]: Taking taylor expansion of k in k
9.466 * [backup-simplify]: Simplify 0 into 0
9.466 * [backup-simplify]: Simplify 1 into 1
9.466 * [backup-simplify]: Simplify (/ 1 1) into 1
9.466 * [taylor]: Taking taylor expansion of 1 in k
9.466 * [backup-simplify]: Simplify 1 into 1
9.466 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
9.466 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
9.466 * [taylor]: Taking taylor expansion of -2 in k
9.466 * [backup-simplify]: Simplify -2 into -2
9.467 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.467 * [taylor]: Taking taylor expansion of PI in k
9.467 * [backup-simplify]: Simplify PI into PI
9.467 * [taylor]: Taking taylor expansion of n in k
9.467 * [backup-simplify]: Simplify n into n
9.467 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.467 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
9.467 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
9.467 * [backup-simplify]: Simplify (+ 1 0) into 1
9.468 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.468 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
9.468 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
9.468 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.468 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.468 * [taylor]: Taking taylor expansion of -1 in k
9.468 * [backup-simplify]: Simplify -1 into -1
9.468 * [taylor]: Taking taylor expansion of k in k
9.468 * [backup-simplify]: Simplify 0 into 0
9.468 * [backup-simplify]: Simplify 1 into 1
9.469 * [backup-simplify]: Simplify (/ -1 1) into -1
9.469 * [backup-simplify]: Simplify (sqrt 0) into 0
9.471 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.471 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
9.471 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
9.471 * [taylor]: Taking taylor expansion of +nan.0 in n
9.471 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.471 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
9.472 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
9.472 * [taylor]: Taking taylor expansion of 1/2 in n
9.472 * [backup-simplify]: Simplify 1/2 into 1/2
9.472 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
9.472 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.472 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.472 * [taylor]: Taking taylor expansion of -2 in n
9.472 * [backup-simplify]: Simplify -2 into -2
9.472 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.472 * [taylor]: Taking taylor expansion of PI in n
9.472 * [backup-simplify]: Simplify PI into PI
9.472 * [taylor]: Taking taylor expansion of n in n
9.472 * [backup-simplify]: Simplify 0 into 0
9.472 * [backup-simplify]: Simplify 1 into 1
9.472 * [backup-simplify]: Simplify (/ PI 1) into PI
9.473 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.474 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.474 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.474 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.474 * [taylor]: Taking taylor expansion of k in n
9.474 * [backup-simplify]: Simplify k into k
9.474 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.474 * [taylor]: Taking taylor expansion of 1 in n
9.474 * [backup-simplify]: Simplify 1 into 1
9.476 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.476 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.477 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
9.478 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
9.479 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
9.481 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
9.482 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
9.483 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
9.486 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.487 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
9.487 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
9.487 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
9.487 * [taylor]: Taking taylor expansion of +nan.0 in n
9.487 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.487 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
9.487 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
9.487 * [taylor]: Taking taylor expansion of 1/2 in n
9.487 * [backup-simplify]: Simplify 1/2 into 1/2
9.487 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
9.487 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.487 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.487 * [taylor]: Taking taylor expansion of -2 in n
9.487 * [backup-simplify]: Simplify -2 into -2
9.487 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.488 * [taylor]: Taking taylor expansion of PI in n
9.488 * [backup-simplify]: Simplify PI into PI
9.488 * [taylor]: Taking taylor expansion of n in n
9.488 * [backup-simplify]: Simplify 0 into 0
9.488 * [backup-simplify]: Simplify 1 into 1
9.488 * [backup-simplify]: Simplify (/ PI 1) into PI
9.489 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.490 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.490 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.490 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.490 * [taylor]: Taking taylor expansion of k in n
9.490 * [backup-simplify]: Simplify k into k
9.490 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.490 * [taylor]: Taking taylor expansion of 1 in n
9.490 * [backup-simplify]: Simplify 1 into 1
9.491 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.492 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.493 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
9.494 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
9.495 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
9.496 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
9.498 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
9.499 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
9.501 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.501 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.501 * [backup-simplify]: Simplify (+ 0 0) into 0
9.502 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.503 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.505 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
9.506 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
9.508 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
9.510 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.511 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
9.511 * [backup-simplify]: Simplify 0 into 0
9.512 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.516 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.518 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
9.518 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
9.518 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
9.518 * [taylor]: Taking taylor expansion of +nan.0 in n
9.518 * [backup-simplify]: Simplify +nan.0 into +nan.0
9.518 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
9.518 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
9.518 * [taylor]: Taking taylor expansion of 1/2 in n
9.518 * [backup-simplify]: Simplify 1/2 into 1/2
9.518 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
9.518 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.518 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.518 * [taylor]: Taking taylor expansion of -2 in n
9.518 * [backup-simplify]: Simplify -2 into -2
9.518 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.518 * [taylor]: Taking taylor expansion of PI in n
9.518 * [backup-simplify]: Simplify PI into PI
9.519 * [taylor]: Taking taylor expansion of n in n
9.519 * [backup-simplify]: Simplify 0 into 0
9.519 * [backup-simplify]: Simplify 1 into 1
9.519 * [backup-simplify]: Simplify (/ PI 1) into PI
9.519 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.520 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.520 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.521 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.521 * [taylor]: Taking taylor expansion of k in n
9.521 * [backup-simplify]: Simplify k into k
9.521 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.521 * [taylor]: Taking taylor expansion of 1 in n
9.521 * [backup-simplify]: Simplify 1 into 1
9.522 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.522 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.523 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
9.524 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
9.525 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
9.527 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
9.528 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
9.529 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
9.533 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
9.533 * * * [progress]: simplifying candidates
9.533 * * * * [progress]: [ 1 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
9.533 * * * * [progress]: [ 2 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
9.533 * * * * [progress]: [ 3 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
9.533 * * * * [progress]: [ 4 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
9.533 * * * * [progress]: [ 5 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
9.533 * * * * [progress]: [ 6 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
9.534 * * * * [progress]: [ 7 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
9.534 * * * * [progress]: [ 8 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))>
9.534 * * * * [progress]: [ 9 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2)))))>
9.534 * * * * [progress]: [ 10 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2)))))>
9.534 * * * * [progress]: [ 11 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2)))))>
9.534 * * * * [progress]: [ 12 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2)))))>
9.534 * * * * [progress]: [ 13 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2))))>
9.534 * * * * [progress]: [ 14 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2)))))>
9.534 * * * * [progress]: [ 15 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2)))))>
9.534 * * * * [progress]: [ 16 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2))))>
9.534 * * * * [progress]: [ 17 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
9.534 * * * * [progress]: [ 18 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
9.534 * * * * [progress]: [ 19 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
9.534 * * * * [progress]: [ 20 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2)))))>
9.534 * * * * [progress]: [ 21 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2)))))>
9.535 * * * * [progress]: [ 22 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2))))>
9.535 * * * * [progress]: [ 23 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2)))))>
9.535 * * * * [progress]: [ 24 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2)))))>
9.535 * * * * [progress]: [ 25 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))))>
9.535 * * * * [progress]: [ 26 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
9.535 * * * * [progress]: [ 27 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
9.535 * * * * [progress]: [ 28 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
9.535 * * * * [progress]: [ 29 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
9.535 * * * * [progress]: [ 30 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) (/ 1 2))))>
9.535 * * * * [progress]: [ 31 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))))>
9.535 * * * * [progress]: [ 32 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1)))>
9.535 * * * * [progress]: [ 33 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
9.535 * * * * [progress]: [ 34 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (log (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
9.535 * * * * [progress]: [ 35 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
9.536 * * * * [progress]: [ 36 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (cbrt (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
9.536 * * * * [progress]: [ 37 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
9.536 * * * * [progress]: [ 38 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
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9.536 * * * * [progress]: [ 40 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (posit16->real (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
9.536 * * * * [progress]: [ 41 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
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9.536 * * * * [progress]: [ 48 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
9.536 * * * * [progress]: [ 49 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
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9.536 * * * * [progress]: [ 51 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))>
9.537 * * * * [progress]: [ 52 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
9.537 * * * * [progress]: [ 53 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 1 (* (* 2 PI) n)) (/ (- 1 k) 2))))>
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9.537 * * * * [progress]: [ 59 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
9.537 * * * * [progress]: [ 60 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
9.537 * * * * [progress]: [ 61 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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9.537 * * * * [progress]: [ 64 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
9.537 * * * * [progress]: [ 65 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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9.538 * * * * [progress]: [ 69 / 188 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
9.538 * * * * [progress]: [ 70 / 188 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
9.538 * * * * [progress]: [ 71 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
9.538 * * * * [progress]: [ 72 / 188 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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9.538 * * * * [progress]: [ 74 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (- 1) (- (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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9.538 * * * * [progress]: [ 76 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1) (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
9.538 * * * * [progress]: [ 77 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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9.538 * * * * [progress]: [ 79 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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9.539 * * * * [progress]: [ 87 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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9.542 * * * * [progress]: [ 124 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
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9.542 * * * * [progress]: [ 129 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
9.542 * * * * [progress]: [ 130 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
9.542 * * * * [progress]: [ 131 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
9.542 * * * * [progress]: [ 132 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
9.542 * * * * [progress]: [ 133 / 188 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
9.542 * * * * [progress]: [ 134 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))))>
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9.543 * * * * [progress]: [ 139 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
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9.543 * * * * [progress]: [ 141 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
9.543 * * * * [progress]: [ 142 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
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9.543 * * * * [progress]: [ 146 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))))>
9.543 * * * * [progress]: [ 147 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
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9.543 * * * * [progress]: [ 152 / 188 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 153 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 154 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 155 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 156 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 157 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 158 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) 1) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 159 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 160 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 161 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 162 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt 1)) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 163 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 164 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 165 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 166 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.544 * * * * [progress]: [ 167 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.545 * * * * [progress]: [ 168 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.545 * * * * [progress]: [ 169 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.545 * * * * [progress]: [ 170 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.545 * * * * [progress]: [ 171 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.545 * * * * [progress]: [ 172 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
9.545 * * * * [progress]: [ 173 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* (* 2 PI) n) (/ k 2))))>
9.545 * * * * [progress]: [ 174 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))>
9.545 * * * * [progress]: [ 175 / 188 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
9.545 * * * * [progress]: [ 176 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
9.545 * * * * [progress]: [ 177 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))))>
9.545 * * * * [progress]: [ 178 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))>
9.545 * * * * [progress]: [ 179 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))>
9.545 * * * * [progress]: [ 180 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
9.545 * * * * [progress]: [ 181 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
9.545 * * * * [progress]: [ 182 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
9.546 * * * * [progress]: [ 183 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
9.546 * * * * [progress]: [ 184 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
9.546 * * * * [progress]: [ 185 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
9.546 * * * * [progress]: [ 186 / 188 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))>
9.546 * * * * [progress]: [ 187 / 188 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
9.546 * * * * [progress]: [ 188 / 188 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
9.549 * [simplify]: Simplifying (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)), (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)), (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)), (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)), (* 1 (/ (- 1 k) 2)), (* 1 (/ (- 1 k) 2)), (* 1 (/ (- 1 k) 2)), (pow (* (* 2 PI) n) (/ 1 2)), (pow (* (* 2 PI) n) (/ k 2)), (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))), (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))), (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))), (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))), (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)), (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))), (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2))), (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1)), (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* (* 2 PI) n) (/ 1 (sqrt 2))), (pow (* (* 2 PI) n) (/ 1 1)), (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))), (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))), (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1)), (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))), (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2))), (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1)), (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* (* 2 PI) n) (/ 1 (sqrt 2))), (pow (* (* 2 PI) n) (/ 1 1)), (pow (* (* 2 PI) n) 1), (pow (* (* 2 PI) n) (- 1 k)), (pow (* 2 PI) (/ (- 1 k) 2)), (pow n (/ (- 1 k) 2)), (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))), (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)), (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)), (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (* 2 PI) n), (* (* 2 PI) n), (+ (+ (log 2) (log PI)) (log n)), (+ (log (* 2 PI)) (log n)), (log (* (* 2 PI) n)), (exp (* (* 2 PI) n)), (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n)), (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n)), (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))), (cbrt (* (* 2 PI) n)), (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n)), (sqrt (* (* 2 PI) n)), (sqrt (* (* 2 PI) n)), (* (* 2 PI) (* (cbrt n) (cbrt n))), (* (* 2 PI) (sqrt n)), (* (* 2 PI) 1), (* PI n), (real->posit16 (* (* 2 PI) n)), (- 1/2), (- 1), (- (/ 1 2)), (- (log (sqrt k))), (- 0 (log (sqrt k))), (- (log 1) (log (sqrt k))), (log (/ 1 (sqrt k))), (exp (/ 1 (sqrt k))), (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))), (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))), (cbrt (/ 1 (sqrt k))), (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))), (sqrt (/ 1 (sqrt k))), (sqrt (/ 1 (sqrt k))), (- 1), (- (sqrt k)), (/ (* (cbrt 1) (cbrt 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9.556 * * [simplify]: iteration 1: (345 enodes)
9.711 * * [simplify]: iteration 2: (1512 enodes)
10.234 * * [simplify]: Extracting #0: cost 94 inf + 0
10.236 * * [simplify]: Extracting #1: cost 526 inf + 3
10.243 * * [simplify]: Extracting #2: cost 910 inf + 8776
10.261 * * [simplify]: Extracting #3: cost 930 inf + 54477
10.291 * * [simplify]: Extracting #4: cost 494 inf + 213166
10.383 * * [simplify]: Extracting #5: cost 139 inf + 372720
10.488 * * [simplify]: Extracting #6: cost 25 inf + 425720
10.591 * * [simplify]: Extracting #7: cost 4 inf + 432072
10.713 * * [simplify]: Extracting #8: cost 0 inf + 433854
10.788 * [simplify]: Simplified to (* (/ (- 1 k) 2) (log (* n (* 2 PI)))), (* (/ (- 1 k) 2) (log (* n (* 2 PI)))), (* (/ (- 1 k) 2) (log (* n (* 2 PI)))), (* (/ (- 1 k) 2) (log (* n (* 2 PI)))), (/ (- 1 k) 2), (/ (- 1 k) 2), (/ (- 1 k) 2), (sqrt (* n (* 2 PI))), (pow (* n (* 2 PI)) (/ k 2)), (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))), (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2))), (pow (* n (* 2 PI)) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2)))), (pow (* n (* 2 PI)) (/ (cbrt (- 1 k)) (/ (sqrt 2) (cbrt (- 1 k))))), (pow (* n (* 2 PI)) (* (cbrt (- 1 k)) (cbrt (- 1 k)))), (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2))), (pow (* n (* 2 PI)) (sqrt (- 1 k))), (pow (* n (* 2 PI)) (/ (/ 1 (cbrt 2)) (cbrt 2))), (pow (* n (* 2 PI)) (/ 1 (sqrt 2))), (* n (* 2 PI)), (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (cbrt 2)) (cbrt 2))), (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2))), (pow (* n (* 2 PI)) (+ 1 (sqrt k))), (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (cbrt 2)) (cbrt 2))), (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2))), (pow (* n (* 2 PI)) (+ 1 (sqrt k))), (pow (* n (* 2 PI)) (/ (/ 1 (cbrt 2)) (cbrt 2))), (pow (* n (* 2 PI)) (/ 1 (sqrt 2))), (* n (* 2 PI)), (* n (* 2 PI)), (pow (* n (* 2 PI)) (- 1 k)), (pow (* 2 PI) (/ (- 1 k) 2)), (pow n (/ (- 1 k) 2)), (* (/ (- 1 k) 2) (log (* n (* 2 PI)))), (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2))), (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))), (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))), (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 3), (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))), (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))), (pow (* n (* 2 PI)) (/ (- 1 k) 4)), (pow (* n (* 2 PI)) (/ (- 1 k) 4)), (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2))), (* n (* 2 PI)), (* n (* 2 PI)), (log (* n (* 2 PI))), (log (* n (* 2 PI))), (log (* n (* 2 PI))), (exp (* n (* 2 PI))), (* (* n (* 2 PI)) (* (* n (* 2 PI)) (* n (* 2 PI)))), (* (* n (* 2 PI)) (* (* n (* 2 PI)) (* n (* 2 PI)))), (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))), (cbrt (* n (* 2 PI))), (* (* n (* 2 PI)) (* (* n (* 2 PI)) (* n (* 2 PI)))), (sqrt (* n (* 2 PI))), (sqrt (* n (* 2 PI))), (* (* 2 PI) (* (cbrt n) (cbrt n))), (* (* 2 PI) (sqrt n)), (* 2 PI), (* PI n), (real->posit16 (* n (* 2 PI))), -1/2, -1, -1/2, (- (log (sqrt k))), (- (log (sqrt k))), (- (log (sqrt k))), (- (log (sqrt k))), (exp (/ 1 (sqrt k))), (/ (/ 1 k) (sqrt k)), (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))), (cbrt (/ 1 (sqrt k))), (* (/ 1 (sqrt k)) (* (/ 1 (sqrt k)) (/ 1 (sqrt k)))), (sqrt (/ 1 (sqrt k))), (sqrt (/ 1 (sqrt k))), -1, (- (sqrt k)), (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))), (/ 1 (cbrt (sqrt k))), (/ 1 (fabs (cbrt k))), (/ 1 (sqrt (cbrt k))), (/ 1 (sqrt (sqrt k))), (/ 1 (sqrt (sqrt k))), 1, (/ 1 (sqrt k)), (/ 1 (sqrt (sqrt k))), (/ 1 (sqrt (sqrt k))), 1, (/ 1 (sqrt k)), (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))), (/ 1 (cbrt (sqrt k))), (/ 1 (fabs (cbrt k))), (/ 1 (sqrt (cbrt k))), (/ 1 (sqrt (sqrt k))), (/ 1 (sqrt (sqrt k))), 1, (/ 1 (sqrt k)), (/ 1 (sqrt (sqrt k))), (/ 1 (sqrt (sqrt k))), 1, (/ 1 (sqrt k)), (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))), (/ 1 (cbrt (sqrt k))), (/ 1 (fabs (cbrt k))), (/ 1 (sqrt (cbrt k))), (/ 1 (sqrt (sqrt k))), (/ 1 (sqrt (sqrt k))), 1, (/ 1 (sqrt k)), (/ 1 (sqrt (sqrt k))), (/ 1 (sqrt (sqrt k))), 1, (/ 1 (sqrt k)), (/ 1 (sqrt k)), (sqrt k), (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))), (/ 1 (fabs (cbrt k))), (/ 1 (sqrt (sqrt k))), 1, (/ 1 (sqrt (sqrt k))), 1, (sqrt k), (sqrt k), (sqrt k), (real->posit16 (/ 1 (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k))), (exp (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))), (/ (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 3) (* k (sqrt k))), (* (* (/ (/ 1 (sqrt k)) (sqrt k)) (/ 1 (sqrt k))) (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 3)), (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))), (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))), (* (* (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))), (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))), (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))), (sqrt (* n (* 2 PI))), (* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k)), (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))), (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))), (* (sqrt (/ 1 (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1 k) 4))), (* (sqrt (/ 1 (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1 k) 4))), (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))), (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)), (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)), (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)), (/ 1 (sqrt k)), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt k)), (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (/ 1 (sqrt k)))), (* (sqrt (/ 1 (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (sqrt (* n (* 2 PI))) (sqrt k)), (pow (* n (* 2 PI)) (/ (- 1 k) 2)), (real->posit16 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))), (- (+ (+ (+ (* (* 1/8 (* (* k (log n)) (* k (log n)))) (exp (* 1/2 (log (* n (* 2 PI)))))) (* (* (exp (* 1/2 (log (* n (* 2 PI))))) (* (* (log n) (* k k)) (log (* 2 PI)))) 1/4)) (* 1/8 (* (* (exp (* 1/2 (log (* n (* 2 PI))))) (* (log (* 2 PI)) (log (* 2 PI)))) (* k k)))) (exp (* 1/2 (log (* n (* 2 PI)))))) (* 1/2 (+ (* (* k (log n)) (exp (* 1/2 (log (* n (* 2 PI)))))) (* (exp (* 1/2 (log (* n (* 2 PI))))) (* k (log (* 2 PI))))))), (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI))))), (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))), (* n (* 2 PI)), (* n (* 2 PI)), (* n (* 2 PI)), (+ (- +nan.0 (* k +nan.0)) (- (* (* k k) +nan.0))), (+ (/ (- +nan.0) (* k k)) (- (/ +nan.0 k) (/ +nan.0 (* (* k k) k)))), (+ (/ (- +nan.0) (* k k)) (- (/ +nan.0 k) +nan.0)), (- (- (- (* +nan.0 (* (* (* PI n) k) (sqrt 2))) (* (* PI n) (* (sqrt 2) +nan.0))) (+ (* +nan.0 (- (* (* (* (* PI n) k) (sqrt 2)) (log (* 2 PI))))) (* (* (sqrt 2) +nan.0) (- (* n (* (log n) (* PI k))) (* (* PI n) (* PI n))))))), (+ (* (/ (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI))))) k) (- +nan.0)) (- (/ (* +nan.0 (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI)))))) (* k k)) (/ (* +nan.0 (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI)))))) (* (* k k) k)))), (+ (/ (- (* +nan.0 (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))))) k) (* +nan.0 (- (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k)) (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))))))
10.811 * * * [progress]: adding candidates to table
12.834 * * [progress]: iteration 4 / 4
12.834 * * * [progress]: picking best candidate
12.863 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
12.863 * * * [progress]: localizing error
12.911 * * * [progress]: generating rewritten candidates
12.912 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2)
12.940 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
12.955 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2)
13.023 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1)
13.043 * * * [progress]: generating series expansions
13.043 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2)
13.043 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) into (pow (* 2 (* n PI)) (* 1/4 (- 1 k)))
13.044 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in (n k) around 0
13.044 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in k
13.044 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in k
13.044 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in k
13.044 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in k
13.044 * [taylor]: Taking taylor expansion of 1/4 in k
13.044 * [backup-simplify]: Simplify 1/4 into 1/4
13.044 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.044 * [taylor]: Taking taylor expansion of 1 in k
13.044 * [backup-simplify]: Simplify 1 into 1
13.044 * [taylor]: Taking taylor expansion of k in k
13.044 * [backup-simplify]: Simplify 0 into 0
13.044 * [backup-simplify]: Simplify 1 into 1
13.044 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
13.044 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
13.044 * [taylor]: Taking taylor expansion of 2 in k
13.044 * [backup-simplify]: Simplify 2 into 2
13.044 * [taylor]: Taking taylor expansion of (* n PI) in k
13.044 * [taylor]: Taking taylor expansion of n in k
13.044 * [backup-simplify]: Simplify n into n
13.044 * [taylor]: Taking taylor expansion of PI in k
13.044 * [backup-simplify]: Simplify PI into PI
13.044 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.044 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
13.044 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
13.044 * [backup-simplify]: Simplify (- 0) into 0
13.045 * [backup-simplify]: Simplify (+ 1 0) into 1
13.045 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
13.045 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
13.045 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
13.045 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
13.045 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
13.045 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
13.045 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
13.045 * [taylor]: Taking taylor expansion of 1/4 in n
13.045 * [backup-simplify]: Simplify 1/4 into 1/4
13.045 * [taylor]: Taking taylor expansion of (- 1 k) in n
13.045 * [taylor]: Taking taylor expansion of 1 in n
13.045 * [backup-simplify]: Simplify 1 into 1
13.045 * [taylor]: Taking taylor expansion of k in n
13.045 * [backup-simplify]: Simplify k into k
13.045 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.045 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.045 * [taylor]: Taking taylor expansion of 2 in n
13.045 * [backup-simplify]: Simplify 2 into 2
13.045 * [taylor]: Taking taylor expansion of (* n PI) in n
13.045 * [taylor]: Taking taylor expansion of n in n
13.045 * [backup-simplify]: Simplify 0 into 0
13.045 * [backup-simplify]: Simplify 1 into 1
13.045 * [taylor]: Taking taylor expansion of PI in n
13.045 * [backup-simplify]: Simplify PI into PI
13.046 * [backup-simplify]: Simplify (* 0 PI) into 0
13.046 * [backup-simplify]: Simplify (* 2 0) into 0
13.047 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.053 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.054 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.054 * [backup-simplify]: Simplify (- k) into (- k)
13.054 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
13.054 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
13.055 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.056 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
13.057 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
13.057 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
13.057 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
13.057 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
13.057 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
13.057 * [taylor]: Taking taylor expansion of 1/4 in n
13.057 * [backup-simplify]: Simplify 1/4 into 1/4
13.057 * [taylor]: Taking taylor expansion of (- 1 k) in n
13.057 * [taylor]: Taking taylor expansion of 1 in n
13.057 * [backup-simplify]: Simplify 1 into 1
13.057 * [taylor]: Taking taylor expansion of k in n
13.057 * [backup-simplify]: Simplify k into k
13.057 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.057 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.057 * [taylor]: Taking taylor expansion of 2 in n
13.057 * [backup-simplify]: Simplify 2 into 2
13.057 * [taylor]: Taking taylor expansion of (* n PI) in n
13.057 * [taylor]: Taking taylor expansion of n in n
13.057 * [backup-simplify]: Simplify 0 into 0
13.057 * [backup-simplify]: Simplify 1 into 1
13.057 * [taylor]: Taking taylor expansion of PI in n
13.057 * [backup-simplify]: Simplify PI into PI
13.057 * [backup-simplify]: Simplify (* 0 PI) into 0
13.058 * [backup-simplify]: Simplify (* 2 0) into 0
13.059 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.059 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.060 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.060 * [backup-simplify]: Simplify (- k) into (- k)
13.060 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
13.060 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
13.061 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.062 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
13.062 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
13.062 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
13.063 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
13.063 * [taylor]: Taking taylor expansion of 1/4 in k
13.063 * [backup-simplify]: Simplify 1/4 into 1/4
13.063 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
13.063 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.063 * [taylor]: Taking taylor expansion of 1 in k
13.063 * [backup-simplify]: Simplify 1 into 1
13.063 * [taylor]: Taking taylor expansion of k in k
13.063 * [backup-simplify]: Simplify 0 into 0
13.063 * [backup-simplify]: Simplify 1 into 1
13.063 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
13.063 * [taylor]: Taking taylor expansion of (log n) in k
13.063 * [taylor]: Taking taylor expansion of n in k
13.063 * [backup-simplify]: Simplify n into n
13.063 * [backup-simplify]: Simplify (log n) into (log n)
13.063 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.063 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.063 * [taylor]: Taking taylor expansion of 2 in k
13.063 * [backup-simplify]: Simplify 2 into 2
13.063 * [taylor]: Taking taylor expansion of PI in k
13.063 * [backup-simplify]: Simplify PI into PI
13.063 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.064 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.064 * [backup-simplify]: Simplify (- 0) into 0
13.064 * [backup-simplify]: Simplify (+ 1 0) into 1
13.065 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.066 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
13.066 * [backup-simplify]: Simplify (* 1/4 (+ (log n) (log (* 2 PI)))) into (* 1/4 (+ (log n) (log (* 2 PI))))
13.067 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
13.067 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
13.068 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.069 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.070 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.070 * [backup-simplify]: Simplify (- 0) into 0
13.070 * [backup-simplify]: Simplify (+ 0 0) into 0
13.071 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 k))) into 0
13.071 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.072 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
13.073 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.073 * [taylor]: Taking taylor expansion of 0 in k
13.073 * [backup-simplify]: Simplify 0 into 0
13.073 * [backup-simplify]: Simplify 0 into 0
13.074 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.074 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.075 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.075 * [backup-simplify]: Simplify (+ 0 0) into 0
13.076 * [backup-simplify]: Simplify (- 1) into -1
13.076 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.077 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
13.078 * [backup-simplify]: Simplify (+ (* 1/4 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
13.080 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
13.082 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
13.083 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.083 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.085 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.086 * [backup-simplify]: Simplify (- 0) into 0
13.086 * [backup-simplify]: Simplify (+ 0 0) into 0
13.086 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
13.087 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.088 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.091 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.091 * [taylor]: Taking taylor expansion of 0 in k
13.091 * [backup-simplify]: Simplify 0 into 0
13.091 * [backup-simplify]: Simplify 0 into 0
13.091 * [backup-simplify]: Simplify 0 into 0
13.092 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.092 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.094 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.094 * [backup-simplify]: Simplify (+ 0 0) into 0
13.095 * [backup-simplify]: Simplify (- 0) into 0
13.095 * [backup-simplify]: Simplify (+ 0 0) into 0
13.096 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.098 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.100 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
13.103 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
13.109 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
13.109 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (/ (- 1 (/ 1 k)) 2) 2)) into (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k))))
13.109 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in (n k) around 0
13.109 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in k
13.109 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
13.109 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
13.109 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in k
13.109 * [taylor]: Taking taylor expansion of 1/4 in k
13.109 * [backup-simplify]: Simplify 1/4 into 1/4
13.109 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.109 * [taylor]: Taking taylor expansion of 1 in k
13.109 * [backup-simplify]: Simplify 1 into 1
13.109 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.109 * [taylor]: Taking taylor expansion of k in k
13.109 * [backup-simplify]: Simplify 0 into 0
13.109 * [backup-simplify]: Simplify 1 into 1
13.110 * [backup-simplify]: Simplify (/ 1 1) into 1
13.110 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
13.110 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
13.110 * [taylor]: Taking taylor expansion of 2 in k
13.110 * [backup-simplify]: Simplify 2 into 2
13.110 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.110 * [taylor]: Taking taylor expansion of PI in k
13.110 * [backup-simplify]: Simplify PI into PI
13.110 * [taylor]: Taking taylor expansion of n in k
13.110 * [backup-simplify]: Simplify n into n
13.110 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.110 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
13.110 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
13.110 * [backup-simplify]: Simplify (- 1) into -1
13.110 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.111 * [backup-simplify]: Simplify (* 1/4 -1) into -1/4
13.111 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
13.111 * [backup-simplify]: Simplify (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
13.111 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
13.111 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.111 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.111 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
13.111 * [taylor]: Taking taylor expansion of 1/4 in n
13.111 * [backup-simplify]: Simplify 1/4 into 1/4
13.111 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.111 * [taylor]: Taking taylor expansion of 1 in n
13.111 * [backup-simplify]: Simplify 1 into 1
13.111 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.111 * [taylor]: Taking taylor expansion of k in n
13.111 * [backup-simplify]: Simplify k into k
13.111 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.111 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.111 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.111 * [taylor]: Taking taylor expansion of 2 in n
13.111 * [backup-simplify]: Simplify 2 into 2
13.111 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.111 * [taylor]: Taking taylor expansion of PI in n
13.111 * [backup-simplify]: Simplify PI into PI
13.111 * [taylor]: Taking taylor expansion of n in n
13.111 * [backup-simplify]: Simplify 0 into 0
13.111 * [backup-simplify]: Simplify 1 into 1
13.112 * [backup-simplify]: Simplify (/ PI 1) into PI
13.112 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.113 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.113 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.113 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.113 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
13.114 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.114 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.115 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.115 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
13.115 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.115 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.115 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
13.115 * [taylor]: Taking taylor expansion of 1/4 in n
13.115 * [backup-simplify]: Simplify 1/4 into 1/4
13.115 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.115 * [taylor]: Taking taylor expansion of 1 in n
13.115 * [backup-simplify]: Simplify 1 into 1
13.115 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.115 * [taylor]: Taking taylor expansion of k in n
13.115 * [backup-simplify]: Simplify k into k
13.115 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.115 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.115 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.115 * [taylor]: Taking taylor expansion of 2 in n
13.115 * [backup-simplify]: Simplify 2 into 2
13.115 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.115 * [taylor]: Taking taylor expansion of PI in n
13.115 * [backup-simplify]: Simplify PI into PI
13.115 * [taylor]: Taking taylor expansion of n in n
13.115 * [backup-simplify]: Simplify 0 into 0
13.115 * [backup-simplify]: Simplify 1 into 1
13.116 * [backup-simplify]: Simplify (/ PI 1) into PI
13.116 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.117 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.117 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.117 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.117 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
13.118 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.118 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.119 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.119 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
13.119 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
13.119 * [taylor]: Taking taylor expansion of 1/4 in k
13.119 * [backup-simplify]: Simplify 1/4 into 1/4
13.119 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
13.119 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.119 * [taylor]: Taking taylor expansion of 1 in k
13.119 * [backup-simplify]: Simplify 1 into 1
13.119 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.119 * [taylor]: Taking taylor expansion of k in k
13.119 * [backup-simplify]: Simplify 0 into 0
13.119 * [backup-simplify]: Simplify 1 into 1
13.120 * [backup-simplify]: Simplify (/ 1 1) into 1
13.120 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
13.120 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.120 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.120 * [taylor]: Taking taylor expansion of 2 in k
13.120 * [backup-simplify]: Simplify 2 into 2
13.120 * [taylor]: Taking taylor expansion of PI in k
13.120 * [backup-simplify]: Simplify PI into PI
13.120 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.121 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.121 * [taylor]: Taking taylor expansion of (log n) in k
13.121 * [taylor]: Taking taylor expansion of n in k
13.121 * [backup-simplify]: Simplify n into n
13.121 * [backup-simplify]: Simplify (log n) into (log n)
13.122 * [backup-simplify]: Simplify (- 1) into -1
13.122 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.122 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.123 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
13.124 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
13.125 * [backup-simplify]: Simplify (* 1/4 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
13.126 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.128 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.129 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.129 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.131 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.131 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.132 * [backup-simplify]: Simplify (- 0) into 0
13.132 * [backup-simplify]: Simplify (+ 0 0) into 0
13.133 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 (/ 1 k)))) into 0
13.134 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.135 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
13.137 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.137 * [taylor]: Taking taylor expansion of 0 in k
13.137 * [backup-simplify]: Simplify 0 into 0
13.137 * [backup-simplify]: Simplify 0 into 0
13.137 * [backup-simplify]: Simplify 0 into 0
13.138 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.140 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.143 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.143 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.144 * [backup-simplify]: Simplify (- 0) into 0
13.144 * [backup-simplify]: Simplify (+ 0 0) into 0
13.145 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
13.147 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.148 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
13.151 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.151 * [taylor]: Taking taylor expansion of 0 in k
13.151 * [backup-simplify]: Simplify 0 into 0
13.151 * [backup-simplify]: Simplify 0 into 0
13.151 * [backup-simplify]: Simplify 0 into 0
13.151 * [backup-simplify]: Simplify 0 into 0
13.152 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.159 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.165 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
13.166 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.166 * [backup-simplify]: Simplify (- 0) into 0
13.167 * [backup-simplify]: Simplify (+ 0 0) into 0
13.168 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
13.170 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.172 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
13.174 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.174 * [taylor]: Taking taylor expansion of 0 in k
13.174 * [backup-simplify]: Simplify 0 into 0
13.174 * [backup-simplify]: Simplify 0 into 0
13.176 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
13.176 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (/ (- 1 (/ 1 (- k))) 2) 2)) into (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1)))
13.176 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in (n k) around 0
13.176 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in k
13.177 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
13.177 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
13.177 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in k
13.177 * [taylor]: Taking taylor expansion of 1/4 in k
13.177 * [backup-simplify]: Simplify 1/4 into 1/4
13.177 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
13.177 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.177 * [taylor]: Taking taylor expansion of k in k
13.177 * [backup-simplify]: Simplify 0 into 0
13.177 * [backup-simplify]: Simplify 1 into 1
13.177 * [backup-simplify]: Simplify (/ 1 1) into 1
13.177 * [taylor]: Taking taylor expansion of 1 in k
13.177 * [backup-simplify]: Simplify 1 into 1
13.177 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.177 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.178 * [taylor]: Taking taylor expansion of -2 in k
13.178 * [backup-simplify]: Simplify -2 into -2
13.178 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.178 * [taylor]: Taking taylor expansion of PI in k
13.178 * [backup-simplify]: Simplify PI into PI
13.178 * [taylor]: Taking taylor expansion of n in k
13.178 * [backup-simplify]: Simplify n into n
13.178 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.178 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.178 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.178 * [backup-simplify]: Simplify (+ 1 0) into 1
13.179 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
13.179 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
13.179 * [backup-simplify]: Simplify (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/4 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
13.179 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
13.179 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
13.179 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
13.179 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
13.179 * [taylor]: Taking taylor expansion of 1/4 in n
13.179 * [backup-simplify]: Simplify 1/4 into 1/4
13.179 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.180 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.180 * [taylor]: Taking taylor expansion of k in n
13.180 * [backup-simplify]: Simplify k into k
13.180 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.180 * [taylor]: Taking taylor expansion of 1 in n
13.180 * [backup-simplify]: Simplify 1 into 1
13.180 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.180 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.180 * [taylor]: Taking taylor expansion of -2 in n
13.180 * [backup-simplify]: Simplify -2 into -2
13.180 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.180 * [taylor]: Taking taylor expansion of PI in n
13.180 * [backup-simplify]: Simplify PI into PI
13.180 * [taylor]: Taking taylor expansion of n in n
13.180 * [backup-simplify]: Simplify 0 into 0
13.180 * [backup-simplify]: Simplify 1 into 1
13.180 * [backup-simplify]: Simplify (/ PI 1) into PI
13.181 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.182 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.182 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.182 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
13.184 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.185 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.186 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.186 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
13.186 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
13.186 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
13.186 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
13.186 * [taylor]: Taking taylor expansion of 1/4 in n
13.186 * [backup-simplify]: Simplify 1/4 into 1/4
13.186 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.186 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.186 * [taylor]: Taking taylor expansion of k in n
13.186 * [backup-simplify]: Simplify k into k
13.186 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.186 * [taylor]: Taking taylor expansion of 1 in n
13.186 * [backup-simplify]: Simplify 1 into 1
13.187 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.187 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.187 * [taylor]: Taking taylor expansion of -2 in n
13.187 * [backup-simplify]: Simplify -2 into -2
13.187 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.187 * [taylor]: Taking taylor expansion of PI in n
13.187 * [backup-simplify]: Simplify PI into PI
13.187 * [taylor]: Taking taylor expansion of n in n
13.187 * [backup-simplify]: Simplify 0 into 0
13.187 * [backup-simplify]: Simplify 1 into 1
13.187 * [backup-simplify]: Simplify (/ PI 1) into PI
13.188 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.189 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.189 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.189 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
13.190 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.191 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.193 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.193 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
13.193 * [taylor]: Taking taylor expansion of (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
13.193 * [taylor]: Taking taylor expansion of 1/4 in k
13.193 * [backup-simplify]: Simplify 1/4 into 1/4
13.193 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
13.193 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
13.193 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.193 * [taylor]: Taking taylor expansion of k in k
13.193 * [backup-simplify]: Simplify 0 into 0
13.193 * [backup-simplify]: Simplify 1 into 1
13.193 * [backup-simplify]: Simplify (/ 1 1) into 1
13.193 * [taylor]: Taking taylor expansion of 1 in k
13.193 * [backup-simplify]: Simplify 1 into 1
13.193 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
13.193 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
13.193 * [taylor]: Taking taylor expansion of (* -2 PI) in k
13.193 * [taylor]: Taking taylor expansion of -2 in k
13.193 * [backup-simplify]: Simplify -2 into -2
13.193 * [taylor]: Taking taylor expansion of PI in k
13.194 * [backup-simplify]: Simplify PI into PI
13.194 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.195 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.195 * [taylor]: Taking taylor expansion of (log n) in k
13.195 * [taylor]: Taking taylor expansion of n in k
13.195 * [backup-simplify]: Simplify n into n
13.195 * [backup-simplify]: Simplify (log n) into (log n)
13.196 * [backup-simplify]: Simplify (+ 1 0) into 1
13.196 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.197 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
13.198 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
13.199 * [backup-simplify]: Simplify (* 1/4 (- (log (* -2 PI)) (log n))) into (* 1/4 (- (log (* -2 PI)) (log n)))
13.200 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.201 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.202 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.203 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.205 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
13.205 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.206 * [backup-simplify]: Simplify (+ 0 0) into 0
13.206 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (+ (/ 1 k) 1))) into 0
13.208 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.209 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
13.211 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.211 * [taylor]: Taking taylor expansion of 0 in k
13.211 * [backup-simplify]: Simplify 0 into 0
13.211 * [backup-simplify]: Simplify 0 into 0
13.211 * [backup-simplify]: Simplify 0 into 0
13.212 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.213 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
13.217 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
13.217 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.217 * [backup-simplify]: Simplify (+ 0 0) into 0
13.218 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
13.220 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.221 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
13.224 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.224 * [taylor]: Taking taylor expansion of 0 in k
13.224 * [backup-simplify]: Simplify 0 into 0
13.224 * [backup-simplify]: Simplify 0 into 0
13.224 * [backup-simplify]: Simplify 0 into 0
13.224 * [backup-simplify]: Simplify 0 into 0
13.225 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.227 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.233 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
13.233 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.234 * [backup-simplify]: Simplify (+ 0 0) into 0
13.235 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
13.236 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.238 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
13.241 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.241 * [taylor]: Taking taylor expansion of 0 in k
13.242 * [backup-simplify]: Simplify 0 into 0
13.242 * [backup-simplify]: Simplify 0 into 0
13.243 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
13.243 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
13.244 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) into (pow (* 2 (* n PI)) (* 1/4 (- 1 k)))
13.244 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in (n k) around 0
13.244 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in k
13.244 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in k
13.244 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in k
13.244 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in k
13.244 * [taylor]: Taking taylor expansion of 1/4 in k
13.244 * [backup-simplify]: Simplify 1/4 into 1/4
13.244 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.244 * [taylor]: Taking taylor expansion of 1 in k
13.244 * [backup-simplify]: Simplify 1 into 1
13.244 * [taylor]: Taking taylor expansion of k in k
13.244 * [backup-simplify]: Simplify 0 into 0
13.244 * [backup-simplify]: Simplify 1 into 1
13.244 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
13.244 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
13.244 * [taylor]: Taking taylor expansion of 2 in k
13.244 * [backup-simplify]: Simplify 2 into 2
13.244 * [taylor]: Taking taylor expansion of (* n PI) in k
13.244 * [taylor]: Taking taylor expansion of n in k
13.244 * [backup-simplify]: Simplify n into n
13.244 * [taylor]: Taking taylor expansion of PI in k
13.244 * [backup-simplify]: Simplify PI into PI
13.244 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.244 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
13.244 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
13.245 * [backup-simplify]: Simplify (- 0) into 0
13.245 * [backup-simplify]: Simplify (+ 1 0) into 1
13.246 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
13.246 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
13.246 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
13.246 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
13.246 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
13.246 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
13.246 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
13.246 * [taylor]: Taking taylor expansion of 1/4 in n
13.246 * [backup-simplify]: Simplify 1/4 into 1/4
13.246 * [taylor]: Taking taylor expansion of (- 1 k) in n
13.246 * [taylor]: Taking taylor expansion of 1 in n
13.246 * [backup-simplify]: Simplify 1 into 1
13.246 * [taylor]: Taking taylor expansion of k in n
13.246 * [backup-simplify]: Simplify k into k
13.246 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.246 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.246 * [taylor]: Taking taylor expansion of 2 in n
13.246 * [backup-simplify]: Simplify 2 into 2
13.246 * [taylor]: Taking taylor expansion of (* n PI) in n
13.246 * [taylor]: Taking taylor expansion of n in n
13.246 * [backup-simplify]: Simplify 0 into 0
13.246 * [backup-simplify]: Simplify 1 into 1
13.246 * [taylor]: Taking taylor expansion of PI in n
13.246 * [backup-simplify]: Simplify PI into PI
13.247 * [backup-simplify]: Simplify (* 0 PI) into 0
13.247 * [backup-simplify]: Simplify (* 2 0) into 0
13.249 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.250 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.252 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.252 * [backup-simplify]: Simplify (- k) into (- k)
13.252 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
13.252 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
13.253 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.254 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
13.256 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
13.256 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
13.256 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
13.256 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
13.256 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
13.256 * [taylor]: Taking taylor expansion of 1/4 in n
13.256 * [backup-simplify]: Simplify 1/4 into 1/4
13.256 * [taylor]: Taking taylor expansion of (- 1 k) in n
13.256 * [taylor]: Taking taylor expansion of 1 in n
13.256 * [backup-simplify]: Simplify 1 into 1
13.256 * [taylor]: Taking taylor expansion of k in n
13.256 * [backup-simplify]: Simplify k into k
13.256 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.256 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.256 * [taylor]: Taking taylor expansion of 2 in n
13.256 * [backup-simplify]: Simplify 2 into 2
13.256 * [taylor]: Taking taylor expansion of (* n PI) in n
13.256 * [taylor]: Taking taylor expansion of n in n
13.256 * [backup-simplify]: Simplify 0 into 0
13.256 * [backup-simplify]: Simplify 1 into 1
13.256 * [taylor]: Taking taylor expansion of PI in n
13.256 * [backup-simplify]: Simplify PI into PI
13.257 * [backup-simplify]: Simplify (* 0 PI) into 0
13.257 * [backup-simplify]: Simplify (* 2 0) into 0
13.259 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.261 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.262 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.262 * [backup-simplify]: Simplify (- k) into (- k)
13.262 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
13.262 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
13.263 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.264 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
13.265 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
13.266 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
13.266 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
13.266 * [taylor]: Taking taylor expansion of 1/4 in k
13.266 * [backup-simplify]: Simplify 1/4 into 1/4
13.266 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
13.266 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.266 * [taylor]: Taking taylor expansion of 1 in k
13.266 * [backup-simplify]: Simplify 1 into 1
13.266 * [taylor]: Taking taylor expansion of k in k
13.266 * [backup-simplify]: Simplify 0 into 0
13.266 * [backup-simplify]: Simplify 1 into 1
13.266 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
13.266 * [taylor]: Taking taylor expansion of (log n) in k
13.266 * [taylor]: Taking taylor expansion of n in k
13.266 * [backup-simplify]: Simplify n into n
13.266 * [backup-simplify]: Simplify (log n) into (log n)
13.266 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.266 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.266 * [taylor]: Taking taylor expansion of 2 in k
13.266 * [backup-simplify]: Simplify 2 into 2
13.266 * [taylor]: Taking taylor expansion of PI in k
13.266 * [backup-simplify]: Simplify PI into PI
13.267 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.268 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.268 * [backup-simplify]: Simplify (- 0) into 0
13.268 * [backup-simplify]: Simplify (+ 1 0) into 1
13.269 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.271 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
13.272 * [backup-simplify]: Simplify (* 1/4 (+ (log n) (log (* 2 PI)))) into (* 1/4 (+ (log n) (log (* 2 PI))))
13.273 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
13.274 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
13.275 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.276 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.278 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.278 * [backup-simplify]: Simplify (- 0) into 0
13.278 * [backup-simplify]: Simplify (+ 0 0) into 0
13.279 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 k))) into 0
13.280 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.281 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
13.283 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.283 * [taylor]: Taking taylor expansion of 0 in k
13.284 * [backup-simplify]: Simplify 0 into 0
13.284 * [backup-simplify]: Simplify 0 into 0
13.285 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.285 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.287 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.288 * [backup-simplify]: Simplify (+ 0 0) into 0
13.288 * [backup-simplify]: Simplify (- 1) into -1
13.288 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.290 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
13.292 * [backup-simplify]: Simplify (+ (* 1/4 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
13.295 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
13.297 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
13.298 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.298 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.300 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.300 * [backup-simplify]: Simplify (- 0) into 0
13.301 * [backup-simplify]: Simplify (+ 0 0) into 0
13.301 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
13.307 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.308 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.309 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.310 * [taylor]: Taking taylor expansion of 0 in k
13.310 * [backup-simplify]: Simplify 0 into 0
13.310 * [backup-simplify]: Simplify 0 into 0
13.310 * [backup-simplify]: Simplify 0 into 0
13.311 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.311 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.313 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.313 * [backup-simplify]: Simplify (+ 0 0) into 0
13.314 * [backup-simplify]: Simplify (- 0) into 0
13.314 * [backup-simplify]: Simplify (+ 0 0) into 0
13.315 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.317 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.319 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
13.322 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
13.328 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
13.329 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (/ (- 1 (/ 1 k)) 2) 2)) into (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k))))
13.329 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in (n k) around 0
13.329 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in k
13.329 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
13.329 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
13.329 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in k
13.329 * [taylor]: Taking taylor expansion of 1/4 in k
13.329 * [backup-simplify]: Simplify 1/4 into 1/4
13.329 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.329 * [taylor]: Taking taylor expansion of 1 in k
13.329 * [backup-simplify]: Simplify 1 into 1
13.329 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.330 * [taylor]: Taking taylor expansion of k in k
13.330 * [backup-simplify]: Simplify 0 into 0
13.330 * [backup-simplify]: Simplify 1 into 1
13.330 * [backup-simplify]: Simplify (/ 1 1) into 1
13.330 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
13.330 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
13.330 * [taylor]: Taking taylor expansion of 2 in k
13.330 * [backup-simplify]: Simplify 2 into 2
13.330 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.330 * [taylor]: Taking taylor expansion of PI in k
13.330 * [backup-simplify]: Simplify PI into PI
13.330 * [taylor]: Taking taylor expansion of n in k
13.330 * [backup-simplify]: Simplify n into n
13.330 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.330 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
13.330 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
13.331 * [backup-simplify]: Simplify (- 1) into -1
13.331 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.332 * [backup-simplify]: Simplify (* 1/4 -1) into -1/4
13.332 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
13.332 * [backup-simplify]: Simplify (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
13.332 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
13.332 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.332 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.332 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
13.332 * [taylor]: Taking taylor expansion of 1/4 in n
13.332 * [backup-simplify]: Simplify 1/4 into 1/4
13.332 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.332 * [taylor]: Taking taylor expansion of 1 in n
13.332 * [backup-simplify]: Simplify 1 into 1
13.332 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.332 * [taylor]: Taking taylor expansion of k in n
13.333 * [backup-simplify]: Simplify k into k
13.333 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.333 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.333 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.333 * [taylor]: Taking taylor expansion of 2 in n
13.333 * [backup-simplify]: Simplify 2 into 2
13.333 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.333 * [taylor]: Taking taylor expansion of PI in n
13.333 * [backup-simplify]: Simplify PI into PI
13.333 * [taylor]: Taking taylor expansion of n in n
13.333 * [backup-simplify]: Simplify 0 into 0
13.333 * [backup-simplify]: Simplify 1 into 1
13.333 * [backup-simplify]: Simplify (/ PI 1) into PI
13.334 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.335 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.335 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.335 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.335 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
13.337 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.338 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.339 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.339 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
13.339 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.339 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.339 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
13.339 * [taylor]: Taking taylor expansion of 1/4 in n
13.339 * [backup-simplify]: Simplify 1/4 into 1/4
13.339 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.339 * [taylor]: Taking taylor expansion of 1 in n
13.339 * [backup-simplify]: Simplify 1 into 1
13.339 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.339 * [taylor]: Taking taylor expansion of k in n
13.339 * [backup-simplify]: Simplify k into k
13.339 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.339 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.339 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.340 * [taylor]: Taking taylor expansion of 2 in n
13.340 * [backup-simplify]: Simplify 2 into 2
13.340 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.340 * [taylor]: Taking taylor expansion of PI in n
13.340 * [backup-simplify]: Simplify PI into PI
13.340 * [taylor]: Taking taylor expansion of n in n
13.340 * [backup-simplify]: Simplify 0 into 0
13.340 * [backup-simplify]: Simplify 1 into 1
13.340 * [backup-simplify]: Simplify (/ PI 1) into PI
13.341 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.342 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.342 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.342 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.342 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
13.343 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.345 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.346 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.346 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
13.346 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
13.346 * [taylor]: Taking taylor expansion of 1/4 in k
13.346 * [backup-simplify]: Simplify 1/4 into 1/4
13.346 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
13.346 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.346 * [taylor]: Taking taylor expansion of 1 in k
13.346 * [backup-simplify]: Simplify 1 into 1
13.346 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.346 * [taylor]: Taking taylor expansion of k in k
13.346 * [backup-simplify]: Simplify 0 into 0
13.347 * [backup-simplify]: Simplify 1 into 1
13.347 * [backup-simplify]: Simplify (/ 1 1) into 1
13.347 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
13.347 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.347 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.347 * [taylor]: Taking taylor expansion of 2 in k
13.347 * [backup-simplify]: Simplify 2 into 2
13.347 * [taylor]: Taking taylor expansion of PI in k
13.347 * [backup-simplify]: Simplify PI into PI
13.348 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.349 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.349 * [taylor]: Taking taylor expansion of (log n) in k
13.349 * [taylor]: Taking taylor expansion of n in k
13.349 * [backup-simplify]: Simplify n into n
13.349 * [backup-simplify]: Simplify (log n) into (log n)
13.349 * [backup-simplify]: Simplify (- 1) into -1
13.350 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.350 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.351 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
13.352 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
13.353 * [backup-simplify]: Simplify (* 1/4 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
13.354 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.355 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.357 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.359 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.359 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.360 * [backup-simplify]: Simplify (- 0) into 0
13.360 * [backup-simplify]: Simplify (+ 0 0) into 0
13.361 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 (/ 1 k)))) into 0
13.362 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.363 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
13.365 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.365 * [taylor]: Taking taylor expansion of 0 in k
13.366 * [backup-simplify]: Simplify 0 into 0
13.366 * [backup-simplify]: Simplify 0 into 0
13.366 * [backup-simplify]: Simplify 0 into 0
13.367 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.368 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.371 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.372 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.372 * [backup-simplify]: Simplify (- 0) into 0
13.373 * [backup-simplify]: Simplify (+ 0 0) into 0
13.374 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
13.375 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.376 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
13.378 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.378 * [taylor]: Taking taylor expansion of 0 in k
13.378 * [backup-simplify]: Simplify 0 into 0
13.378 * [backup-simplify]: Simplify 0 into 0
13.378 * [backup-simplify]: Simplify 0 into 0
13.378 * [backup-simplify]: Simplify 0 into 0
13.379 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.379 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.382 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
13.383 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.383 * [backup-simplify]: Simplify (- 0) into 0
13.383 * [backup-simplify]: Simplify (+ 0 0) into 0
13.384 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
13.385 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.386 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
13.388 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.388 * [taylor]: Taking taylor expansion of 0 in k
13.388 * [backup-simplify]: Simplify 0 into 0
13.388 * [backup-simplify]: Simplify 0 into 0
13.388 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
13.389 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (/ (- 1 (/ 1 (- k))) 2) 2)) into (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1)))
13.389 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in (n k) around 0
13.389 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in k
13.389 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
13.389 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
13.389 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in k
13.389 * [taylor]: Taking taylor expansion of 1/4 in k
13.389 * [backup-simplify]: Simplify 1/4 into 1/4
13.389 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
13.389 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.389 * [taylor]: Taking taylor expansion of k in k
13.389 * [backup-simplify]: Simplify 0 into 0
13.389 * [backup-simplify]: Simplify 1 into 1
13.389 * [backup-simplify]: Simplify (/ 1 1) into 1
13.389 * [taylor]: Taking taylor expansion of 1 in k
13.389 * [backup-simplify]: Simplify 1 into 1
13.389 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.389 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.389 * [taylor]: Taking taylor expansion of -2 in k
13.389 * [backup-simplify]: Simplify -2 into -2
13.389 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.389 * [taylor]: Taking taylor expansion of PI in k
13.389 * [backup-simplify]: Simplify PI into PI
13.389 * [taylor]: Taking taylor expansion of n in k
13.389 * [backup-simplify]: Simplify n into n
13.389 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.390 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.390 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.390 * [backup-simplify]: Simplify (+ 1 0) into 1
13.390 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
13.390 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
13.390 * [backup-simplify]: Simplify (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/4 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
13.390 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
13.390 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
13.390 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
13.390 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
13.390 * [taylor]: Taking taylor expansion of 1/4 in n
13.390 * [backup-simplify]: Simplify 1/4 into 1/4
13.390 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.390 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.390 * [taylor]: Taking taylor expansion of k in n
13.391 * [backup-simplify]: Simplify k into k
13.391 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.391 * [taylor]: Taking taylor expansion of 1 in n
13.391 * [backup-simplify]: Simplify 1 into 1
13.391 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.391 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.391 * [taylor]: Taking taylor expansion of -2 in n
13.391 * [backup-simplify]: Simplify -2 into -2
13.391 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.391 * [taylor]: Taking taylor expansion of PI in n
13.391 * [backup-simplify]: Simplify PI into PI
13.391 * [taylor]: Taking taylor expansion of n in n
13.391 * [backup-simplify]: Simplify 0 into 0
13.391 * [backup-simplify]: Simplify 1 into 1
13.391 * [backup-simplify]: Simplify (/ PI 1) into PI
13.391 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.392 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.392 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.392 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
13.393 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.394 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.394 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.394 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
13.394 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
13.394 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
13.394 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
13.395 * [taylor]: Taking taylor expansion of 1/4 in n
13.395 * [backup-simplify]: Simplify 1/4 into 1/4
13.395 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.395 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.395 * [taylor]: Taking taylor expansion of k in n
13.395 * [backup-simplify]: Simplify k into k
13.395 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.395 * [taylor]: Taking taylor expansion of 1 in n
13.395 * [backup-simplify]: Simplify 1 into 1
13.395 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.395 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.395 * [taylor]: Taking taylor expansion of -2 in n
13.395 * [backup-simplify]: Simplify -2 into -2
13.395 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.395 * [taylor]: Taking taylor expansion of PI in n
13.395 * [backup-simplify]: Simplify PI into PI
13.395 * [taylor]: Taking taylor expansion of n in n
13.395 * [backup-simplify]: Simplify 0 into 0
13.395 * [backup-simplify]: Simplify 1 into 1
13.395 * [backup-simplify]: Simplify (/ PI 1) into PI
13.395 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.396 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.396 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.396 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
13.397 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.398 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.399 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.399 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
13.399 * [taylor]: Taking taylor expansion of (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
13.399 * [taylor]: Taking taylor expansion of 1/4 in k
13.399 * [backup-simplify]: Simplify 1/4 into 1/4
13.399 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
13.399 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
13.399 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.399 * [taylor]: Taking taylor expansion of k in k
13.399 * [backup-simplify]: Simplify 0 into 0
13.399 * [backup-simplify]: Simplify 1 into 1
13.399 * [backup-simplify]: Simplify (/ 1 1) into 1
13.399 * [taylor]: Taking taylor expansion of 1 in k
13.399 * [backup-simplify]: Simplify 1 into 1
13.399 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
13.399 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
13.399 * [taylor]: Taking taylor expansion of (* -2 PI) in k
13.399 * [taylor]: Taking taylor expansion of -2 in k
13.399 * [backup-simplify]: Simplify -2 into -2
13.400 * [taylor]: Taking taylor expansion of PI in k
13.400 * [backup-simplify]: Simplify PI into PI
13.400 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.400 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.400 * [taylor]: Taking taylor expansion of (log n) in k
13.400 * [taylor]: Taking taylor expansion of n in k
13.400 * [backup-simplify]: Simplify n into n
13.400 * [backup-simplify]: Simplify (log n) into (log n)
13.401 * [backup-simplify]: Simplify (+ 1 0) into 1
13.401 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.401 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
13.402 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
13.403 * [backup-simplify]: Simplify (* 1/4 (- (log (* -2 PI)) (log n))) into (* 1/4 (- (log (* -2 PI)) (log n)))
13.403 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.404 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.405 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.406 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
13.406 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.406 * [backup-simplify]: Simplify (+ 0 0) into 0
13.407 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (+ (/ 1 k) 1))) into 0
13.408 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.409 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
13.411 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.411 * [taylor]: Taking taylor expansion of 0 in k
13.411 * [backup-simplify]: Simplify 0 into 0
13.411 * [backup-simplify]: Simplify 0 into 0
13.411 * [backup-simplify]: Simplify 0 into 0
13.412 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.413 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
13.416 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
13.417 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.417 * [backup-simplify]: Simplify (+ 0 0) into 0
13.425 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
13.427 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.428 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
13.431 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.431 * [taylor]: Taking taylor expansion of 0 in k
13.431 * [backup-simplify]: Simplify 0 into 0
13.431 * [backup-simplify]: Simplify 0 into 0
13.431 * [backup-simplify]: Simplify 0 into 0
13.431 * [backup-simplify]: Simplify 0 into 0
13.432 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.433 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.439 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
13.439 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.440 * [backup-simplify]: Simplify (+ 0 0) into 0
13.441 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
13.442 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.444 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
13.447 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.447 * [taylor]: Taking taylor expansion of 0 in k
13.447 * [backup-simplify]: Simplify 0 into 0
13.447 * [backup-simplify]: Simplify 0 into 0
13.448 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
13.448 * * * * [progress]: [ 3 / 4 ] generating series at (2 2)
13.449 * [backup-simplify]: Simplify (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) into (pow (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) 2)
13.449 * [approximate]: Taking taylor expansion of (pow (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) 2) in (n k) around 0
13.449 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) 2) in k
13.449 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in k
13.449 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in k
13.449 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in k
13.449 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in k
13.449 * [taylor]: Taking taylor expansion of 1/4 in k
13.449 * [backup-simplify]: Simplify 1/4 into 1/4
13.449 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.449 * [taylor]: Taking taylor expansion of 1 in k
13.449 * [backup-simplify]: Simplify 1 into 1
13.449 * [taylor]: Taking taylor expansion of k in k
13.449 * [backup-simplify]: Simplify 0 into 0
13.449 * [backup-simplify]: Simplify 1 into 1
13.449 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
13.449 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
13.449 * [taylor]: Taking taylor expansion of 2 in k
13.449 * [backup-simplify]: Simplify 2 into 2
13.449 * [taylor]: Taking taylor expansion of (* n PI) in k
13.449 * [taylor]: Taking taylor expansion of n in k
13.449 * [backup-simplify]: Simplify n into n
13.449 * [taylor]: Taking taylor expansion of PI in k
13.449 * [backup-simplify]: Simplify PI into PI
13.449 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.449 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
13.449 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
13.450 * [backup-simplify]: Simplify (- 0) into 0
13.450 * [backup-simplify]: Simplify (+ 1 0) into 1
13.450 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
13.450 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
13.450 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
13.450 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) 2) in n
13.450 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
13.450 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
13.451 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
13.451 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
13.451 * [taylor]: Taking taylor expansion of 1/4 in n
13.451 * [backup-simplify]: Simplify 1/4 into 1/4
13.451 * [taylor]: Taking taylor expansion of (- 1 k) in n
13.451 * [taylor]: Taking taylor expansion of 1 in n
13.451 * [backup-simplify]: Simplify 1 into 1
13.451 * [taylor]: Taking taylor expansion of k in n
13.451 * [backup-simplify]: Simplify k into k
13.451 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.451 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.451 * [taylor]: Taking taylor expansion of 2 in n
13.451 * [backup-simplify]: Simplify 2 into 2
13.451 * [taylor]: Taking taylor expansion of (* n PI) in n
13.451 * [taylor]: Taking taylor expansion of n in n
13.451 * [backup-simplify]: Simplify 0 into 0
13.451 * [backup-simplify]: Simplify 1 into 1
13.451 * [taylor]: Taking taylor expansion of PI in n
13.451 * [backup-simplify]: Simplify PI into PI
13.451 * [backup-simplify]: Simplify (* 0 PI) into 0
13.451 * [backup-simplify]: Simplify (* 2 0) into 0
13.452 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.453 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.454 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.454 * [backup-simplify]: Simplify (- k) into (- k)
13.454 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
13.454 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
13.455 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.455 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
13.456 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
13.456 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) 2) in n
13.456 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
13.456 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
13.456 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
13.456 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
13.456 * [taylor]: Taking taylor expansion of 1/4 in n
13.456 * [backup-simplify]: Simplify 1/4 into 1/4
13.456 * [taylor]: Taking taylor expansion of (- 1 k) in n
13.456 * [taylor]: Taking taylor expansion of 1 in n
13.456 * [backup-simplify]: Simplify 1 into 1
13.456 * [taylor]: Taking taylor expansion of k in n
13.456 * [backup-simplify]: Simplify k into k
13.456 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.456 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.456 * [taylor]: Taking taylor expansion of 2 in n
13.456 * [backup-simplify]: Simplify 2 into 2
13.456 * [taylor]: Taking taylor expansion of (* n PI) in n
13.456 * [taylor]: Taking taylor expansion of n in n
13.456 * [backup-simplify]: Simplify 0 into 0
13.456 * [backup-simplify]: Simplify 1 into 1
13.456 * [taylor]: Taking taylor expansion of PI in n
13.457 * [backup-simplify]: Simplify PI into PI
13.457 * [backup-simplify]: Simplify (* 0 PI) into 0
13.457 * [backup-simplify]: Simplify (* 2 0) into 0
13.458 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.459 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.459 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.460 * [backup-simplify]: Simplify (- k) into (- k)
13.460 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
13.460 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
13.460 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.461 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
13.462 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
13.463 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) into (pow (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 2)
13.463 * [taylor]: Taking taylor expansion of (pow (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 2) in k
13.463 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
13.463 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
13.463 * [taylor]: Taking taylor expansion of 1/4 in k
13.463 * [backup-simplify]: Simplify 1/4 into 1/4
13.463 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
13.463 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.463 * [taylor]: Taking taylor expansion of 1 in k
13.463 * [backup-simplify]: Simplify 1 into 1
13.463 * [taylor]: Taking taylor expansion of k in k
13.463 * [backup-simplify]: Simplify 0 into 0
13.463 * [backup-simplify]: Simplify 1 into 1
13.463 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
13.463 * [taylor]: Taking taylor expansion of (log n) in k
13.463 * [taylor]: Taking taylor expansion of n in k
13.463 * [backup-simplify]: Simplify n into n
13.463 * [backup-simplify]: Simplify (log n) into (log n)
13.464 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.464 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.464 * [taylor]: Taking taylor expansion of 2 in k
13.464 * [backup-simplify]: Simplify 2 into 2
13.464 * [taylor]: Taking taylor expansion of PI in k
13.464 * [backup-simplify]: Simplify PI into PI
13.464 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.464 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.465 * [backup-simplify]: Simplify (- 0) into 0
13.465 * [backup-simplify]: Simplify (+ 1 0) into 1
13.466 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.466 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
13.467 * [backup-simplify]: Simplify (* 1/4 (+ (log n) (log (* 2 PI)))) into (* 1/4 (+ (log n) (log (* 2 PI))))
13.467 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
13.469 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) into (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)
13.469 * [backup-simplify]: Simplify (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) into (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)
13.470 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.471 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.472 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.472 * [backup-simplify]: Simplify (- 0) into 0
13.472 * [backup-simplify]: Simplify (+ 0 0) into 0
13.472 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 k))) into 0
13.473 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.474 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
13.475 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.477 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))))) into 0
13.477 * [taylor]: Taking taylor expansion of 0 in k
13.477 * [backup-simplify]: Simplify 0 into 0
13.477 * [backup-simplify]: Simplify 0 into 0
13.478 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.479 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.480 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.481 * [backup-simplify]: Simplify (+ 0 0) into 0
13.481 * [backup-simplify]: Simplify (- 1) into -1
13.482 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.483 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
13.485 * [backup-simplify]: Simplify (+ (* 1/4 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
13.488 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
13.497 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log n))) (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log (* 2 PI))))))
13.500 * [backup-simplify]: Simplify (- (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log n))) (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log (* 2 PI)))))) into (- (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log n))) (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log (* 2 PI))))))
13.502 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.503 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.506 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.507 * [backup-simplify]: Simplify (- 0) into 0
13.507 * [backup-simplify]: Simplify (+ 0 0) into 0
13.508 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
13.510 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.512 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.514 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.517 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))))) into 0
13.517 * [taylor]: Taking taylor expansion of 0 in k
13.517 * [backup-simplify]: Simplify 0 into 0
13.517 * [backup-simplify]: Simplify 0 into 0
13.517 * [backup-simplify]: Simplify 0 into 0
13.518 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.520 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.523 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.523 * [backup-simplify]: Simplify (+ 0 0) into 0
13.524 * [backup-simplify]: Simplify (- 0) into 0
13.524 * [backup-simplify]: Simplify (+ 0 0) into 0
13.526 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.528 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.532 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
13.557 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) into (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log n) 2))) (+ (* 1/4 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI))))) (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))))
13.564 * [backup-simplify]: Simplify (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log n) 2))) (+ (* 1/4 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI))))) (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2))))) into (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log n) 2))) (+ (* 1/4 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI))))) (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))))
13.572 * [backup-simplify]: Simplify (+ (* (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log n) 2))) (+ (* 1/4 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI))))) (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log n))) (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log (* 2 PI)))))) (* k 1)) (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2))) into (- (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/4 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI)))))) (+ (* 1/8 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))) (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)))) (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) k)))))
13.573 * [backup-simplify]: Simplify (* (pow (* (* 2 PI) (/ 1 n)) (/ (/ (- 1 (/ 1 k)) 2) 2)) (pow (* (* 2 PI) (/ 1 n)) (/ (/ (- 1 (/ 1 k)) 2) 2))) into (pow (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) 2)
13.573 * [approximate]: Taking taylor expansion of (pow (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) 2) in (n k) around 0
13.573 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) 2) in k
13.573 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in k
13.573 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
13.573 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
13.573 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in k
13.573 * [taylor]: Taking taylor expansion of 1/4 in k
13.573 * [backup-simplify]: Simplify 1/4 into 1/4
13.573 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.573 * [taylor]: Taking taylor expansion of 1 in k
13.573 * [backup-simplify]: Simplify 1 into 1
13.573 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.573 * [taylor]: Taking taylor expansion of k in k
13.573 * [backup-simplify]: Simplify 0 into 0
13.573 * [backup-simplify]: Simplify 1 into 1
13.574 * [backup-simplify]: Simplify (/ 1 1) into 1
13.574 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
13.574 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
13.574 * [taylor]: Taking taylor expansion of 2 in k
13.574 * [backup-simplify]: Simplify 2 into 2
13.574 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.574 * [taylor]: Taking taylor expansion of PI in k
13.574 * [backup-simplify]: Simplify PI into PI
13.574 * [taylor]: Taking taylor expansion of n in k
13.574 * [backup-simplify]: Simplify n into n
13.574 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.574 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
13.574 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
13.574 * [backup-simplify]: Simplify (- 1) into -1
13.575 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.575 * [backup-simplify]: Simplify (* 1/4 -1) into -1/4
13.575 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
13.575 * [backup-simplify]: Simplify (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
13.575 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) 2) in n
13.575 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
13.575 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.575 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.575 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
13.575 * [taylor]: Taking taylor expansion of 1/4 in n
13.575 * [backup-simplify]: Simplify 1/4 into 1/4
13.575 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.575 * [taylor]: Taking taylor expansion of 1 in n
13.575 * [backup-simplify]: Simplify 1 into 1
13.575 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.575 * [taylor]: Taking taylor expansion of k in n
13.575 * [backup-simplify]: Simplify k into k
13.575 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.575 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.575 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.575 * [taylor]: Taking taylor expansion of 2 in n
13.575 * [backup-simplify]: Simplify 2 into 2
13.575 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.575 * [taylor]: Taking taylor expansion of PI in n
13.575 * [backup-simplify]: Simplify PI into PI
13.575 * [taylor]: Taking taylor expansion of n in n
13.575 * [backup-simplify]: Simplify 0 into 0
13.575 * [backup-simplify]: Simplify 1 into 1
13.576 * [backup-simplify]: Simplify (/ PI 1) into PI
13.576 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.577 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.577 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.577 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.577 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
13.578 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.578 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.579 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.579 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) 2) in n
13.579 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
13.579 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.579 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.579 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
13.579 * [taylor]: Taking taylor expansion of 1/4 in n
13.579 * [backup-simplify]: Simplify 1/4 into 1/4
13.579 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.579 * [taylor]: Taking taylor expansion of 1 in n
13.579 * [backup-simplify]: Simplify 1 into 1
13.579 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.579 * [taylor]: Taking taylor expansion of k in n
13.579 * [backup-simplify]: Simplify k into k
13.579 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.579 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.579 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.579 * [taylor]: Taking taylor expansion of 2 in n
13.579 * [backup-simplify]: Simplify 2 into 2
13.579 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.579 * [taylor]: Taking taylor expansion of PI in n
13.579 * [backup-simplify]: Simplify PI into PI
13.579 * [taylor]: Taking taylor expansion of n in n
13.579 * [backup-simplify]: Simplify 0 into 0
13.579 * [backup-simplify]: Simplify 1 into 1
13.580 * [backup-simplify]: Simplify (/ PI 1) into PI
13.580 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.581 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.581 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.581 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.581 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
13.582 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.582 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.583 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.584 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (pow (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 2)
13.585 * [taylor]: Taking taylor expansion of (pow (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 2) in k
13.586 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
13.586 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
13.586 * [taylor]: Taking taylor expansion of 1/4 in k
13.586 * [backup-simplify]: Simplify 1/4 into 1/4
13.586 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
13.586 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.586 * [taylor]: Taking taylor expansion of 1 in k
13.586 * [backup-simplify]: Simplify 1 into 1
13.586 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.586 * [taylor]: Taking taylor expansion of k in k
13.586 * [backup-simplify]: Simplify 0 into 0
13.586 * [backup-simplify]: Simplify 1 into 1
13.586 * [backup-simplify]: Simplify (/ 1 1) into 1
13.586 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
13.586 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.586 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.586 * [taylor]: Taking taylor expansion of 2 in k
13.586 * [backup-simplify]: Simplify 2 into 2
13.586 * [taylor]: Taking taylor expansion of PI in k
13.586 * [backup-simplify]: Simplify PI into PI
13.586 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.587 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.587 * [taylor]: Taking taylor expansion of (log n) in k
13.587 * [taylor]: Taking taylor expansion of n in k
13.587 * [backup-simplify]: Simplify n into n
13.587 * [backup-simplify]: Simplify (log n) into (log n)
13.587 * [backup-simplify]: Simplify (- 1) into -1
13.588 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.588 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.588 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
13.589 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
13.590 * [backup-simplify]: Simplify (* 1/4 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
13.591 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.592 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (pow (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 2)
13.593 * [backup-simplify]: Simplify (pow (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 2) into (pow (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 2)
13.594 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.594 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.595 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.595 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.595 * [backup-simplify]: Simplify (- 0) into 0
13.596 * [backup-simplify]: Simplify (+ 0 0) into 0
13.596 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 (/ 1 k)))) into 0
13.598 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.599 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
13.601 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.603 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
13.603 * [taylor]: Taking taylor expansion of 0 in k
13.603 * [backup-simplify]: Simplify 0 into 0
13.603 * [backup-simplify]: Simplify 0 into 0
13.606 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
13.606 * [backup-simplify]: Simplify 0 into 0
13.607 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.608 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.611 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.611 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.612 * [backup-simplify]: Simplify (- 0) into 0
13.612 * [backup-simplify]: Simplify (+ 0 0) into 0
13.613 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
13.615 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.616 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
13.618 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.621 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0
13.621 * [taylor]: Taking taylor expansion of 0 in k
13.621 * [backup-simplify]: Simplify 0 into 0
13.621 * [backup-simplify]: Simplify 0 into 0
13.621 * [backup-simplify]: Simplify 0 into 0
13.624 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0
13.624 * [backup-simplify]: Simplify 0 into 0
13.626 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.627 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.632 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
13.633 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.633 * [backup-simplify]: Simplify (- 0) into 0
13.634 * [backup-simplify]: Simplify (+ 0 0) into 0
13.635 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
13.636 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.638 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
13.641 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.645 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))) into 0
13.645 * [taylor]: Taking taylor expansion of 0 in k
13.645 * [backup-simplify]: Simplify 0 into 0
13.645 * [backup-simplify]: Simplify 0 into 0
13.646 * [backup-simplify]: Simplify (pow (exp (* 1/4 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) 2) into (pow (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 2)
13.647 * [backup-simplify]: Simplify (* (pow (* (* 2 PI) (/ 1 (- n))) (/ (/ (- 1 (/ 1 (- k))) 2) 2)) (pow (* (* 2 PI) (/ 1 (- n))) (/ (/ (- 1 (/ 1 (- k))) 2) 2))) into (pow (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) 2)
13.647 * [approximate]: Taking taylor expansion of (pow (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) 2) in (n k) around 0
13.647 * [taylor]: Taking taylor expansion of (pow (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) 2) in k
13.647 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in k
13.647 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
13.648 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
13.648 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in k
13.648 * [taylor]: Taking taylor expansion of 1/4 in k
13.648 * [backup-simplify]: Simplify 1/4 into 1/4
13.648 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
13.648 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.648 * [taylor]: Taking taylor expansion of k in k
13.648 * [backup-simplify]: Simplify 0 into 0
13.648 * [backup-simplify]: Simplify 1 into 1
13.648 * [backup-simplify]: Simplify (/ 1 1) into 1
13.648 * [taylor]: Taking taylor expansion of 1 in k
13.648 * [backup-simplify]: Simplify 1 into 1
13.648 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.648 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.648 * [taylor]: Taking taylor expansion of -2 in k
13.648 * [backup-simplify]: Simplify -2 into -2
13.648 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.648 * [taylor]: Taking taylor expansion of PI in k
13.648 * [backup-simplify]: Simplify PI into PI
13.648 * [taylor]: Taking taylor expansion of n in k
13.648 * [backup-simplify]: Simplify n into n
13.648 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.649 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.649 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.649 * [backup-simplify]: Simplify (+ 1 0) into 1
13.650 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
13.650 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
13.650 * [backup-simplify]: Simplify (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/4 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
13.650 * [taylor]: Taking taylor expansion of (pow (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) 2) in n
13.650 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
13.650 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
13.650 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
13.650 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
13.650 * [taylor]: Taking taylor expansion of 1/4 in n
13.650 * [backup-simplify]: Simplify 1/4 into 1/4
13.650 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.650 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.650 * [taylor]: Taking taylor expansion of k in n
13.650 * [backup-simplify]: Simplify k into k
13.650 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.650 * [taylor]: Taking taylor expansion of 1 in n
13.650 * [backup-simplify]: Simplify 1 into 1
13.650 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.650 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.650 * [taylor]: Taking taylor expansion of -2 in n
13.650 * [backup-simplify]: Simplify -2 into -2
13.650 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.650 * [taylor]: Taking taylor expansion of PI in n
13.650 * [backup-simplify]: Simplify PI into PI
13.650 * [taylor]: Taking taylor expansion of n in n
13.651 * [backup-simplify]: Simplify 0 into 0
13.651 * [backup-simplify]: Simplify 1 into 1
13.651 * [backup-simplify]: Simplify (/ PI 1) into PI
13.651 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.652 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.652 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.652 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
13.654 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.655 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.656 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.656 * [taylor]: Taking taylor expansion of (pow (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) 2) in n
13.656 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
13.656 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
13.656 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
13.656 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
13.656 * [taylor]: Taking taylor expansion of 1/4 in n
13.656 * [backup-simplify]: Simplify 1/4 into 1/4
13.656 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.656 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.656 * [taylor]: Taking taylor expansion of k in n
13.656 * [backup-simplify]: Simplify k into k
13.656 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.656 * [taylor]: Taking taylor expansion of 1 in n
13.656 * [backup-simplify]: Simplify 1 into 1
13.656 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.656 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.656 * [taylor]: Taking taylor expansion of -2 in n
13.656 * [backup-simplify]: Simplify -2 into -2
13.656 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.657 * [taylor]: Taking taylor expansion of PI in n
13.657 * [backup-simplify]: Simplify PI into PI
13.657 * [taylor]: Taking taylor expansion of n in n
13.657 * [backup-simplify]: Simplify 0 into 0
13.657 * [backup-simplify]: Simplify 1 into 1
13.657 * [backup-simplify]: Simplify (/ PI 1) into PI
13.658 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.659 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.659 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.659 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
13.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.661 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.662 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.665 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (pow (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 2)
13.665 * [taylor]: Taking taylor expansion of (pow (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 2) in k
13.665 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
13.665 * [taylor]: Taking taylor expansion of (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
13.665 * [taylor]: Taking taylor expansion of 1/4 in k
13.665 * [backup-simplify]: Simplify 1/4 into 1/4
13.665 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
13.665 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
13.665 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.665 * [taylor]: Taking taylor expansion of k in k
13.665 * [backup-simplify]: Simplify 0 into 0
13.665 * [backup-simplify]: Simplify 1 into 1
13.665 * [backup-simplify]: Simplify (/ 1 1) into 1
13.665 * [taylor]: Taking taylor expansion of 1 in k
13.665 * [backup-simplify]: Simplify 1 into 1
13.665 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
13.666 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
13.666 * [taylor]: Taking taylor expansion of (* -2 PI) in k
13.666 * [taylor]: Taking taylor expansion of -2 in k
13.666 * [backup-simplify]: Simplify -2 into -2
13.666 * [taylor]: Taking taylor expansion of PI in k
13.666 * [backup-simplify]: Simplify PI into PI
13.666 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.667 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.667 * [taylor]: Taking taylor expansion of (log n) in k
13.667 * [taylor]: Taking taylor expansion of n in k
13.667 * [backup-simplify]: Simplify n into n
13.667 * [backup-simplify]: Simplify (log n) into (log n)
13.668 * [backup-simplify]: Simplify (+ 1 0) into 1
13.668 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.669 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
13.670 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
13.671 * [backup-simplify]: Simplify (* 1/4 (- (log (* -2 PI)) (log n))) into (* 1/4 (- (log (* -2 PI)) (log n)))
13.672 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.674 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (pow (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 2)
13.675 * [backup-simplify]: Simplify (pow (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 2) into (pow (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 2)
13.676 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.683 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.685 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
13.685 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.685 * [backup-simplify]: Simplify (+ 0 0) into 0
13.686 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (+ (/ 1 k) 1))) into 0
13.687 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.689 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
13.691 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.693 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 0) (* 0 (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
13.693 * [taylor]: Taking taylor expansion of 0 in k
13.693 * [backup-simplify]: Simplify 0 into 0
13.693 * [backup-simplify]: Simplify 0 into 0
13.695 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 0) (* 0 (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
13.695 * [backup-simplify]: Simplify 0 into 0
13.696 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.697 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
13.701 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
13.702 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.702 * [backup-simplify]: Simplify (+ 0 0) into 0
13.703 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
13.705 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.707 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
13.709 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.712 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) into 0
13.712 * [taylor]: Taking taylor expansion of 0 in k
13.712 * [backup-simplify]: Simplify 0 into 0
13.712 * [backup-simplify]: Simplify 0 into 0
13.712 * [backup-simplify]: Simplify 0 into 0
13.715 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) into 0
13.715 * [backup-simplify]: Simplify 0 into 0
13.716 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.717 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.723 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
13.723 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.724 * [backup-simplify]: Simplify (+ 0 0) into 0
13.725 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
13.727 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.729 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
13.731 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.734 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))) into 0
13.734 * [taylor]: Taking taylor expansion of 0 in k
13.734 * [backup-simplify]: Simplify 0 into 0
13.734 * [backup-simplify]: Simplify 0 into 0
13.736 * [backup-simplify]: Simplify (pow (exp (* 1/4 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) 2) into (pow (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 2)
13.736 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1)
13.736 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
13.736 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
13.736 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.736 * [taylor]: Taking taylor expansion of 2 in n
13.736 * [backup-simplify]: Simplify 2 into 2
13.736 * [taylor]: Taking taylor expansion of (* n PI) in n
13.736 * [taylor]: Taking taylor expansion of n in n
13.736 * [backup-simplify]: Simplify 0 into 0
13.736 * [backup-simplify]: Simplify 1 into 1
13.736 * [taylor]: Taking taylor expansion of PI in n
13.737 * [backup-simplify]: Simplify PI into PI
13.737 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.737 * [taylor]: Taking taylor expansion of 2 in n
13.737 * [backup-simplify]: Simplify 2 into 2
13.737 * [taylor]: Taking taylor expansion of (* n PI) in n
13.737 * [taylor]: Taking taylor expansion of n in n
13.737 * [backup-simplify]: Simplify 0 into 0
13.737 * [backup-simplify]: Simplify 1 into 1
13.737 * [taylor]: Taking taylor expansion of PI in n
13.737 * [backup-simplify]: Simplify PI into PI
13.737 * [backup-simplify]: Simplify (* 0 PI) into 0
13.738 * [backup-simplify]: Simplify (* 2 0) into 0
13.738 * [backup-simplify]: Simplify 0 into 0
13.739 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.741 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.741 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.742 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.743 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.743 * [backup-simplify]: Simplify 0 into 0
13.744 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.745 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.745 * [backup-simplify]: Simplify 0 into 0
13.745 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.746 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.746 * [backup-simplify]: Simplify 0 into 0
13.747 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.748 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
13.748 * [backup-simplify]: Simplify 0 into 0
13.749 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.749 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
13.750 * [backup-simplify]: Simplify 0 into 0
13.751 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
13.752 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
13.752 * [backup-simplify]: Simplify 0 into 0
13.752 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
13.752 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
13.752 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
13.752 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.752 * [taylor]: Taking taylor expansion of 2 in n
13.752 * [backup-simplify]: Simplify 2 into 2
13.752 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.752 * [taylor]: Taking taylor expansion of PI in n
13.752 * [backup-simplify]: Simplify PI into PI
13.752 * [taylor]: Taking taylor expansion of n in n
13.752 * [backup-simplify]: Simplify 0 into 0
13.752 * [backup-simplify]: Simplify 1 into 1
13.753 * [backup-simplify]: Simplify (/ PI 1) into PI
13.753 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.753 * [taylor]: Taking taylor expansion of 2 in n
13.753 * [backup-simplify]: Simplify 2 into 2
13.753 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.753 * [taylor]: Taking taylor expansion of PI in n
13.753 * [backup-simplify]: Simplify PI into PI
13.753 * [taylor]: Taking taylor expansion of n in n
13.753 * [backup-simplify]: Simplify 0 into 0
13.753 * [backup-simplify]: Simplify 1 into 1
13.753 * [backup-simplify]: Simplify (/ PI 1) into PI
13.753 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.754 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.754 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.755 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.755 * [backup-simplify]: Simplify 0 into 0
13.755 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.756 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.756 * [backup-simplify]: Simplify 0 into 0
13.756 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.757 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.757 * [backup-simplify]: Simplify 0 into 0
13.758 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.758 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.758 * [backup-simplify]: Simplify 0 into 0
13.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.760 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.760 * [backup-simplify]: Simplify 0 into 0
13.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.762 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.762 * [backup-simplify]: Simplify 0 into 0
13.762 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
13.762 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n))
13.762 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
13.762 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.762 * [taylor]: Taking taylor expansion of -2 in n
13.762 * [backup-simplify]: Simplify -2 into -2
13.762 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.762 * [taylor]: Taking taylor expansion of PI in n
13.762 * [backup-simplify]: Simplify PI into PI
13.762 * [taylor]: Taking taylor expansion of n in n
13.762 * [backup-simplify]: Simplify 0 into 0
13.762 * [backup-simplify]: Simplify 1 into 1
13.763 * [backup-simplify]: Simplify (/ PI 1) into PI
13.763 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.763 * [taylor]: Taking taylor expansion of -2 in n
13.764 * [backup-simplify]: Simplify -2 into -2
13.764 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.764 * [taylor]: Taking taylor expansion of PI in n
13.764 * [backup-simplify]: Simplify PI into PI
13.764 * [taylor]: Taking taylor expansion of n in n
13.764 * [backup-simplify]: Simplify 0 into 0
13.764 * [backup-simplify]: Simplify 1 into 1
13.764 * [backup-simplify]: Simplify (/ PI 1) into PI
13.764 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.765 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.765 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.766 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.766 * [backup-simplify]: Simplify 0 into 0
13.766 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.767 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
13.767 * [backup-simplify]: Simplify 0 into 0
13.767 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.768 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.768 * [backup-simplify]: Simplify 0 into 0
13.769 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.769 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.770 * [backup-simplify]: Simplify 0 into 0
13.770 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.771 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.771 * [backup-simplify]: Simplify 0 into 0
13.772 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.773 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.774 * [backup-simplify]: Simplify 0 into 0
13.774 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
13.774 * * * [progress]: simplifying candidates
13.774 * * * * [progress]: [ 1 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (exp (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2))))))>
13.774 * * * * [progress]: [ 2 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (exp (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2))))))>
13.774 * * * * [progress]: [ 3 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (exp (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))))>
13.775 * * * * [progress]: [ 4 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (exp (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))))>
13.775 * * * * [progress]: [ 5 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (* 1 (/ (/ (- 1 k) 2) 2))))))>
13.775 * * * * [progress]: [ 6 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (* 1 (/ (/ (- 1 k) 2) 2))))))>
13.775 * * * * [progress]: [ 7 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (* 1 (/ (/ (- 1 k) 2) 2))))))>
13.775 * * * * [progress]: [ 8 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (/ (pow (* (* 2 PI) n) (/ (/ 1 2) 2)) (pow (* (* 2 PI) n) (/ (/ k 2) 2))))))>
13.775 * * * * [progress]: [ 9 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (/ (- 1 k) 2) 2)) (cbrt (/ (/ (- 1 k) 2) 2)))) (cbrt (/ (/ (- 1 k) 2) 2))))))>
13.775 * * * * [progress]: [ 10 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (sqrt (/ (/ (- 1 k) 2) 2))) (sqrt (/ (/ (- 1 k) 2) 2))))))>
13.775 * * * * [progress]: [ 11 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (/ (- 1 k) 2)) (cbrt 2))))))>
13.775 * * * * [progress]: [ 12 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (sqrt 2))) (/ (cbrt (/ (- 1 k) 2)) (sqrt 2))))))>
13.775 * * * * [progress]: [ 13 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) 1)) (/ (cbrt (/ (- 1 k) 2)) 2)))))>
13.775 * * * * [progress]: [ 14 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (sqrt (/ (- 1 k) 2)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (/ (- 1 k) 2)) (cbrt 2))))))>
13.775 * * * * [progress]: [ 15 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2))) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2))))))>
13.775 * * * * [progress]: [ 16 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (sqrt (/ (- 1 k) 2)) 1)) (/ (sqrt (/ (- 1 k) 2)) 2)))))>
13.775 * * * * [progress]: [ 17 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2))))))>
13.776 * * * * [progress]: [ 18 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (sqrt 2))))))>
13.776 * * * * [progress]: [ 19 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (cbrt (- 1 k)) (cbrt 2)) 2)))))>
13.776 * * * * [progress]: [ 20 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt 2))))))>
13.776 * * * * [progress]: [ 21 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (sqrt 2))) (/ (/ (cbrt (- 1 k)) (sqrt 2)) (sqrt 2))))))>
13.776 * * * * [progress]: [ 22 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) 1)) (/ (/ (cbrt (- 1 k)) (sqrt 2)) 2)))))>
13.776 * * * * [progress]: [ 23 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) 2) (cbrt 2))))))>
13.776 * * * * [progress]: [ 24 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (sqrt 2))) (/ (/ (cbrt (- 1 k)) 2) (sqrt 2))))))>
13.777 * * * * [progress]: [ 25 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1)) (/ (/ (cbrt (- 1 k)) 2) 2)))))>
13.777 * * * * [progress]: [ 26 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2))))))>
13.777 * * * * [progress]: [ 27 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (sqrt 2))))))>
13.777 * * * * [progress]: [ 28 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) 2)))))>
13.777 * * * * [progress]: [ 29 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (cbrt 2))))))>
13.777 * * * * [progress]: [ 30 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2))) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2))))))>
13.777 * * * * [progress]: [ 31 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 1)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 2)))))>
13.777 * * * * [progress]: [ 32 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) 2) (cbrt 2))))))>
13.777 * * * * [progress]: [ 33 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) 1) (sqrt 2))) (/ (/ (sqrt (- 1 k)) 2) (sqrt 2))))))>
13.777 * * * * [progress]: [ 34 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) 1) 1)) (/ (/ (sqrt (- 1 k)) 2) 2)))))>
13.777 * * * * [progress]: [ 35 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2))))))>
13.778 * * * * [progress]: [ 36 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 k) (cbrt 2)) (sqrt 2))))))>
13.778 * * * * [progress]: [ 37 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 k) (cbrt 2)) 2)))))>
13.778 * * * * [progress]: [ 38 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (sqrt 2)) (cbrt 2))))))>
13.778 * * * * [progress]: [ 39 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 (sqrt 2)) (sqrt 2))) (/ (/ (- 1 k) (sqrt 2)) (sqrt 2))))))>
13.778 * * * * [progress]: [ 40 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 (sqrt 2)) 1)) (/ (/ (- 1 k) (sqrt 2)) 2)))))>
13.778 * * * * [progress]: [ 41 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2))))))>
13.778 * * * * [progress]: [ 42 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 1) (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2))))))>
13.778 * * * * [progress]: [ 43 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 1) 1)) (/ (/ (- 1 k) 2) 2)))))>
13.778 * * * * [progress]: [ 44 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) (cbrt 2))))))>
13.778 * * * * [progress]: [ 45 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) (sqrt 2))))))>
13.778 * * * * [progress]: [ 46 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) 2)))))>
13.778 * * * * [progress]: [ 47 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) (cbrt 2))))))>
13.779 * * * * [progress]: [ 48 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2))))))>
13.779 * * * * [progress]: [ 49 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) 1)) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) 2)))))>
13.779 * * * * [progress]: [ 50 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) 2) (cbrt 2))))))>
13.779 * * * * [progress]: [ 51 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) 2) (sqrt 2))))))>
13.779 * * * * [progress]: [ 52 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) 1) 1)) (/ (/ (- (sqrt 1) (sqrt k)) 2) 2)))))>
13.779 * * * * [progress]: [ 53 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) (cbrt 2)) (cbrt 2))))))>
13.779 * * * * [progress]: [ 54 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 (sqrt k)) (cbrt 2)) (sqrt 2))))))>
13.779 * * * * [progress]: [ 55 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 (sqrt k)) (cbrt 2)) 2)))))>
13.779 * * * * [progress]: [ 56 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) (sqrt 2)) (cbrt 2))))))>
13.779 * * * * [progress]: [ 57 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (sqrt 2))) (/ (/ (- 1 (sqrt k)) (sqrt 2)) (sqrt 2))))))>
13.779 * * * * [progress]: [ 58 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) 1)) (/ (/ (- 1 (sqrt k)) (sqrt 2)) 2)))))>
13.779 * * * * [progress]: [ 59 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) 2) (cbrt 2))))))>
13.780 * * * * [progress]: [ 60 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) 1) (sqrt 2))) (/ (/ (- 1 (sqrt k)) 2) (sqrt 2))))))>
13.780 * * * * [progress]: [ 61 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) 1) 1)) (/ (/ (- 1 (sqrt k)) 2) 2)))))>
13.780 * * * * [progress]: [ 62 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2))))))>
13.780 * * * * [progress]: [ 63 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 k) (cbrt 2)) (sqrt 2))))))>
13.780 * * * * [progress]: [ 64 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 k) (cbrt 2)) 2)))))>
13.780 * * * * [progress]: [ 65 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (sqrt 2)) (cbrt 2))))))>
13.780 * * * * [progress]: [ 66 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 (sqrt 2)) (sqrt 2))) (/ (/ (- 1 k) (sqrt 2)) (sqrt 2))))))>
13.780 * * * * [progress]: [ 67 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 (sqrt 2)) 1)) (/ (/ (- 1 k) (sqrt 2)) 2)))))>
13.780 * * * * [progress]: [ 68 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2))))))>
13.780 * * * * [progress]: [ 69 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 1) (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2))))))>
13.780 * * * * [progress]: [ 70 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ 1 1) 1)) (/ (/ (- 1 k) 2) 2)))))>
13.780 * * * * [progress]: [ 71 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2))))))>
13.780 * * * * [progress]: [ 72 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2))))))>
13.781 * * * * [progress]: [ 73 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (/ (- 1 k) 2) 2)))))>
13.781 * * * * [progress]: [ 74 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) (* (cbrt 2) (cbrt 2)))) (/ (/ 1 2) (cbrt 2))))))>
13.781 * * * * [progress]: [ 75 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) (sqrt 2))) (/ (/ 1 2) (sqrt 2))))))>
13.781 * * * * [progress]: [ 76 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) 1)) (/ (/ 1 2) 2)))))>
13.781 * * * * [progress]: [ 77 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) 1) (/ (/ (- 1 k) 2) 2)))))>
13.781 * * * * [progress]: [ 78 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 2)))))>
13.781 * * * * [progress]: [ 79 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (/ (- 1 k) 2) 2))))))>
13.781 * * * * [progress]: [ 80 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) 1))))>
13.781 * * * * [progress]: [ 81 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (exp (log (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.781 * * * * [progress]: [ 82 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (log (exp (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.781 * * * * [progress]: [ 83 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (* (* (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.781 * * * * [progress]: [ 84 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (cbrt (* (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.781 * * * * [progress]: [ 85 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (* (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.782 * * * * [progress]: [ 86 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (* 1 (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))))>
13.782 * * * * [progress]: [ 87 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (* (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2))))))>
13.782 * * * * [progress]: [ 88 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (posit16->real (real->posit16 (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.782 * * * * [progress]: [ 89 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (exp (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.782 * * * * [progress]: [ 90 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (exp (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.782 * * * * [progress]: [ 91 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (exp (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.782 * * * * [progress]: [ 92 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (exp (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.782 * * * * [progress]: [ 93 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (* 1 (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.782 * * * * [progress]: [ 94 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (* 1 (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.782 * * * * [progress]: [ 95 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (* 1 (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.782 * * * * [progress]: [ 96 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (/ (pow (* (* 2 PI) n) (/ (/ 1 2) 2)) (pow (* (* 2 PI) n) (/ (/ k 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.782 * * * * [progress]: [ 97 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (* (cbrt (/ (/ (- 1 k) 2) 2)) (cbrt (/ (/ (- 1 k) 2) 2)))) (cbrt (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.782 * * * * [progress]: [ 98 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (sqrt (/ (/ (- 1 k) 2) 2))) (sqrt (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.782 * * * * [progress]: [ 99 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (/ (- 1 k) 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.783 * * * * [progress]: [ 100 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (sqrt 2))) (/ (cbrt (/ (- 1 k) 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.783 * * * * [progress]: [ 101 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) 1)) (/ (cbrt (/ (- 1 k) 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.783 * * * * [progress]: [ 102 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (sqrt (/ (- 1 k) 2)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (/ (- 1 k) 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.783 * * * * [progress]: [ 103 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2))) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.783 * * * * [progress]: [ 104 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (sqrt (/ (- 1 k) 2)) 1)) (/ (sqrt (/ (- 1 k) 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.783 * * * * [progress]: [ 105 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.783 * * * * [progress]: [ 106 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.783 * * * * [progress]: [ 107 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (cbrt (- 1 k)) (cbrt 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.783 * * * * [progress]: [ 108 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.783 * * * * [progress]: [ 109 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (sqrt 2))) (/ (/ (cbrt (- 1 k)) (sqrt 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.783 * * * * [progress]: [ 110 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) 1)) (/ (/ (cbrt (- 1 k)) (sqrt 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.783 * * * * [progress]: [ 111 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) 2) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.784 * * * * [progress]: [ 112 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (sqrt 2))) (/ (/ (cbrt (- 1 k)) 2) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.784 * * * * [progress]: [ 113 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1)) (/ (/ (cbrt (- 1 k)) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.784 * * * * [progress]: [ 114 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.784 * * * * [progress]: [ 115 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.784 * * * * [progress]: [ 116 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.784 * * * * [progress]: [ 117 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.784 * * * * [progress]: [ 118 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2))) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.784 * * * * [progress]: [ 119 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 1)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.784 * * * * [progress]: [ 120 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) 2) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.784 * * * * [progress]: [ 121 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) 1) (sqrt 2))) (/ (/ (sqrt (- 1 k)) 2) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.784 * * * * [progress]: [ 122 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (sqrt (- 1 k)) 1) 1)) (/ (/ (sqrt (- 1 k)) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.784 * * * * [progress]: [ 123 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.785 * * * * [progress]: [ 124 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 k) (cbrt 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.785 * * * * [progress]: [ 125 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 k) (cbrt 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.785 * * * * [progress]: [ 126 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (sqrt 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.785 * * * * [progress]: [ 127 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 (sqrt 2)) (sqrt 2))) (/ (/ (- 1 k) (sqrt 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.785 * * * * [progress]: [ 128 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 (sqrt 2)) 1)) (/ (/ (- 1 k) (sqrt 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.785 * * * * [progress]: [ 129 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.785 * * * * [progress]: [ 130 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 1) (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.785 * * * * [progress]: [ 131 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 1) 1)) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.785 * * * * [progress]: [ 132 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.785 * * * * [progress]: [ 133 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.785 * * * * [progress]: [ 134 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.785 * * * * [progress]: [ 135 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 136 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 137 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) 1)) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 138 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) 2) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 139 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) 2) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 140 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ (sqrt 1) (sqrt k)) 1) 1)) (/ (/ (- (sqrt 1) (sqrt k)) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 141 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) (cbrt 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 142 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 (sqrt k)) (cbrt 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 143 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 (sqrt k)) (cbrt 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 144 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) (sqrt 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 145 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (sqrt 2))) (/ (/ (- 1 (sqrt k)) (sqrt 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 146 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) 1)) (/ (/ (- 1 (sqrt k)) (sqrt 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 147 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) 2) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.786 * * * * [progress]: [ 148 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) 1) (sqrt 2))) (/ (/ (- 1 (sqrt k)) 2) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.787 * * * * [progress]: [ 149 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (+ 1 (sqrt k)) 1) 1)) (/ (/ (- 1 (sqrt k)) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.787 * * * * [progress]: [ 150 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.787 * * * * [progress]: [ 151 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 k) (cbrt 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.787 * * * * [progress]: [ 152 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 k) (cbrt 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.787 * * * * [progress]: [ 153 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (sqrt 2)) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.787 * * * * [progress]: [ 154 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 (sqrt 2)) (sqrt 2))) (/ (/ (- 1 k) (sqrt 2)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.787 * * * * [progress]: [ 155 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 (sqrt 2)) 1)) (/ (/ (- 1 k) (sqrt 2)) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.787 * * * * [progress]: [ 156 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.787 * * * * [progress]: [ 157 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 1) (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.787 * * * * [progress]: [ 158 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ 1 1) 1)) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.787 * * * * [progress]: [ 159 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.787 * * * * [progress]: [ 160 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 161 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 162 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (- 1 k) (* (cbrt 2) (cbrt 2)))) (/ (/ 1 2) (cbrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 163 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (- 1 k) (sqrt 2))) (/ (/ 1 2) (sqrt 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 164 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (- 1 k) 1)) (/ (/ 1 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 165 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) 1) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 166 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 167 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 168 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) 1) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 169 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (exp (log (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 170 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (log (exp (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 171 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (* (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 172 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (cbrt (* (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 173 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 174 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* 1 (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.788 * * * * [progress]: [ 175 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.789 * * * * [progress]: [ 176 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (posit16->real (real->posit16 (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.789 * * * * [progress]: [ 177 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (+ (/ (/ (- 1 k) 2) 2) (/ (/ (- 1 k) 2) 2)))))>
13.789 * * * * [progress]: [ 178 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) n) (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))>
13.789 * * * * [progress]: [ 179 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) 2)))>
13.789 * * * * [progress]: [ 180 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) 1)))>
13.789 * * * * [progress]: [ 181 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2)) (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2))))))>
13.789 * * * * [progress]: [ 182 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2)) (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2))))))>
13.789 * * * * [progress]: [ 183 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2)) (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))))>
13.789 * * * * [progress]: [ 184 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2)) (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))))>
13.789 * * * * [progress]: [ 185 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2)) (log (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.789 * * * * [progress]: [ 186 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2)) (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2))))))>
13.789 * * * * [progress]: [ 187 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2)) (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2))))))>
13.789 * * * * [progress]: [ 188 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2)) (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))))>
13.789 * * * * [progress]: [ 189 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2)) (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))))>
13.789 * * * * [progress]: [ 190 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2)) (log (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.790 * * * * [progress]: [ 191 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)) (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2))))))>
13.790 * * * * [progress]: [ 192 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)) (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2))))))>
13.790 * * * * [progress]: [ 193 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)) (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))))>
13.790 * * * * [progress]: [ 194 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)) (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))))>
13.790 * * * * [progress]: [ 195 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)) (log (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.790 * * * * [progress]: [ 196 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)) (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2))))))>
13.790 * * * * [progress]: [ 197 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)) (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2))))))>
13.790 * * * * [progress]: [ 198 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)) (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))))>
13.790 * * * * [progress]: [ 199 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)) (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))))>
13.790 * * * * [progress]: [ 200 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)) (log (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.790 * * * * [progress]: [ 201 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (log (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2))))))>
13.790 * * * * [progress]: [ 202 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (log (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2))))))>
13.790 * * * * [progress]: [ 203 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (log (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))))>
13.790 * * * * [progress]: [ 204 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (log (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2))))))>
13.791 * * * * [progress]: [ 205 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (+ (log (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (log (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.791 * * * * [progress]: [ 206 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (log (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.791 * * * * [progress]: [ 207 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (log (exp (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.791 * * * * [progress]: [ 208 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (cbrt (* (* (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.791 * * * * [progress]: [ 209 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (cbrt (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (cbrt (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))) (cbrt (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.791 * * * * [progress]: [ 210 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (cbrt (* (* (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.791 * * * * [progress]: [ 211 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (sqrt (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (sqrt (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.791 * * * * [progress]: [ 212 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ (* (pow (* (* 2 PI) n) (/ (/ 1 2) 2)) (pow (* (* 2 PI) n) (/ (/ 1 2) 2))) (* (pow (* (* 2 PI) n) (/ (/ k 2) 2)) (pow (* (* 2 PI) n) (/ (/ k 2) 2))))))>
13.791 * * * * [progress]: [ 213 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* 1 (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))))>
13.791 * * * * [progress]: [ 214 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (* (pow n (/ (/ (- 1 k) 2) 2)) (pow n (/ (/ (- 1 k) 2) 2))))))>
13.791 * * * * [progress]: [ 215 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (* (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (* (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))) (* (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.791 * * * * [progress]: [ 216 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (* (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.792 * * * * [progress]: [ 217 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* 1 1) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))))>
13.792 * * * * [progress]: [ 218 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2))) (* (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2))))))>
13.792 * * * * [progress]: [ 219 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (* (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.792 * * * * [progress]: [ 220 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2))) (* (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2))))))>
13.792 * * * * [progress]: [ 221 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2)) (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (* (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2)) (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.792 * * * * [progress]: [ 222 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2))) (* (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2))))))>
13.792 * * * * [progress]: [ 223 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 2 (/ (/ (- 1 k) 2) 2)))))>
13.792 * * * * [progress]: [ 224 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow n (/ (/ (- 1 k) 2) 2)))))>
13.792 * * * * [progress]: [ 225 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (* (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))) (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))))>
13.792 * * * * [progress]: [ 226 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))))>
13.792 * * * * [progress]: [ 227 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) 1) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.792 * * * * [progress]: [ 228 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2)))))>
13.792 * * * * [progress]: [ 229 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (* (pow n (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))))>
13.793 * * * * [progress]: [ 230 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))) (* (cbrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))))>
13.793 * * * * [progress]: [ 231 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (sqrt (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))))>
13.793 * * * * [progress]: [ 232 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* 1 (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))))>
13.793 * * * * [progress]: [ 233 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2)) (* (pow (* (* 2 PI) n) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))))>
13.793 * * * * [progress]: [ 234 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ 1 2) 2))) (pow (* (* 2 PI) n) (/ (/ k 2) 2)))))>
13.793 * * * * [progress]: [ 235 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ (* (pow (* (* 2 PI) n) (/ (/ 1 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ k 2) 2)))))>
13.793 * * * * [progress]: [ 236 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (posit16->real (real->posit16 (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))))>
13.793 * * * * [progress]: [ 237 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.793 * * * * [progress]: [ 238 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) 1) (/ (/ (- 1 k) 2) 2)))))>
13.793 * * * * [progress]: [ 239 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) 1) (/ (/ (- 1 k) 2) 2)))))>
13.793 * * * * [progress]: [ 240 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (pow (* (* 2 PI) n) 1) (/ (/ (- 1 k) 2) 2)))))>
13.793 * * * * [progress]: [ 241 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (exp (+ (+ (log 2) (log PI)) (log n))) (/ (/ (- 1 k) 2) 2)))))>
13.793 * * * * [progress]: [ 242 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (exp (+ (log (* 2 PI)) (log n))) (/ (/ (- 1 k) 2) 2)))))>
13.793 * * * * [progress]: [ 243 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (exp (log (* (* 2 PI) n))) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 244 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (log (exp (* (* 2 PI) n))) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 245 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (cbrt (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 246 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (cbrt (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 247 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) (cbrt (* (* 2 PI) n))) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 248 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 249 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n))) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 250 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* 1 (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 251 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 252 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 253 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* (* 2 PI) 1) n) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 254 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* 2 (* PI n)) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 255 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (posit16->real (real->posit16 (* (* 2 PI) n))) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 256 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
13.794 * * * * [progress]: [ 257 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))))))>
13.795 * * * * [progress]: [ 258 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))))>
13.795 * * * * [progress]: [ 259 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))>
13.795 * * * * [progress]: [ 260 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.795 * * * * [progress]: [ 261 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.795 * * * * [progress]: [ 262 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
13.795 * * * * [progress]: [ 263 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (- (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/4 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI)))))) (+ (* 1/8 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))) (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)))) (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) k)))))))>
13.795 * * * * [progress]: [ 264 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 2)))>
13.795 * * * * [progress]: [ 265 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 2)))>
13.795 * * * * [progress]: [ 266 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))))>
13.795 * * * * [progress]: [ 267 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))))>
13.795 * * * * [progress]: [ 268 / 268 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))))>
13.800 * [simplify]: Simplifying (* (+ (+ (log 2) (log PI)) (log n)) (/ (/ (- 1 k) 2) 2)), (* (+ (log (* 2 PI)) (log n)) (/ (/ (- 1 k) 2) 2)), (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)), (* (log (* (* 2 PI) n)) (/ (/ (- 1 k) 2) 2)), (* 1 (/ (/ (- 1 k) 2) 2)), (* 1 (/ (/ (- 1 k) 2) 2)), (* 1 (/ (/ (- 1 k) 2) 2)), (pow (* (* 2 PI) n) (/ (/ 1 2) 2)), (pow (* (* 2 PI) n) (/ (/ k 2) 2)), (pow (* (* 2 PI) n) (* (cbrt (/ (/ (- 1 k) 2) 2)) (cbrt (/ (/ (- 1 k) 2) 2)))), (pow (* (* 2 PI) n) (sqrt (/ (/ (- 1 k) 2) 2))), (pow (* (* 2 PI) n) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (* (cbrt 2) (cbrt 2)))), (pow (* (* 2 PI) n) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (sqrt 2))), (pow (* (* 2 PI) n) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) 1)), (pow (* (* 2 PI) n) (/ (sqrt (/ (- 1 k) 2)) (* (cbrt 2) (cbrt 2)))), (pow (* (* 2 PI) n) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2))), (pow (* (* 2 PI) n) (/ (sqrt (/ (- 1 k) 2)) 1)), (pow (* (* 2 PI) n) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 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13.810 * * [simplify]: iteration 1: (332 enodes)
13.979 * * [simplify]: iteration 2: (1553 enodes)
14.686 * * [simplify]: Extracting #0: cost 94 inf + 0
14.688 * * [simplify]: Extracting #1: cost 691 inf + 1
14.695 * * [simplify]: Extracting #2: cost 1308 inf + 4133
14.718 * * [simplify]: Extracting #3: cost 1367 inf + 55417
14.775 * * [simplify]: Extracting #4: cost 1035 inf + 161282
14.850 * * [simplify]: Extracting #5: cost 429 inf + 383006
14.948 * * [simplify]: Extracting #6: cost 59 inf + 564903
15.086 * * [simplify]: Extracting #7: cost 2 inf + 592465
15.217 * * [simplify]: Extracting #8: cost 0 inf + 593535
15.359 * [simplify]: Simplified to (/ (* (log (* (* PI n) 2)) (- 1 k)) 4), (/ (* (log (* (* PI n) 2)) (- 1 k)) 4), (/ (* (log (* (* PI n) 2)) (- 1 k)) 4), (/ (* (log (* (* PI n) 2)) (- 1 k)) 4), (/ (- 1 k) 4), (/ (- 1 k) 4), (/ (- 1 k) 4), (exp (* (log (* (* PI n) 2)) 1/4)), (pow (* (* PI n) 2) (/ k 4)), (pow (* (* PI n) 2) (* (cbrt (/ (- 1 k) 4)) (cbrt (/ (- 1 k) 4)))), (pow (* (* PI n) 2) (sqrt (/ (- 1 k) 4))), (pow (* (* PI n) 2) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)))), (pow (* (* PI n) 2) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))), (pow (* (* PI n) 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))), (pow (* (* PI n) 2) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))), (pow (* (* PI n) 2) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))), (pow (* (* PI n) 2) (sqrt (- 1/2 (/ k 2)))), (pow (* (* PI n) 2) (* (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2)) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2)))), (pow (* (* PI n) 2) (/ (* (/ (cbrt (- 1 k)) 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1 k)) 4), (/ (* (log (* (* PI n) 2)) (- 1 k)) 4), (/ (* (log (* (* PI n) 2)) (- 1 k)) 4), (/ (* (log (* (* PI n) 2)) (- 1 k)) 4), (/ (- 1 k) 4), (/ (- 1 k) 4), (/ (- 1 k) 4), (exp (* (log (* (* PI n) 2)) 1/4)), (pow (* (* PI n) 2) (/ k 4)), (pow (* (* PI n) 2) (* (cbrt (/ (- 1 k) 4)) (cbrt (/ (- 1 k) 4)))), (pow (* (* PI n) 2) (sqrt (/ (- 1 k) 4))), (pow (* (* PI n) 2) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)))), (pow (* (* PI n) 2) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))), (pow (* (* PI n) 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))), (pow (* (* PI n) 2) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))), (pow (* (* PI n) 2) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))), (pow (* (* PI n) 2) (sqrt (- 1/2 (/ k 2)))), (pow (* (* PI n) 2) (* (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2)) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2)))), (pow (* (* PI n) 2) (/ (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt 2))), (pow (* (* PI n) 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1 k) 4))))) (* (* (pow (* (* PI n) 2) (/ (- 1 k) 4)) (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 4)))) (* (pow (* (* PI n) 2) (/ (- 1 k) 4)) (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 4)))))), (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))), (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))), (* (* (* (pow (* (* PI n) 2) (/ (- 1 k) 4)) (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 4)))) (* (pow (* (* PI n) 2) (/ (- 1 k) 4)) (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 4))))) (* (* (pow (* (* PI n) 2) (/ (- 1 k) 4)) (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 4)))) (* (pow (* (* PI n) 2) (/ (- 1 k) 4)) (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 4)))))), (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))), (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))), (sqrt (* (* PI n) 2)), (pow (* (* PI n) 2) (/ (* 2 k) 4)), (pow (* 2 PI) (+ (/ (- 1 k) 4) (/ (- 1 k) 4))), (* (pow n (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))), (* (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 4))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 4)))) (* (cbrt 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2) (/ (- 1 k) 4)))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 4)))), (* (pow (* (* PI n) 2) (/ (- 1 k) 4)) (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 4)))), (pow (* (* PI n) 2) (/ (- 1 k) 4)), (* (pow (* (* PI n) 2) (- 1/8 (/ k 8))) (pow (* (* PI n) 2) (/ (- 1 k) 4))), (* (pow (* (* PI n) 2) (/ (- 1 k) 4)) (pow n (/ (- 1 k) 4))), (* (pow (* (* PI n) 2) (/ (- 1 k) 4)) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 4)))), (* (pow (* (* PI n) 2) (/ (- 1 k) 4)) (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 4)))), (pow (* (* PI n) 2) (- 1/2 (/ k 2))), (* (pow (* (* PI n) 2) (- 1/8 (/ k 8))) (* (pow (* (* PI n) 2) (- 1/8 (/ k 8))) (pow (* (* PI n) 2) (- 1/8 (/ k 8))))), (* (exp (* (log (* (* PI n) 2)) 1/4)) (pow (* (* PI n) 2) (/ (- 1 k) 4))), (* (exp (* (log (* (* PI n) 2)) 1/4)) (pow (* (* PI n) 2) (/ (- 1 k) 4))), (real->posit16 (pow (* (* PI n) 2) (- 1/2 (/ k 2)))), (* (* PI n) 2), (* (* PI n) 2), (log (* (* PI n) 2)), (log (* (* PI n) 2)), (log (* (* PI n) 2)), (* (exp (* PI n)) (exp (* PI n))), (* (* (* 8 (* PI PI)) PI) (* n (* n n))), (* (* (* (* PI n) 2) (* (* PI n) 2)) (* (* PI n) 2)), (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))), (cbrt (* (* PI n) 2)), (* (* (* (* PI n) 2) (* (* PI n) 2)) (* (* PI n) 2)), (sqrt (* (* PI n) 2)), (sqrt (* (* PI n) 2)), (* (* PI (* (cbrt n) (cbrt n))) 2), (* (* 2 PI) (sqrt n)), (* 2 PI), (* PI n), (real->posit16 (* (* PI n) 2)), (+ (+ (exp (* (log (* (* PI n) 2)) 1/4)) (* (* (* k k) (+ (* (exp (* (log (* (* PI n) 2)) 1/4)) (* (log n) (log n))) (* (log (* 2 PI)) (* (log (* 2 PI)) (exp (* (log (* (* PI n) 2)) 1/4)))))) 1/32)) (- (* (log (* 2 PI)) (* (* (* (log n) (exp (* (log (* (* PI n) 2)) 1/4))) (* k k)) 1/16)) (* 1/4 (* k (+ (* (log n) (exp (* (log (* (* PI n) 2)) 1/4))) (* (log (* 2 PI)) (exp (* (log (* (* PI n) 2)) 1/4)))))))), (exp (* 1/4 (* (- 1 k) (log (* (* PI n) 2))))), (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (* (- 1 k) 1/4))), (+ (+ (exp (* (log (* (* PI n) 2)) 1/4)) (* (* (* k k) (+ (* (exp (* (log (* (* PI n) 2)) 1/4)) (* (log n) (log n))) (* (log (* 2 PI)) (* (log (* 2 PI)) (exp (* (log (* (* PI n) 2)) 1/4)))))) 1/32)) (- (* (log (* 2 PI)) (* (* (* (log n) (exp (* (log (* (* PI n) 2)) 1/4))) (* k k)) 1/16)) (* 1/4 (* k (+ (* (log n) (exp (* (log (* (* PI n) 2)) 1/4))) (* (log (* 2 PI)) (exp (* (log (* (* PI n) 2)) 1/4)))))))), (exp (* 1/4 (* (- 1 k) (log (* (* PI n) 2))))), (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (* (- 1 k) 1/4))), (+ (+ (* (* k k) (* (* (* (sqrt (* (* PI n) 2)) (log n)) (log (* 2 PI))) 1/4)) (* (* (* (sqrt (* (* PI n) 2)) 1/8) (* (log n) (log n))) (* k k))) (- (+ (sqrt (* (* PI n) 2)) (* (* 1/8 (* (sqrt (* (* PI n) 2)) (* k k))) (* (log (* 2 PI)) (log (* 2 PI))))) (* 1/2 (* k (+ (* (sqrt (* (* PI n) 2)) (log n)) (* (sqrt (* (* PI n) 2)) (log (* 2 PI)))))))), (exp (+ (* 1/4 (* (- 1 k) (log (* (* PI n) 2)))) (* 1/4 (* (- 1 k) (log (* (* PI n) 2)))))), (exp (+ (* (- (log (* -2 PI)) (log (/ -1 n))) (* (- 1 k) 1/4)) (* (- (log (* -2 PI)) (log (/ -1 n))) (* (- 1 k) 1/4)))), (* (* PI n) 2), (* (* PI n) 2), (* (* PI n) 2)
15.399 * * * [progress]: adding candidates to table
19.044 * [progress]: [Phase 3 of 3] Extracting.
19.044 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))> #<alt (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))> #<alt (λ (k n) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))>)
19.046 * * * [regime-changes]: Trying 4 branch expressions: (n (* (* 2 PI) n) k (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
19.046 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))> #<alt (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))> #<alt (λ (k n) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))>)
19.119 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (* (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))> #<alt (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))> #<alt (λ (k n) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))>)
19.184 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))> #<alt (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))> #<alt (λ (k n) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))>)
19.270 * * * * [regimes]: Trying to branch on (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) from (#<alt (λ (k n) (* (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* PI 2)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))> #<alt (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))> #<alt (λ (k n) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))>)
19.363 * * * [regime]: Found split indices: #<option (#s(si 2 255))>
19.363 * [simplify]: Simplifying (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))
19.364 * * [simplify]: iteration 1: (15 enodes)
19.366 * * [simplify]: iteration 2: (20 enodes)
19.369 * * [simplify]: Extracting #0: cost 1 inf + 0
19.369 * * [simplify]: Extracting #1: cost 3 inf + 0
19.369 * * [simplify]: Extracting #2: cost 6 inf + 0
19.370 * * [simplify]: Extracting #3: cost 8 inf + 1
19.370 * * [simplify]: Extracting #4: cost 9 inf + 125
19.370 * * [simplify]: Extracting #5: cost 9 inf + 127
19.370 * * [simplify]: Extracting #6: cost 7 inf + 170
19.370 * * [simplify]: Extracting #7: cost 3 inf + 501
19.371 * * [simplify]: Extracting #8: cost 1 inf + 1371
19.371 * * [simplify]: Extracting #9: cost 0 inf + 1946
19.371 * [simplify]: Simplified to (* (/ 1 (sqrt k)) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
27.417 * [regime-testing]: Baseline error score: 0.4796720639002131
27.422 * [regime-testing]: Oracle error score: 0.04564910675396203
27.426 * [regime-testing]: End program error score: 0.4796720639002131