0.001 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.226 * * * [progress]: [2/2] Setting up program.
0.232 * [progress]: [Phase 2 of 3] Improving.
0.232 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.233 * [simplify]: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.233 * * [simplify]: iteration 1: (13 enodes)
0.242 * * [simplify]: iteration 2: (57 enodes)
0.266 * * [simplify]: iteration 3: (102 enodes)
0.306 * * [simplify]: iteration 4: (189 enodes)
0.381 * * [simplify]: iteration 5: (376 enodes)
0.607 * * [simplify]: iteration 6: (949 enodes)
1.459 * * [simplify]: Extracting #0: cost 1 inf + 0
1.459 * * [simplify]: Extracting #1: cost 59 inf + 0
1.461 * * [simplify]: Extracting #2: cost 220 inf + 1
1.464 * * [simplify]: Extracting #3: cost 281 inf + 210
1.467 * * [simplify]: Extracting #4: cost 293 inf + 1056
1.475 * * [simplify]: Extracting #5: cost 217 inf + 10983
1.492 * * [simplify]: Extracting #6: cost 139 inf + 50407
1.531 * * [simplify]: Extracting #7: cost 26 inf + 145304
1.603 * * [simplify]: Extracting #8: cost 0 inf + 167058
1.677 * * [simplify]: Extracting #9: cost 0 inf + 165504
1.754 * * [simplify]: Extracting #10: cost 0 inf + 164849
1.793 * [simplify]: Simplified to (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
1.800 * * [progress]: iteration 1 / 4
1.800 * * * [progress]: picking best candidate
1.809 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))>
1.809 * * * [progress]: localizing error
1.843 * * * [progress]: generating rewritten candidates
1.843 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
1.862 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
1.888 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
1.947 * * * [progress]: generating series expansions
1.947 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
1.948 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
1.948 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
1.948 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
1.948 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
1.948 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
1.948 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
1.948 * [taylor]: Taking taylor expansion of 1/2 in k
1.948 * [backup-simplify]: Simplify 1/2 into 1/2
1.948 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
1.948 * [taylor]: Taking taylor expansion of 1/2 in k
1.948 * [backup-simplify]: Simplify 1/2 into 1/2
1.948 * [taylor]: Taking taylor expansion of k in k
1.948 * [backup-simplify]: Simplify 0 into 0
1.948 * [backup-simplify]: Simplify 1 into 1
1.948 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
1.948 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
1.948 * [taylor]: Taking taylor expansion of 2 in k
1.949 * [backup-simplify]: Simplify 2 into 2
1.949 * [taylor]: Taking taylor expansion of (* n PI) in k
1.949 * [taylor]: Taking taylor expansion of n in k
1.949 * [backup-simplify]: Simplify n into n
1.949 * [taylor]: Taking taylor expansion of PI in k
1.949 * [backup-simplify]: Simplify PI into PI
1.949 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.949 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
1.949 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
1.950 * [backup-simplify]: Simplify (* 1/2 0) into 0
1.950 * [backup-simplify]: Simplify (- 0) into 0
1.951 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.951 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
1.951 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
1.951 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
1.951 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
1.951 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
1.951 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
1.951 * [taylor]: Taking taylor expansion of 1/2 in n
1.951 * [backup-simplify]: Simplify 1/2 into 1/2
1.951 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
1.951 * [taylor]: Taking taylor expansion of 1/2 in n
1.951 * [backup-simplify]: Simplify 1/2 into 1/2
1.951 * [taylor]: Taking taylor expansion of k in n
1.951 * [backup-simplify]: Simplify k into k
1.951 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.951 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.951 * [taylor]: Taking taylor expansion of 2 in n
1.951 * [backup-simplify]: Simplify 2 into 2
1.951 * [taylor]: Taking taylor expansion of (* n PI) in n
1.951 * [taylor]: Taking taylor expansion of n in n
1.951 * [backup-simplify]: Simplify 0 into 0
1.951 * [backup-simplify]: Simplify 1 into 1
1.951 * [taylor]: Taking taylor expansion of PI in n
1.951 * [backup-simplify]: Simplify PI into PI
1.952 * [backup-simplify]: Simplify (* 0 PI) into 0
1.952 * [backup-simplify]: Simplify (* 2 0) into 0
1.954 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.955 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.956 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.956 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
1.957 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
1.957 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
1.958 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.959 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
1.960 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
1.960 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
1.960 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
1.960 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
1.960 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
1.960 * [taylor]: Taking taylor expansion of 1/2 in n
1.960 * [backup-simplify]: Simplify 1/2 into 1/2
1.960 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
1.960 * [taylor]: Taking taylor expansion of 1/2 in n
1.960 * [backup-simplify]: Simplify 1/2 into 1/2
1.961 * [taylor]: Taking taylor expansion of k in n
1.961 * [backup-simplify]: Simplify k into k
1.961 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.961 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.961 * [taylor]: Taking taylor expansion of 2 in n
1.961 * [backup-simplify]: Simplify 2 into 2
1.961 * [taylor]: Taking taylor expansion of (* n PI) in n
1.961 * [taylor]: Taking taylor expansion of n in n
1.961 * [backup-simplify]: Simplify 0 into 0
1.961 * [backup-simplify]: Simplify 1 into 1
1.961 * [taylor]: Taking taylor expansion of PI in n
1.961 * [backup-simplify]: Simplify PI into PI
1.961 * [backup-simplify]: Simplify (* 0 PI) into 0
1.962 * [backup-simplify]: Simplify (* 2 0) into 0
1.963 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.965 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.966 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.966 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
1.966 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
1.966 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
1.967 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.968 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
1.969 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
1.970 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
1.970 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
1.970 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
1.970 * [taylor]: Taking taylor expansion of 1/2 in k
1.970 * [backup-simplify]: Simplify 1/2 into 1/2
1.970 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
1.970 * [taylor]: Taking taylor expansion of 1/2 in k
1.970 * [backup-simplify]: Simplify 1/2 into 1/2
1.970 * [taylor]: Taking taylor expansion of k in k
1.970 * [backup-simplify]: Simplify 0 into 0
1.970 * [backup-simplify]: Simplify 1 into 1
1.970 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
1.970 * [taylor]: Taking taylor expansion of (log n) in k
1.970 * [taylor]: Taking taylor expansion of n in k
1.970 * [backup-simplify]: Simplify n into n
1.970 * [backup-simplify]: Simplify (log n) into (log n)
1.970 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.970 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.970 * [taylor]: Taking taylor expansion of 2 in k
1.970 * [backup-simplify]: Simplify 2 into 2
1.970 * [taylor]: Taking taylor expansion of PI in k
1.970 * [backup-simplify]: Simplify PI into PI
1.971 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.972 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.972 * [backup-simplify]: Simplify (* 1/2 0) into 0
1.972 * [backup-simplify]: Simplify (- 0) into 0
1.973 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.974 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.975 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
1.976 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.977 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.978 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.979 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.981 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.981 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
1.982 * [backup-simplify]: Simplify (- 0) into 0
1.982 * [backup-simplify]: Simplify (+ 0 0) into 0
1.983 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.984 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
1.986 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.986 * [taylor]: Taking taylor expansion of 0 in k
1.986 * [backup-simplify]: Simplify 0 into 0
1.986 * [backup-simplify]: Simplify 0 into 0
1.987 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
1.988 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.990 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.990 * [backup-simplify]: Simplify (+ 0 0) into 0
1.991 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
1.991 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.991 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.993 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
1.996 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.999 * [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)))))))
2.000 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.001 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.004 * [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
2.005 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
2.006 * [backup-simplify]: Simplify (- 0) into 0
2.006 * [backup-simplify]: Simplify (+ 0 0) into 0
2.007 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.009 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.012 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.012 * [taylor]: Taking taylor expansion of 0 in k
2.012 * [backup-simplify]: Simplify 0 into 0
2.012 * [backup-simplify]: Simplify 0 into 0
2.012 * [backup-simplify]: Simplify 0 into 0
2.014 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
2.015 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.018 * [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
2.019 * [backup-simplify]: Simplify (+ 0 0) into 0
2.020 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
2.020 * [backup-simplify]: Simplify (- 0) into 0
2.020 * [backup-simplify]: Simplify (+ 0 0) into 0
2.022 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.026 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
2.031 * [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)))))
2.040 * [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)))))
2.040 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
2.040 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
2.040 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
2.040 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
2.040 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
2.040 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.040 * [taylor]: Taking taylor expansion of 1/2 in k
2.040 * [backup-simplify]: Simplify 1/2 into 1/2
2.040 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.040 * [taylor]: Taking taylor expansion of 1/2 in k
2.040 * [backup-simplify]: Simplify 1/2 into 1/2
2.040 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.040 * [taylor]: Taking taylor expansion of k in k
2.040 * [backup-simplify]: Simplify 0 into 0
2.040 * [backup-simplify]: Simplify 1 into 1
2.041 * [backup-simplify]: Simplify (/ 1 1) into 1
2.041 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
2.041 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
2.041 * [taylor]: Taking taylor expansion of 2 in k
2.041 * [backup-simplify]: Simplify 2 into 2
2.041 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.041 * [taylor]: Taking taylor expansion of PI in k
2.041 * [backup-simplify]: Simplify PI into PI
2.041 * [taylor]: Taking taylor expansion of n in k
2.041 * [backup-simplify]: Simplify n into n
2.041 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.041 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
2.041 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
2.041 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.042 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.042 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.042 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
2.042 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
2.042 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.042 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.042 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.042 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.042 * [taylor]: Taking taylor expansion of 1/2 in n
2.042 * [backup-simplify]: Simplify 1/2 into 1/2
2.042 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.042 * [taylor]: Taking taylor expansion of 1/2 in n
2.042 * [backup-simplify]: Simplify 1/2 into 1/2
2.042 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.042 * [taylor]: Taking taylor expansion of k in n
2.042 * [backup-simplify]: Simplify k into k
2.042 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.042 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.042 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.042 * [taylor]: Taking taylor expansion of 2 in n
2.042 * [backup-simplify]: Simplify 2 into 2
2.042 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.042 * [taylor]: Taking taylor expansion of PI in n
2.042 * [backup-simplify]: Simplify PI into PI
2.042 * [taylor]: Taking taylor expansion of n in n
2.042 * [backup-simplify]: Simplify 0 into 0
2.042 * [backup-simplify]: Simplify 1 into 1
2.043 * [backup-simplify]: Simplify (/ PI 1) into PI
2.043 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.044 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.044 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.044 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.044 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.045 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.045 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
2.046 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.046 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.046 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.046 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.046 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.046 * [taylor]: Taking taylor expansion of 1/2 in n
2.046 * [backup-simplify]: Simplify 1/2 into 1/2
2.046 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.046 * [taylor]: Taking taylor expansion of 1/2 in n
2.046 * [backup-simplify]: Simplify 1/2 into 1/2
2.046 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.046 * [taylor]: Taking taylor expansion of k in n
2.046 * [backup-simplify]: Simplify k into k
2.046 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.046 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.046 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.046 * [taylor]: Taking taylor expansion of 2 in n
2.046 * [backup-simplify]: Simplify 2 into 2
2.046 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.046 * [taylor]: Taking taylor expansion of PI in n
2.046 * [backup-simplify]: Simplify PI into PI
2.046 * [taylor]: Taking taylor expansion of n in n
2.046 * [backup-simplify]: Simplify 0 into 0
2.046 * [backup-simplify]: Simplify 1 into 1
2.047 * [backup-simplify]: Simplify (/ PI 1) into PI
2.047 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.048 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.048 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.048 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.048 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.049 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.049 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
2.050 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.050 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
2.050 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
2.050 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.050 * [taylor]: Taking taylor expansion of 1/2 in k
2.050 * [backup-simplify]: Simplify 1/2 into 1/2
2.050 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.050 * [taylor]: Taking taylor expansion of 1/2 in k
2.050 * [backup-simplify]: Simplify 1/2 into 1/2
2.050 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.050 * [taylor]: Taking taylor expansion of k in k
2.050 * [backup-simplify]: Simplify 0 into 0
2.050 * [backup-simplify]: Simplify 1 into 1
2.051 * [backup-simplify]: Simplify (/ 1 1) into 1
2.051 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
2.051 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.051 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.051 * [taylor]: Taking taylor expansion of 2 in k
2.051 * [backup-simplify]: Simplify 2 into 2
2.051 * [taylor]: Taking taylor expansion of PI in k
2.051 * [backup-simplify]: Simplify PI into PI
2.051 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.052 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.052 * [taylor]: Taking taylor expansion of (log n) in k
2.052 * [taylor]: Taking taylor expansion of n in k
2.052 * [backup-simplify]: Simplify n into n
2.052 * [backup-simplify]: Simplify (log n) into (log n)
2.052 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.052 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.053 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.053 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.053 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
2.054 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
2.059 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.060 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.061 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.061 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.062 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.063 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.063 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.063 * [backup-simplify]: Simplify (- 0) into 0
2.063 * [backup-simplify]: Simplify (+ 0 0) into 0
2.064 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.065 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
2.066 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.066 * [taylor]: Taking taylor expansion of 0 in k
2.066 * [backup-simplify]: Simplify 0 into 0
2.066 * [backup-simplify]: Simplify 0 into 0
2.066 * [backup-simplify]: Simplify 0 into 0
2.067 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.068 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.069 * [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
2.069 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.070 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.071 * [backup-simplify]: Simplify (- 0) into 0
2.071 * [backup-simplify]: Simplify (+ 0 0) into 0
2.072 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.074 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
2.076 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.076 * [taylor]: Taking taylor expansion of 0 in k
2.076 * [backup-simplify]: Simplify 0 into 0
2.076 * [backup-simplify]: Simplify 0 into 0
2.076 * [backup-simplify]: Simplify 0 into 0
2.076 * [backup-simplify]: Simplify 0 into 0
2.078 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.079 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.084 * [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
2.085 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.086 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
2.086 * [backup-simplify]: Simplify (- 0) into 0
2.087 * [backup-simplify]: Simplify (+ 0 0) into 0
2.088 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.090 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
2.093 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.093 * [taylor]: Taking taylor expansion of 0 in k
2.093 * [backup-simplify]: Simplify 0 into 0
2.093 * [backup-simplify]: Simplify 0 into 0
2.094 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
2.095 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
2.095 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
2.095 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
2.095 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
2.095 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
2.095 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.095 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.095 * [taylor]: Taking taylor expansion of 1/2 in k
2.095 * [backup-simplify]: Simplify 1/2 into 1/2
2.095 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.095 * [taylor]: Taking taylor expansion of k in k
2.095 * [backup-simplify]: Simplify 0 into 0
2.095 * [backup-simplify]: Simplify 1 into 1
2.095 * [backup-simplify]: Simplify (/ 1 1) into 1
2.095 * [taylor]: Taking taylor expansion of 1/2 in k
2.095 * [backup-simplify]: Simplify 1/2 into 1/2
2.096 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
2.096 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
2.096 * [taylor]: Taking taylor expansion of -2 in k
2.096 * [backup-simplify]: Simplify -2 into -2
2.096 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.096 * [taylor]: Taking taylor expansion of PI in k
2.096 * [backup-simplify]: Simplify PI into PI
2.096 * [taylor]: Taking taylor expansion of n in k
2.096 * [backup-simplify]: Simplify n into n
2.096 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.096 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
2.096 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
2.096 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.097 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.097 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
2.097 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
2.097 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.097 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.097 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.097 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.097 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.097 * [taylor]: Taking taylor expansion of 1/2 in n
2.097 * [backup-simplify]: Simplify 1/2 into 1/2
2.097 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.097 * [taylor]: Taking taylor expansion of k in n
2.098 * [backup-simplify]: Simplify k into k
2.098 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.098 * [taylor]: Taking taylor expansion of 1/2 in n
2.098 * [backup-simplify]: Simplify 1/2 into 1/2
2.098 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.098 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.098 * [taylor]: Taking taylor expansion of -2 in n
2.098 * [backup-simplify]: Simplify -2 into -2
2.098 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.098 * [taylor]: Taking taylor expansion of PI in n
2.098 * [backup-simplify]: Simplify PI into PI
2.098 * [taylor]: Taking taylor expansion of n in n
2.098 * [backup-simplify]: Simplify 0 into 0
2.098 * [backup-simplify]: Simplify 1 into 1
2.098 * [backup-simplify]: Simplify (/ PI 1) into PI
2.099 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.100 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.100 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.100 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.102 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.103 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
2.104 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.104 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.104 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.104 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.104 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.104 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.104 * [taylor]: Taking taylor expansion of 1/2 in n
2.104 * [backup-simplify]: Simplify 1/2 into 1/2
2.104 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.104 * [taylor]: Taking taylor expansion of k in n
2.104 * [backup-simplify]: Simplify k into k
2.104 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.104 * [taylor]: Taking taylor expansion of 1/2 in n
2.104 * [backup-simplify]: Simplify 1/2 into 1/2
2.104 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.104 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.104 * [taylor]: Taking taylor expansion of -2 in n
2.104 * [backup-simplify]: Simplify -2 into -2
2.104 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.104 * [taylor]: Taking taylor expansion of PI in n
2.104 * [backup-simplify]: Simplify PI into PI
2.104 * [taylor]: Taking taylor expansion of n in n
2.104 * [backup-simplify]: Simplify 0 into 0
2.104 * [backup-simplify]: Simplify 1 into 1
2.105 * [backup-simplify]: Simplify (/ PI 1) into PI
2.105 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.106 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.106 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.107 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.108 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.109 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
2.110 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.110 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
2.110 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
2.110 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.110 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.110 * [taylor]: Taking taylor expansion of 1/2 in k
2.110 * [backup-simplify]: Simplify 1/2 into 1/2
2.110 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.111 * [taylor]: Taking taylor expansion of k in k
2.111 * [backup-simplify]: Simplify 0 into 0
2.111 * [backup-simplify]: Simplify 1 into 1
2.111 * [backup-simplify]: Simplify (/ 1 1) into 1
2.111 * [taylor]: Taking taylor expansion of 1/2 in k
2.111 * [backup-simplify]: Simplify 1/2 into 1/2
2.111 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
2.111 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
2.111 * [taylor]: Taking taylor expansion of (* -2 PI) in k
2.111 * [taylor]: Taking taylor expansion of -2 in k
2.111 * [backup-simplify]: Simplify -2 into -2
2.111 * [taylor]: Taking taylor expansion of PI in k
2.111 * [backup-simplify]: Simplify PI into PI
2.111 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.112 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.112 * [taylor]: Taking taylor expansion of (log n) in k
2.112 * [taylor]: Taking taylor expansion of n in k
2.112 * [backup-simplify]: Simplify n into n
2.112 * [backup-simplify]: Simplify (log n) into (log n)
2.112 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.113 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.113 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.113 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
2.114 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
2.115 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.116 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.116 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.117 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.118 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
2.118 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.118 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.119 * [backup-simplify]: Simplify (+ 0 0) into 0
2.119 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.120 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
2.122 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.122 * [taylor]: Taking taylor expansion of 0 in k
2.122 * [backup-simplify]: Simplify 0 into 0
2.122 * [backup-simplify]: Simplify 0 into 0
2.122 * [backup-simplify]: Simplify 0 into 0
2.122 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.123 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.125 * [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
2.125 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.125 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.126 * [backup-simplify]: Simplify (+ 0 0) into 0
2.127 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.128 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
2.129 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.129 * [taylor]: Taking taylor expansion of 0 in k
2.129 * [backup-simplify]: Simplify 0 into 0
2.129 * [backup-simplify]: Simplify 0 into 0
2.129 * [backup-simplify]: Simplify 0 into 0
2.129 * [backup-simplify]: Simplify 0 into 0
2.130 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.131 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.134 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
2.134 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.135 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
2.135 * [backup-simplify]: Simplify (+ 0 0) into 0
2.136 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.137 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
2.139 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.139 * [taylor]: Taking taylor expansion of 0 in k
2.139 * [backup-simplify]: Simplify 0 into 0
2.139 * [backup-simplify]: Simplify 0 into 0
2.139 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
2.139 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
2.140 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
2.140 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
2.140 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.140 * [taylor]: Taking taylor expansion of 2 in n
2.140 * [backup-simplify]: Simplify 2 into 2
2.140 * [taylor]: Taking taylor expansion of (* n PI) in n
2.140 * [taylor]: Taking taylor expansion of n in n
2.140 * [backup-simplify]: Simplify 0 into 0
2.140 * [backup-simplify]: Simplify 1 into 1
2.140 * [taylor]: Taking taylor expansion of PI in n
2.140 * [backup-simplify]: Simplify PI into PI
2.140 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.140 * [taylor]: Taking taylor expansion of 2 in n
2.140 * [backup-simplify]: Simplify 2 into 2
2.140 * [taylor]: Taking taylor expansion of (* n PI) in n
2.140 * [taylor]: Taking taylor expansion of n in n
2.140 * [backup-simplify]: Simplify 0 into 0
2.140 * [backup-simplify]: Simplify 1 into 1
2.140 * [taylor]: Taking taylor expansion of PI in n
2.140 * [backup-simplify]: Simplify PI into PI
2.140 * [backup-simplify]: Simplify (* 0 PI) into 0
2.141 * [backup-simplify]: Simplify (* 2 0) into 0
2.141 * [backup-simplify]: Simplify 0 into 0
2.142 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.143 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.143 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.143 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.144 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.144 * [backup-simplify]: Simplify 0 into 0
2.145 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.145 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.145 * [backup-simplify]: Simplify 0 into 0
2.146 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.147 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.147 * [backup-simplify]: Simplify 0 into 0
2.148 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.149 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
2.149 * [backup-simplify]: Simplify 0 into 0
2.150 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.151 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
2.151 * [backup-simplify]: Simplify 0 into 0
2.152 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
2.153 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
2.153 * [backup-simplify]: Simplify 0 into 0
2.154 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
2.154 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
2.154 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
2.154 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.154 * [taylor]: Taking taylor expansion of 2 in n
2.154 * [backup-simplify]: Simplify 2 into 2
2.154 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.154 * [taylor]: Taking taylor expansion of PI in n
2.154 * [backup-simplify]: Simplify PI into PI
2.154 * [taylor]: Taking taylor expansion of n in n
2.154 * [backup-simplify]: Simplify 0 into 0
2.154 * [backup-simplify]: Simplify 1 into 1
2.155 * [backup-simplify]: Simplify (/ PI 1) into PI
2.155 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.155 * [taylor]: Taking taylor expansion of 2 in n
2.155 * [backup-simplify]: Simplify 2 into 2
2.155 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.155 * [taylor]: Taking taylor expansion of PI in n
2.155 * [backup-simplify]: Simplify PI into PI
2.155 * [taylor]: Taking taylor expansion of n in n
2.155 * [backup-simplify]: Simplify 0 into 0
2.155 * [backup-simplify]: Simplify 1 into 1
2.155 * [backup-simplify]: Simplify (/ PI 1) into PI
2.156 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.156 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.156 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.157 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.157 * [backup-simplify]: Simplify 0 into 0
2.158 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.158 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.158 * [backup-simplify]: Simplify 0 into 0
2.159 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.160 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.160 * [backup-simplify]: Simplify 0 into 0
2.160 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.161 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.161 * [backup-simplify]: Simplify 0 into 0
2.162 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.162 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.163 * [backup-simplify]: Simplify 0 into 0
2.163 * [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
2.166 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.166 * [backup-simplify]: Simplify 0 into 0
2.166 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
2.167 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
2.167 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
2.167 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.167 * [taylor]: Taking taylor expansion of -2 in n
2.167 * [backup-simplify]: Simplify -2 into -2
2.167 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.167 * [taylor]: Taking taylor expansion of PI in n
2.167 * [backup-simplify]: Simplify PI into PI
2.167 * [taylor]: Taking taylor expansion of n in n
2.167 * [backup-simplify]: Simplify 0 into 0
2.167 * [backup-simplify]: Simplify 1 into 1
2.167 * [backup-simplify]: Simplify (/ PI 1) into PI
2.167 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.167 * [taylor]: Taking taylor expansion of -2 in n
2.167 * [backup-simplify]: Simplify -2 into -2
2.167 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.167 * [taylor]: Taking taylor expansion of PI in n
2.167 * [backup-simplify]: Simplify PI into PI
2.167 * [taylor]: Taking taylor expansion of n in n
2.167 * [backup-simplify]: Simplify 0 into 0
2.167 * [backup-simplify]: Simplify 1 into 1
2.168 * [backup-simplify]: Simplify (/ PI 1) into PI
2.168 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.168 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.169 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.169 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.169 * [backup-simplify]: Simplify 0 into 0
2.170 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.171 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.171 * [backup-simplify]: Simplify 0 into 0
2.172 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.173 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.173 * [backup-simplify]: Simplify 0 into 0
2.173 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.174 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.174 * [backup-simplify]: Simplify 0 into 0
2.175 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.176 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.176 * [backup-simplify]: Simplify 0 into 0
2.176 * [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
2.177 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.177 * [backup-simplify]: Simplify 0 into 0
2.178 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
2.178 * * * * [progress]: [ 3 / 3 ] generating series at (2)
2.178 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))))
2.178 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
2.178 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
2.178 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.178 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.178 * [taylor]: Taking taylor expansion of k in k
2.178 * [backup-simplify]: Simplify 0 into 0
2.178 * [backup-simplify]: Simplify 1 into 1
2.179 * [backup-simplify]: Simplify (/ 1 1) into 1
2.179 * [backup-simplify]: Simplify (sqrt 0) into 0
2.180 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.180 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
2.180 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
2.180 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
2.180 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.180 * [taylor]: Taking taylor expansion of 1/2 in k
2.180 * [backup-simplify]: Simplify 1/2 into 1/2
2.180 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.180 * [taylor]: Taking taylor expansion of 1/2 in k
2.180 * [backup-simplify]: Simplify 1/2 into 1/2
2.180 * [taylor]: Taking taylor expansion of k in k
2.180 * [backup-simplify]: Simplify 0 into 0
2.180 * [backup-simplify]: Simplify 1 into 1
2.180 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
2.180 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
2.180 * [taylor]: Taking taylor expansion of 2 in k
2.180 * [backup-simplify]: Simplify 2 into 2
2.180 * [taylor]: Taking taylor expansion of (* n PI) in k
2.180 * [taylor]: Taking taylor expansion of n in k
2.180 * [backup-simplify]: Simplify n into n
2.180 * [taylor]: Taking taylor expansion of PI in k
2.180 * [backup-simplify]: Simplify PI into PI
2.180 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.180 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
2.180 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
2.181 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.181 * [backup-simplify]: Simplify (- 0) into 0
2.181 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.181 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
2.181 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
2.181 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
2.181 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.181 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.181 * [taylor]: Taking taylor expansion of k in n
2.181 * [backup-simplify]: Simplify k into k
2.181 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.181 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.181 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.182 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.182 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.182 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.182 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.182 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.182 * [taylor]: Taking taylor expansion of 1/2 in n
2.182 * [backup-simplify]: Simplify 1/2 into 1/2
2.182 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.182 * [taylor]: Taking taylor expansion of 1/2 in n
2.182 * [backup-simplify]: Simplify 1/2 into 1/2
2.182 * [taylor]: Taking taylor expansion of k in n
2.182 * [backup-simplify]: Simplify k into k
2.182 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.182 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.182 * [taylor]: Taking taylor expansion of 2 in n
2.182 * [backup-simplify]: Simplify 2 into 2
2.182 * [taylor]: Taking taylor expansion of (* n PI) in n
2.182 * [taylor]: Taking taylor expansion of n in n
2.182 * [backup-simplify]: Simplify 0 into 0
2.182 * [backup-simplify]: Simplify 1 into 1
2.182 * [taylor]: Taking taylor expansion of PI in n
2.182 * [backup-simplify]: Simplify PI into PI
2.182 * [backup-simplify]: Simplify (* 0 PI) into 0
2.182 * [backup-simplify]: Simplify (* 2 0) into 0
2.183 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.184 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.185 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.185 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.185 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.185 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.186 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.187 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.187 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
2.187 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
2.187 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.187 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.187 * [taylor]: Taking taylor expansion of k in n
2.187 * [backup-simplify]: Simplify k into k
2.187 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.188 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.188 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.188 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.188 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.188 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.188 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.188 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.188 * [taylor]: Taking taylor expansion of 1/2 in n
2.188 * [backup-simplify]: Simplify 1/2 into 1/2
2.188 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.188 * [taylor]: Taking taylor expansion of 1/2 in n
2.188 * [backup-simplify]: Simplify 1/2 into 1/2
2.188 * [taylor]: Taking taylor expansion of k in n
2.188 * [backup-simplify]: Simplify k into k
2.188 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.188 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.188 * [taylor]: Taking taylor expansion of 2 in n
2.188 * [backup-simplify]: Simplify 2 into 2
2.188 * [taylor]: Taking taylor expansion of (* n PI) in n
2.188 * [taylor]: Taking taylor expansion of n in n
2.188 * [backup-simplify]: Simplify 0 into 0
2.188 * [backup-simplify]: Simplify 1 into 1
2.188 * [taylor]: Taking taylor expansion of PI in n
2.188 * [backup-simplify]: Simplify PI into PI
2.188 * [backup-simplify]: Simplify (* 0 PI) into 0
2.189 * [backup-simplify]: Simplify (* 2 0) into 0
2.189 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.190 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.191 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.191 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.191 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.191 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.192 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.193 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.194 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
2.195 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k)))
2.195 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
2.195 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
2.195 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
2.195 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.195 * [taylor]: Taking taylor expansion of 1/2 in k
2.195 * [backup-simplify]: Simplify 1/2 into 1/2
2.195 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.195 * [taylor]: Taking taylor expansion of 1/2 in k
2.195 * [backup-simplify]: Simplify 1/2 into 1/2
2.195 * [taylor]: Taking taylor expansion of k in k
2.195 * [backup-simplify]: Simplify 0 into 0
2.195 * [backup-simplify]: Simplify 1 into 1
2.195 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
2.195 * [taylor]: Taking taylor expansion of (log n) in k
2.195 * [taylor]: Taking taylor expansion of n in k
2.195 * [backup-simplify]: Simplify n into n
2.195 * [backup-simplify]: Simplify (log n) into (log n)
2.195 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.195 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.195 * [taylor]: Taking taylor expansion of 2 in k
2.195 * [backup-simplify]: Simplify 2 into 2
2.195 * [taylor]: Taking taylor expansion of PI in k
2.195 * [backup-simplify]: Simplify PI into PI
2.196 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.197 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.197 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.198 * [backup-simplify]: Simplify (- 0) into 0
2.198 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.199 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.200 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
2.201 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
2.202 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.202 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.202 * [taylor]: Taking taylor expansion of k in k
2.202 * [backup-simplify]: Simplify 0 into 0
2.202 * [backup-simplify]: Simplify 1 into 1
2.202 * [backup-simplify]: Simplify (/ 1 1) into 1
2.202 * [backup-simplify]: Simplify (sqrt 0) into 0
2.204 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.205 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
2.205 * [backup-simplify]: Simplify 0 into 0
2.206 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.207 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.209 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.210 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
2.210 * [backup-simplify]: Simplify (- 0) into 0
2.210 * [backup-simplify]: Simplify (+ 0 0) into 0
2.212 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.213 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
2.215 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.216 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
2.216 * [taylor]: Taking taylor expansion of 0 in k
2.216 * [backup-simplify]: Simplify 0 into 0
2.217 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
2.218 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.220 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.220 * [backup-simplify]: Simplify (+ 0 0) into 0
2.221 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
2.221 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.222 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.223 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
2.225 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.227 * [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)))))))
2.228 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.229 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.229 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.231 * [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
2.232 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
2.232 * [backup-simplify]: Simplify (- 0) into 0
2.232 * [backup-simplify]: Simplify (+ 0 0) into 0
2.233 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.234 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.236 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.236 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.236 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
2.237 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
2.237 * [taylor]: Taking taylor expansion of 0 in k
2.237 * [backup-simplify]: Simplify 0 into 0
2.237 * [backup-simplify]: Simplify 0 into 0
2.238 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
2.240 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.241 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
2.242 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.243 * [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
2.244 * [backup-simplify]: Simplify (+ 0 0) into 0
2.244 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
2.245 * [backup-simplify]: Simplify (- 0) into 0
2.245 * [backup-simplify]: Simplify (+ 0 0) into 0
2.246 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.248 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
2.254 * [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))))))))
2.257 * [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))))))))
2.258 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.259 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.262 * [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
2.263 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
2.263 * [backup-simplify]: Simplify (- 0) into 0
2.264 * [backup-simplify]: Simplify (+ 0 0) into 0
2.264 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.267 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.269 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.269 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.270 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
2.271 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0
2.271 * [taylor]: Taking taylor expansion of 0 in k
2.271 * [backup-simplify]: Simplify 0 into 0
2.271 * [backup-simplify]: Simplify 0 into 0
2.271 * [backup-simplify]: Simplify 0 into 0
2.272 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.274 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.276 * [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
2.277 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.280 * [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
2.280 * [backup-simplify]: Simplify (+ 0 0) into 0
2.281 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
2.281 * [backup-simplify]: Simplify (- 0) into 0
2.281 * [backup-simplify]: Simplify (+ 0 0) into 0
2.283 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.287 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.297 * [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))))))))))))))
2.304 * [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))))))))))))))
2.318 * [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))))))))))))))))))))))
2.319 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
2.319 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
2.319 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
2.319 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.319 * [taylor]: Taking taylor expansion of k in k
2.319 * [backup-simplify]: Simplify 0 into 0
2.319 * [backup-simplify]: Simplify 1 into 1
2.320 * [backup-simplify]: Simplify (sqrt 0) into 0
2.321 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.321 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
2.321 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
2.321 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
2.321 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.321 * [taylor]: Taking taylor expansion of 1/2 in k
2.321 * [backup-simplify]: Simplify 1/2 into 1/2
2.321 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.321 * [taylor]: Taking taylor expansion of 1/2 in k
2.321 * [backup-simplify]: Simplify 1/2 into 1/2
2.321 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.321 * [taylor]: Taking taylor expansion of k in k
2.322 * [backup-simplify]: Simplify 0 into 0
2.322 * [backup-simplify]: Simplify 1 into 1
2.322 * [backup-simplify]: Simplify (/ 1 1) into 1
2.322 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
2.322 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
2.322 * [taylor]: Taking taylor expansion of 2 in k
2.322 * [backup-simplify]: Simplify 2 into 2
2.322 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.322 * [taylor]: Taking taylor expansion of PI in k
2.322 * [backup-simplify]: Simplify PI into PI
2.322 * [taylor]: Taking taylor expansion of n in k
2.322 * [backup-simplify]: Simplify n into n
2.322 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.322 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
2.322 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
2.323 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.323 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.324 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.324 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
2.324 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
2.324 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
2.324 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.324 * [taylor]: Taking taylor expansion of k in n
2.324 * [backup-simplify]: Simplify k into k
2.324 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.324 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.324 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.324 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.324 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.324 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.325 * [taylor]: Taking taylor expansion of 1/2 in n
2.325 * [backup-simplify]: Simplify 1/2 into 1/2
2.325 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.325 * [taylor]: Taking taylor expansion of 1/2 in n
2.325 * [backup-simplify]: Simplify 1/2 into 1/2
2.325 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.325 * [taylor]: Taking taylor expansion of k in n
2.325 * [backup-simplify]: Simplify k into k
2.325 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.325 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.325 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.325 * [taylor]: Taking taylor expansion of 2 in n
2.325 * [backup-simplify]: Simplify 2 into 2
2.325 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.325 * [taylor]: Taking taylor expansion of PI in n
2.325 * [backup-simplify]: Simplify PI into PI
2.325 * [taylor]: Taking taylor expansion of n in n
2.325 * [backup-simplify]: Simplify 0 into 0
2.325 * [backup-simplify]: Simplify 1 into 1
2.326 * [backup-simplify]: Simplify (/ PI 1) into PI
2.326 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.327 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.327 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.327 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.327 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.329 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.330 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
2.331 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.332 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
2.332 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.332 * [taylor]: Taking taylor expansion of k in n
2.332 * [backup-simplify]: Simplify k into k
2.332 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.332 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.332 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.332 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.332 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.332 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.332 * [taylor]: Taking taylor expansion of 1/2 in n
2.332 * [backup-simplify]: Simplify 1/2 into 1/2
2.332 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.332 * [taylor]: Taking taylor expansion of 1/2 in n
2.332 * [backup-simplify]: Simplify 1/2 into 1/2
2.332 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.332 * [taylor]: Taking taylor expansion of k in n
2.332 * [backup-simplify]: Simplify k into k
2.332 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.332 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.332 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.332 * [taylor]: Taking taylor expansion of 2 in n
2.332 * [backup-simplify]: Simplify 2 into 2
2.332 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.332 * [taylor]: Taking taylor expansion of PI in n
2.333 * [backup-simplify]: Simplify PI into PI
2.333 * [taylor]: Taking taylor expansion of n in n
2.333 * [backup-simplify]: Simplify 0 into 0
2.333 * [backup-simplify]: Simplify 1 into 1
2.333 * [backup-simplify]: Simplify (/ PI 1) into PI
2.334 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.335 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.335 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.335 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.335 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.336 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.337 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
2.339 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.340 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
2.340 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
2.340 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
2.340 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
2.340 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.340 * [taylor]: Taking taylor expansion of 1/2 in k
2.340 * [backup-simplify]: Simplify 1/2 into 1/2
2.340 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.340 * [taylor]: Taking taylor expansion of 1/2 in k
2.340 * [backup-simplify]: Simplify 1/2 into 1/2
2.340 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.340 * [taylor]: Taking taylor expansion of k in k
2.340 * [backup-simplify]: Simplify 0 into 0
2.340 * [backup-simplify]: Simplify 1 into 1
2.341 * [backup-simplify]: Simplify (/ 1 1) into 1
2.341 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
2.341 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.341 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.341 * [taylor]: Taking taylor expansion of 2 in k
2.341 * [backup-simplify]: Simplify 2 into 2
2.341 * [taylor]: Taking taylor expansion of PI in k
2.341 * [backup-simplify]: Simplify PI into PI
2.341 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.342 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.342 * [taylor]: Taking taylor expansion of (log n) in k
2.342 * [taylor]: Taking taylor expansion of n in k
2.342 * [backup-simplify]: Simplify n into n
2.342 * [backup-simplify]: Simplify (log n) into (log n)
2.343 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.343 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.344 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.344 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.345 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
2.346 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
2.347 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.347 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.347 * [taylor]: Taking taylor expansion of k in k
2.347 * [backup-simplify]: Simplify 0 into 0
2.347 * [backup-simplify]: Simplify 1 into 1
2.347 * [backup-simplify]: Simplify (sqrt 0) into 0
2.349 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.350 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
2.350 * [backup-simplify]: Simplify 0 into 0
2.351 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.352 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.354 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.354 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.354 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.355 * [backup-simplify]: Simplify (- 0) into 0
2.355 * [backup-simplify]: Simplify (+ 0 0) into 0
2.357 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.358 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
2.360 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.361 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
2.361 * [taylor]: Taking taylor expansion of 0 in k
2.361 * [backup-simplify]: Simplify 0 into 0
2.361 * [backup-simplify]: Simplify 0 into 0
2.363 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.364 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.365 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.366 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.370 * [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
2.370 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.371 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.371 * [backup-simplify]: Simplify (- 0) into 0
2.371 * [backup-simplify]: Simplify (+ 0 0) into 0
2.373 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.375 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
2.381 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.382 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
2.383 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
2.383 * [taylor]: Taking taylor expansion of 0 in k
2.383 * [backup-simplify]: Simplify 0 into 0
2.383 * [backup-simplify]: Simplify 0 into 0
2.383 * [backup-simplify]: Simplify 0 into 0
2.385 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.386 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.387 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.388 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.389 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.392 * [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
2.392 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.393 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
2.393 * [backup-simplify]: Simplify (- 0) into 0
2.393 * [backup-simplify]: Simplify (+ 0 0) into 0
2.394 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.395 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
2.397 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.397 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
2.399 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0
2.399 * [taylor]: Taking taylor expansion of 0 in k
2.399 * [backup-simplify]: Simplify 0 into 0
2.399 * [backup-simplify]: Simplify 0 into 0
2.399 * [backup-simplify]: Simplify 0 into 0
2.399 * [backup-simplify]: Simplify 0 into 0
2.401 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.402 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.403 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.405 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
2.406 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
2.406 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
2.406 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
2.406 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
2.406 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
2.406 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
2.406 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.406 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.406 * [taylor]: Taking taylor expansion of 1/2 in k
2.406 * [backup-simplify]: Simplify 1/2 into 1/2
2.406 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.406 * [taylor]: Taking taylor expansion of k in k
2.406 * [backup-simplify]: Simplify 0 into 0
2.406 * [backup-simplify]: Simplify 1 into 1
2.407 * [backup-simplify]: Simplify (/ 1 1) into 1
2.407 * [taylor]: Taking taylor expansion of 1/2 in k
2.407 * [backup-simplify]: Simplify 1/2 into 1/2
2.407 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
2.407 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
2.407 * [taylor]: Taking taylor expansion of -2 in k
2.407 * [backup-simplify]: Simplify -2 into -2
2.407 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.407 * [taylor]: Taking taylor expansion of PI in k
2.407 * [backup-simplify]: Simplify PI into PI
2.407 * [taylor]: Taking taylor expansion of n in k
2.407 * [backup-simplify]: Simplify n into n
2.407 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.407 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
2.407 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
2.407 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.407 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.407 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
2.408 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
2.408 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.408 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.408 * [taylor]: Taking taylor expansion of -1 in k
2.408 * [backup-simplify]: Simplify -1 into -1
2.408 * [taylor]: Taking taylor expansion of k in k
2.408 * [backup-simplify]: Simplify 0 into 0
2.408 * [backup-simplify]: Simplify 1 into 1
2.408 * [backup-simplify]: Simplify (/ -1 1) into -1
2.408 * [backup-simplify]: Simplify (sqrt 0) into 0
2.409 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.409 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
2.409 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
2.409 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.409 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.409 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.409 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.409 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.409 * [taylor]: Taking taylor expansion of 1/2 in n
2.409 * [backup-simplify]: Simplify 1/2 into 1/2
2.409 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.409 * [taylor]: Taking taylor expansion of k in n
2.409 * [backup-simplify]: Simplify k into k
2.409 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.409 * [taylor]: Taking taylor expansion of 1/2 in n
2.410 * [backup-simplify]: Simplify 1/2 into 1/2
2.410 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.410 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.410 * [taylor]: Taking taylor expansion of -2 in n
2.410 * [backup-simplify]: Simplify -2 into -2
2.410 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.410 * [taylor]: Taking taylor expansion of PI in n
2.410 * [backup-simplify]: Simplify PI into PI
2.410 * [taylor]: Taking taylor expansion of n in n
2.410 * [backup-simplify]: Simplify 0 into 0
2.410 * [backup-simplify]: Simplify 1 into 1
2.410 * [backup-simplify]: Simplify (/ PI 1) into PI
2.410 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.411 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.411 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.411 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.412 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.413 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
2.413 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.413 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.413 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.413 * [taylor]: Taking taylor expansion of -1 in n
2.413 * [backup-simplify]: Simplify -1 into -1
2.413 * [taylor]: Taking taylor expansion of k in n
2.413 * [backup-simplify]: Simplify k into k
2.413 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.413 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.414 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.414 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.415 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
2.415 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
2.415 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.415 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.415 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.415 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.415 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.415 * [taylor]: Taking taylor expansion of 1/2 in n
2.415 * [backup-simplify]: Simplify 1/2 into 1/2
2.415 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.415 * [taylor]: Taking taylor expansion of k in n
2.415 * [backup-simplify]: Simplify k into k
2.415 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.415 * [taylor]: Taking taylor expansion of 1/2 in n
2.415 * [backup-simplify]: Simplify 1/2 into 1/2
2.415 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.415 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.415 * [taylor]: Taking taylor expansion of -2 in n
2.415 * [backup-simplify]: Simplify -2 into -2
2.415 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.415 * [taylor]: Taking taylor expansion of PI in n
2.415 * [backup-simplify]: Simplify PI into PI
2.415 * [taylor]: Taking taylor expansion of n in n
2.415 * [backup-simplify]: Simplify 0 into 0
2.416 * [backup-simplify]: Simplify 1 into 1
2.416 * [backup-simplify]: Simplify (/ PI 1) into PI
2.417 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.418 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.418 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.418 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.419 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.420 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
2.422 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.422 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.422 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.422 * [taylor]: Taking taylor expansion of -1 in n
2.422 * [backup-simplify]: Simplify -1 into -1
2.422 * [taylor]: Taking taylor expansion of k in n
2.422 * [backup-simplify]: Simplify k into k
2.422 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.422 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.422 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.422 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.423 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
2.423 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
2.424 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
2.424 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
2.424 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.424 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.424 * [taylor]: Taking taylor expansion of 1/2 in k
2.424 * [backup-simplify]: Simplify 1/2 into 1/2
2.424 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.424 * [taylor]: Taking taylor expansion of k in k
2.424 * [backup-simplify]: Simplify 0 into 0
2.424 * [backup-simplify]: Simplify 1 into 1
2.424 * [backup-simplify]: Simplify (/ 1 1) into 1
2.424 * [taylor]: Taking taylor expansion of 1/2 in k
2.424 * [backup-simplify]: Simplify 1/2 into 1/2
2.424 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
2.424 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
2.424 * [taylor]: Taking taylor expansion of (* -2 PI) in k
2.424 * [taylor]: Taking taylor expansion of -2 in k
2.424 * [backup-simplify]: Simplify -2 into -2
2.424 * [taylor]: Taking taylor expansion of PI in k
2.424 * [backup-simplify]: Simplify PI into PI
2.425 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.426 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.426 * [taylor]: Taking taylor expansion of (log n) in k
2.426 * [taylor]: Taking taylor expansion of n in k
2.426 * [backup-simplify]: Simplify n into n
2.426 * [backup-simplify]: Simplify (log n) into (log n)
2.427 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.427 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.427 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.428 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
2.429 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
2.430 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.430 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.430 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.431 * [taylor]: Taking taylor expansion of -1 in k
2.431 * [backup-simplify]: Simplify -1 into -1
2.431 * [taylor]: Taking taylor expansion of k in k
2.431 * [backup-simplify]: Simplify 0 into 0
2.431 * [backup-simplify]: Simplify 1 into 1
2.431 * [backup-simplify]: Simplify (/ -1 1) into -1
2.431 * [backup-simplify]: Simplify (sqrt 0) into 0
2.432 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.433 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
2.434 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
2.434 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.435 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.436 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
2.436 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.436 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.436 * [backup-simplify]: Simplify (+ 0 0) into 0
2.437 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.438 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
2.439 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.440 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
2.440 * [taylor]: Taking taylor expansion of 0 in k
2.440 * [backup-simplify]: Simplify 0 into 0
2.440 * [backup-simplify]: Simplify 0 into 0
2.441 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
2.443 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.444 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.445 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.445 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.446 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.448 * [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
2.448 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.449 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.449 * [backup-simplify]: Simplify (+ 0 0) into 0
2.450 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.451 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
2.453 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.453 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.453 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
2.454 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
2.454 * [taylor]: Taking taylor expansion of 0 in k
2.454 * [backup-simplify]: Simplify 0 into 0
2.454 * [backup-simplify]: Simplify 0 into 0
2.454 * [backup-simplify]: Simplify 0 into 0
2.455 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.457 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.460 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.460 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.463 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
2.463 * * * [progress]: simplifying candidates
2.463 * * * * [progress]: [ 1 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (log1p (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.463 * * * * [progress]: [ 2 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (expm1 (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.463 * * * * [progress]: [ 3 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.463 * * * * [progress]: [ 4 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.463 * * * * [progress]: [ 5 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.463 * * * * [progress]: [ 6 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.463 * * * * [progress]: [ 7 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.463 * * * * [progress]: [ 8 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.463 * * * * [progress]: [ 9 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.463 * * * * [progress]: [ 10 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))>
2.463 * * * * [progress]: [ 11 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
2.463 * * * * [progress]: [ 12 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
2.463 * * * * [progress]: [ 13 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.463 * * * * [progress]: [ 14 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))>
2.464 * * * * [progress]: [ 15 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))>
2.464 * * * * [progress]: [ 16 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.464 * * * * [progress]: [ 17 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt k)))>
2.464 * * * * [progress]: [ 18 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt k)))>
2.464 * * * * [progress]: [ 19 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt k)))>
2.464 * * * * [progress]: [ 20 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt k)))>
2.464 * * * * [progress]: [ 21 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt k)))>
2.464 * * * * [progress]: [ 22 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt k)))>
2.464 * * * * [progress]: [ 23 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt k)))>
2.464 * * * * [progress]: [ 24 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt k)))>
2.464 * * * * [progress]: [ 25 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt k)))>
2.464 * * * * [progress]: [ 26 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt k)))>
2.464 * * * * [progress]: [ 27 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1))))) (sqrt k)))>
2.464 * * * * [progress]: [ 28 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1)))) (sqrt k)))>
2.464 * * * * [progress]: [ 29 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k)))) (sqrt k)))>
2.464 * * * * [progress]: [ 30 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt k)))>
2.464 * * * * [progress]: [ 31 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt k)))>
2.464 * * * * [progress]: [ 32 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt k)))>
2.464 * * * * [progress]: [ 33 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt k)))>
2.465 * * * * [progress]: [ 34 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt k)))>
2.465 * * * * [progress]: [ 35 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt k)))>
2.465 * * * * [progress]: [ 36 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt k)))>
2.465 * * * * [progress]: [ 37 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt k)))>
2.465 * * * * [progress]: [ 38 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt k)))>
2.465 * * * * [progress]: [ 39 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt k)))>
2.465 * * * * [progress]: [ 40 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) (/ 1 1))))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1))))) (sqrt k)))>
2.465 * * * * [progress]: [ 41 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) 1)))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1)))) (sqrt k)))>
2.465 * * * * [progress]: [ 42 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k)))) (sqrt k)))>
2.465 * * * * [progress]: [ 43 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt k)))>
2.465 * * * * [progress]: [ 44 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt k)))>
2.465 * * * * [progress]: [ 45 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt k)))>
2.465 * * * * [progress]: [ 46 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt k)))>
2.465 * * * * [progress]: [ 47 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt k)))>
2.465 * * * * [progress]: [ 48 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt k)))>
2.465 * * * * [progress]: [ 49 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt k)))>
2.465 * * * * [progress]: [ 50 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt k)))>
2.465 * * * * [progress]: [ 51 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt k)))>
2.465 * * * * [progress]: [ 52 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt k)))>
2.465 * * * * [progress]: [ 53 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) (/ 1 1))))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1))))) (sqrt k)))>
2.465 * * * * [progress]: [ 54 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) 1)))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1)))) (sqrt k)))>
2.465 * * * * [progress]: [ 55 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k)))) (sqrt k)))>
2.466 * * * * [progress]: [ 56 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt k)))>
2.466 * * * * [progress]: [ 57 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt k)))>
2.466 * * * * [progress]: [ 58 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt k)))>
2.466 * * * * [progress]: [ 59 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
2.466 * * * * [progress]: [ 60 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.466 * * * * [progress]: [ 61 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.466 * * * * [progress]: [ 62 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.466 * * * * [progress]: [ 63 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.466 * * * * [progress]: [ 64 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.466 * * * * [progress]: [ 65 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
2.466 * * * * [progress]: [ 66 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 67 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.466 * * * * [progress]: [ 68 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log1p (expm1 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 69 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (expm1 (log1p (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 70 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 71 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 72 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 73 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 74 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 75 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 76 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 77 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 78 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 79 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.466 * * * * [progress]: [ 80 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.467 * * * * [progress]: [ 81 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.467 * * * * [progress]: [ 82 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.467 * * * * [progress]: [ 83 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
2.467 * * * * [progress]: [ 84 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.467 * * * * [progress]: [ 85 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.467 * * * * [progress]: [ 86 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.467 * * * * [progress]: [ 87 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.467 * * * * [progress]: [ 88 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))>
2.467 * * * * [progress]: [ 89 / 445 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.467 * * * * [progress]: [ 90 / 445 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.467 * * * * [progress]: [ 91 / 445 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) 1))>
2.467 * * * * [progress]: [ 92 / 445 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.467 * * * * [progress]: [ 93 / 445 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.467 * * * * [progress]: [ 94 / 445 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.467 * * * * [progress]: [ 95 / 445 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.467 * * * * [progress]: [ 96 / 445 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
2.467 * * * * [progress]: [ 97 / 445 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.467 * * * * [progress]: [ 98 / 445 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.467 * * * * [progress]: [ 99 / 445 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
2.467 * * * * [progress]: [ 100 / 445 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.467 * * * * [progress]: [ 101 / 445 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.467 * * * * [progress]: [ 102 / 445 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.467 * * * * [progress]: [ 103 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (- (sqrt k))))>
2.467 * * * * [progress]: [ 104 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (cbrt (sqrt k)))))>
2.467 * * * * [progress]: [ 105 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (cbrt k)))))>
2.468 * * * * [progress]: [ 106 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (sqrt k)))))>
2.468 * * * * [progress]: [ 107 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt k))))>
2.468 * * * * [progress]: [ 108 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (sqrt k)))))>
2.468 * * * * [progress]: [ 109 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt k))))>
2.468 * * * * [progress]: [ 110 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (cbrt (sqrt k)))))>
2.468 * * * * [progress]: [ 111 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt (cbrt k)))))>
2.468 * * * * [progress]: [ 112 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt (sqrt k)))))>
2.468 * * * * [progress]: [ 113 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt k))))>
2.468 * * * * [progress]: [ 114 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt (sqrt k)))))>
2.468 * * * * [progress]: [ 115 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt k))))>
2.468 * * * * [progress]: [ 116 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (cbrt (sqrt k)))))>
2.468 * * * * [progress]: [ 117 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt (cbrt k)))))>
2.468 * * * * [progress]: [ 118 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.468 * * * * [progress]: [ 119 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.468 * * * * [progress]: [ 120 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.468 * * * * [progress]: [ 121 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.468 * * * * [progress]: [ 122 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (cbrt (sqrt k)))))>
2.468 * * * * [progress]: [ 123 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt (cbrt k)))))>
2.469 * * * * [progress]: [ 124 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt (sqrt k)))))>
2.469 * * * * [progress]: [ 125 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt k))))>
2.469 * * * * [progress]: [ 126 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt (sqrt k)))))>
2.469 * * * * [progress]: [ 127 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt k))))>
2.469 * * * * [progress]: [ 128 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (cbrt (sqrt k)))))>
2.469 * * * * [progress]: [ 129 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt (cbrt k)))))>
2.469 * * * * [progress]: [ 130 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt (sqrt k)))))>
2.469 * * * * [progress]: [ 131 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt k))))>
2.469 * * * * [progress]: [ 132 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt (sqrt k)))))>
2.469 * * * * [progress]: [ 133 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt k))))>
2.469 * * * * [progress]: [ 134 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (cbrt (sqrt k)))))>
2.469 * * * * [progress]: [ 135 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt (cbrt k)))))>
2.469 * * * * [progress]: [ 136 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.469 * * * * [progress]: [ 137 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.469 * * * * [progress]: [ 138 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.469 * * * * [progress]: [ 139 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.469 * * * * [progress]: [ 140 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (cbrt (sqrt k)))))>
2.469 * * * * [progress]: [ 141 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt (cbrt k)))))>
2.470 * * * * [progress]: [ 142 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt (sqrt k)))))>
2.470 * * * * [progress]: [ 143 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt k))))>
2.470 * * * * [progress]: [ 144 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt (sqrt k)))))>
2.470 * * * * [progress]: [ 145 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt k))))>
2.470 * * * * [progress]: [ 146 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (cbrt (sqrt k)))))>
2.470 * * * * [progress]: [ 147 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt (cbrt k)))))>
2.470 * * * * [progress]: [ 148 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt (sqrt k)))))>
2.470 * * * * [progress]: [ 149 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt k))))>
2.470 * * * * [progress]: [ 150 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt (sqrt k)))))>
2.470 * * * * [progress]: [ 151 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt k))))>
2.470 * * * * [progress]: [ 152 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (cbrt (sqrt k)))))>
2.470 * * * * [progress]: [ 153 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt (cbrt k)))))>
2.470 * * * * [progress]: [ 154 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.470 * * * * [progress]: [ 155 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.470 * * * * [progress]: [ 156 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.470 * * * * [progress]: [ 157 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.470 * * * * [progress]: [ 158 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (cbrt (sqrt k)))))>
2.470 * * * * [progress]: [ 159 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt (cbrt k)))))>
2.470 * * * * [progress]: [ 160 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt (sqrt k)))))>
2.470 * * * * [progress]: [ 161 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt k))))>
2.471 * * * * [progress]: [ 162 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt (sqrt k)))))>
2.471 * * * * [progress]: [ 163 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt k))))>
2.471 * * * * [progress]: [ 164 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (cbrt (sqrt k)))))>
2.471 * * * * [progress]: [ 165 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt (cbrt k)))))>
2.471 * * * * [progress]: [ 166 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt (sqrt k)))))>
2.471 * * * * [progress]: [ 167 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt k))))>
2.471 * * * * [progress]: [ 168 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt (sqrt k)))))>
2.471 * * * * [progress]: [ 169 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt k))))>
2.471 * * * * [progress]: [ 170 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (cbrt (sqrt k)))))>
2.472 * * * * [progress]: [ 171 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt (cbrt k)))))>
2.472 * * * * [progress]: [ 172 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt (sqrt k)))))>
2.472 * * * * [progress]: [ 173 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt k))))>
2.472 * * * * [progress]: [ 174 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt (sqrt k)))))>
2.472 * * * * [progress]: [ 175 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt k))))>
2.472 * * * * [progress]: [ 176 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (cbrt (sqrt k)))))>
2.472 * * * * [progress]: [ 177 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt (cbrt k)))))>
2.472 * * * * [progress]: [ 178 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt (sqrt k)))))>
2.472 * * * * [progress]: [ 179 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt k))))>
2.472 * * * * [progress]: [ 180 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt (sqrt k)))))>
2.472 * * * * [progress]: [ 181 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt k))))>
2.472 * * * * [progress]: [ 182 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (cbrt (sqrt k)))))>
2.472 * * * * [progress]: [ 183 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (cbrt k)))))>
2.472 * * * * [progress]: [ 184 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (sqrt k)))))>
2.472 * * * * [progress]: [ 185 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt k))))>
2.472 * * * * [progress]: [ 186 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (sqrt k)))))>
2.472 * * * * [progress]: [ 187 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt k))))>
2.472 * * * * [progress]: [ 188 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (cbrt (sqrt k)))))>
2.472 * * * * [progress]: [ 189 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt (cbrt k)))))>
2.473 * * * * [progress]: [ 190 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt (sqrt k)))))>
2.473 * * * * [progress]: [ 191 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt k))))>
2.473 * * * * [progress]: [ 192 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt (sqrt k)))))>
2.473 * * * * [progress]: [ 193 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt k))))>
2.473 * * * * [progress]: [ 194 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (cbrt (sqrt k)))))>
2.473 * * * * [progress]: [ 195 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt (cbrt k)))))>
2.473 * * * * [progress]: [ 196 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.473 * * * * [progress]: [ 197 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.473 * * * * [progress]: [ 198 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.473 * * * * [progress]: [ 199 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.473 * * * * [progress]: [ 200 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (cbrt (sqrt k)))))>
2.473 * * * * [progress]: [ 201 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt (cbrt k)))))>
2.473 * * * * [progress]: [ 202 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt (sqrt k)))))>
2.473 * * * * [progress]: [ 203 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt k))))>
2.473 * * * * [progress]: [ 204 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt (sqrt k)))))>
2.473 * * * * [progress]: [ 205 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt k))))>
2.473 * * * * [progress]: [ 206 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (cbrt (sqrt k)))))>
2.473 * * * * [progress]: [ 207 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt (cbrt k)))))>
2.473 * * * * [progress]: [ 208 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt (sqrt k)))))>
2.474 * * * * [progress]: [ 209 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt k))))>
2.474 * * * * [progress]: [ 210 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt (sqrt k)))))>
2.474 * * * * [progress]: [ 211 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt k))))>
2.474 * * * * [progress]: [ 212 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (cbrt (sqrt k)))))>
2.474 * * * * [progress]: [ 213 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt (cbrt k)))))>
2.474 * * * * [progress]: [ 214 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.474 * * * * [progress]: [ 215 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.474 * * * * [progress]: [ 216 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.474 * * * * [progress]: [ 217 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.474 * * * * [progress]: [ 218 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (cbrt (sqrt k)))))>
2.474 * * * * [progress]: [ 219 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt (cbrt k)))))>
2.474 * * * * [progress]: [ 220 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt (sqrt k)))))>
2.474 * * * * [progress]: [ 221 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt k))))>
2.474 * * * * [progress]: [ 222 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt (sqrt k)))))>
2.474 * * * * [progress]: [ 223 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt k))))>
2.474 * * * * [progress]: [ 224 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (cbrt (sqrt k)))))>
2.474 * * * * [progress]: [ 225 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt (cbrt k)))))>
2.474 * * * * [progress]: [ 226 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt (sqrt k)))))>
2.474 * * * * [progress]: [ 227 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt k))))>
2.474 * * * * [progress]: [ 228 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt (sqrt k)))))>
2.475 * * * * [progress]: [ 229 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt k))))>
2.475 * * * * [progress]: [ 230 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (cbrt (sqrt k)))))>
2.475 * * * * [progress]: [ 231 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt (cbrt k)))))>
2.475 * * * * [progress]: [ 232 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.475 * * * * [progress]: [ 233 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.475 * * * * [progress]: [ 234 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.475 * * * * [progress]: [ 235 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.475 * * * * [progress]: [ 236 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (cbrt (sqrt k)))))>
2.475 * * * * [progress]: [ 237 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt (cbrt k)))))>
2.475 * * * * [progress]: [ 238 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt (sqrt k)))))>
2.475 * * * * [progress]: [ 239 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt k))))>
2.475 * * * * [progress]: [ 240 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt (sqrt k)))))>
2.475 * * * * [progress]: [ 241 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt k))))>
2.475 * * * * [progress]: [ 242 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) (/ 1 1))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (cbrt (sqrt k)))))>
2.475 * * * * [progress]: [ 243 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) (/ 1 1))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt (cbrt k)))))>
2.475 * * * * [progress]: [ 244 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) (/ 1 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt (sqrt k)))))>
2.475 * * * * [progress]: [ 245 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) (/ 1 1))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt k))))>
2.475 * * * * [progress]: [ 246 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) (/ 1 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt (sqrt k)))))>
2.475 * * * * [progress]: [ 247 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) (/ 1 1))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt k))))>
2.475 * * * * [progress]: [ 248 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) 1)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (cbrt (sqrt k)))))>
2.476 * * * * [progress]: [ 249 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) 1)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt (cbrt k)))))>
2.476 * * * * [progress]: [ 250 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) 1)))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt (sqrt k)))))>
2.476 * * * * [progress]: [ 251 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) 1)))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt k))))>
2.476 * * * * [progress]: [ 252 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) 1)))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt (sqrt k)))))>
2.476 * * * * [progress]: [ 253 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) 1)))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt k))))>
2.476 * * * * [progress]: [ 254 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (cbrt (sqrt k)))))>
2.476 * * * * [progress]: [ 255 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt (cbrt k)))))>
2.476 * * * * [progress]: [ 256 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k)))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt (sqrt k)))))>
2.476 * * * * [progress]: [ 257 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k)))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt k))))>
2.476 * * * * [progress]: [ 258 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k)))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt (sqrt k)))))>
2.476 * * * * [progress]: [ 259 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k)))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt k))))>
2.476 * * * * [progress]: [ 260 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (cbrt (sqrt k)))))>
2.476 * * * * [progress]: [ 261 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (cbrt k)))))>
2.476 * * * * [progress]: [ 262 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (sqrt k)))))>
2.476 * * * * [progress]: [ 263 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt k))))>
2.476 * * * * [progress]: [ 264 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (sqrt k)))))>
2.476 * * * * [progress]: [ 265 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt k))))>
2.476 * * * * [progress]: [ 266 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (cbrt (sqrt k)))))>
2.476 * * * * [progress]: [ 267 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt (cbrt k)))))>
2.476 * * * * [progress]: [ 268 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt (sqrt k)))))>
2.476 * * * * [progress]: [ 269 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt k))))>
2.477 * * * * [progress]: [ 270 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt (sqrt k)))))>
2.477 * * * * [progress]: [ 271 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (sqrt k))))>
2.477 * * * * [progress]: [ 272 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (cbrt (sqrt k)))))>
2.477 * * * * [progress]: [ 273 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt (cbrt k)))))>
2.477 * * * * [progress]: [ 274 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.477 * * * * [progress]: [ 275 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.477 * * * * [progress]: [ 276 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.477 * * * * [progress]: [ 277 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.477 * * * * [progress]: [ 278 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (cbrt (sqrt k)))))>
2.477 * * * * [progress]: [ 279 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt (cbrt k)))))>
2.477 * * * * [progress]: [ 280 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt (sqrt k)))))>
2.477 * * * * [progress]: [ 281 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt k))))>
2.477 * * * * [progress]: [ 282 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt (sqrt k)))))>
2.477 * * * * [progress]: [ 283 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (sqrt k))))>
2.477 * * * * [progress]: [ 284 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (cbrt (sqrt k)))))>
2.477 * * * * [progress]: [ 285 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt (cbrt k)))))>
2.477 * * * * [progress]: [ 286 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt (sqrt k)))))>
2.477 * * * * [progress]: [ 287 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt k))))>
2.477 * * * * [progress]: [ 288 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt (sqrt k)))))>
2.477 * * * * [progress]: [ 289 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (sqrt k))))>
2.478 * * * * [progress]: [ 290 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (cbrt (sqrt k)))))>
2.478 * * * * [progress]: [ 291 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt (cbrt k)))))>
2.478 * * * * [progress]: [ 292 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.478 * * * * [progress]: [ 293 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.478 * * * * [progress]: [ 294 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.478 * * * * [progress]: [ 295 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.478 * * * * [progress]: [ 296 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (cbrt (sqrt k)))))>
2.478 * * * * [progress]: [ 297 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt (cbrt k)))))>
2.478 * * * * [progress]: [ 298 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt (sqrt k)))))>
2.478 * * * * [progress]: [ 299 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt k))))>
2.478 * * * * [progress]: [ 300 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt (sqrt k)))))>
2.478 * * * * [progress]: [ 301 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (sqrt k))))>
2.478 * * * * [progress]: [ 302 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (cbrt (sqrt k)))))>
2.478 * * * * [progress]: [ 303 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt (cbrt k)))))>
2.478 * * * * [progress]: [ 304 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt (sqrt k)))))>
2.478 * * * * [progress]: [ 305 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt k))))>
2.478 * * * * [progress]: [ 306 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt (sqrt k)))))>
2.478 * * * * [progress]: [ 307 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (sqrt k))))>
2.478 * * * * [progress]: [ 308 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (cbrt (sqrt k)))))>
2.478 * * * * [progress]: [ 309 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt (cbrt k)))))>
2.479 * * * * [progress]: [ 310 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.479 * * * * [progress]: [ 311 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.479 * * * * [progress]: [ 312 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt (sqrt k)))))>
2.479 * * * * [progress]: [ 313 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (sqrt k))))>
2.479 * * * * [progress]: [ 314 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (cbrt (sqrt k)))))>
2.479 * * * * [progress]: [ 315 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt (cbrt k)))))>
2.479 * * * * [progress]: [ 316 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt (sqrt k)))))>
2.479 * * * * [progress]: [ 317 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt k))))>
2.479 * * * * [progress]: [ 318 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt (sqrt k)))))>
2.479 * * * * [progress]: [ 319 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (sqrt k))))>
2.479 * * * * [progress]: [ 320 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) (/ 1 1))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (cbrt (sqrt k)))))>
2.479 * * * * [progress]: [ 321 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) (/ 1 1))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt (cbrt k)))))>
2.479 * * * * [progress]: [ 322 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) (/ 1 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt (sqrt k)))))>
2.479 * * * * [progress]: [ 323 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) (/ 1 1))))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt k))))>
2.479 * * * * [progress]: [ 324 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) (/ 1 1))))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt (sqrt k)))))>
2.479 * * * * [progress]: [ 325 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) (/ 1 1))))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (sqrt k))))>
2.479 * * * * [progress]: [ 326 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) 1)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (cbrt (sqrt k)))))>
2.479 * * * * [progress]: [ 327 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) 1)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt (cbrt k)))))>
2.479 * * * * [progress]: [ 328 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) 1)))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt (sqrt k)))))>
2.479 * * * * [progress]: [ 329 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) 1)))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt k))))>
2.480 * * * * [progress]: [ 330 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) 1)))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt (sqrt k)))))>
2.480 * * * * [progress]: [ 331 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) 1)))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (sqrt k))))>
2.480 * * * * [progress]: [ 332 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ 1 2) k)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (cbrt (sqrt k)))))>
2.480 * * * * [progress]: [ 333 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ 1 2) k)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt (cbrt k)))))>
2.480 * * * * [progress]: [ 334 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ 1 2) k)))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt (sqrt k)))))>
2.480 * * * * [progress]: [ 335 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ 1 2) k)))) (sqrt 1)) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt k))))>
2.480 * * * * [progress]: [ 336 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ 1 2) k)))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt (sqrt k)))))>
2.480 * * * * [progress]: [ 337 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ 1 2) k)))) 1) (/ (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (sqrt k))))>
2.480 * * * * [progress]: [ 338 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
2.480 * * * * [progress]: [ 339 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))))>
2.480 * * * * [progress]: [ 340 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.480 * * * * [progress]: [ 341 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1)) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.480 * * * * [progress]: [ 342 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.480 * * * * [progress]: [ 343 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.480 * * * * [progress]: [ 344 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
2.480 * * * * [progress]: [ 345 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))))>
2.480 * * * * [progress]: [ 346 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.480 * * * * [progress]: [ 347 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1)) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.480 * * * * [progress]: [ 348 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.480 * * * * [progress]: [ 349 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.480 * * * * [progress]: [ 350 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
2.480 * * * * [progress]: [ 351 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
2.480 * * * * [progress]: [ 352 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.480 * * * * [progress]: [ 353 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.481 * * * * [progress]: [ 354 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.481 * * * * [progress]: [ 355 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) 1) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.481 * * * * [progress]: [ 356 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
2.481 * * * * [progress]: [ 357 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
2.481 * * * * [progress]: [ 358 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.481 * * * * [progress]: [ 359 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt 1)) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.481 * * * * [progress]: [ 360 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.481 * * * * [progress]: [ 361 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.481 * * * * [progress]: [ 362 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
2.481 * * * * [progress]: [ 363 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
2.481 * * * * [progress]: [ 364 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.481 * * * * [progress]: [ 365 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.481 * * * * [progress]: [ 366 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.481 * * * * [progress]: [ 367 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.481 * * * * [progress]: [ 368 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
2.481 * * * * [progress]: [ 369 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
2.481 * * * * [progress]: [ 370 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.481 * * * * [progress]: [ 371 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
2.481 * * * * [progress]: [ 372 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.481 * * * * [progress]: [ 373 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
2.481 * * * * [progress]: [ 374 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))>
2.481 * * * * [progress]: [ 375 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))>
2.481 * * * * [progress]: [ 376 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
2.482 * * * * [progress]: [ 377 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
2.482 * * * * [progress]: [ 378 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
2.482 * * * * [progress]: [ 379 / 445 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
2.482 * * * * [progress]: [ 380 / 445 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
2.482 * * * * [progress]: [ 381 / 445 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
2.482 * * * * [progress]: [ 382 / 445 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
2.482 * * * * [progress]: [ 383 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
2.482 * * * * [progress]: [ 384 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
2.482 * * * * [progress]: [ 385 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.482 * * * * [progress]: [ 386 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k)))>
2.482 * * * * [progress]: [ 387 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.482 * * * * [progress]: [ 388 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
2.482 * * * * [progress]: [ 389 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))))>
2.482 * * * * [progress]: [ 390 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))))))>
2.482 * * * * [progress]: [ 391 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))))))>
2.482 * * * * [progress]: [ 392 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))))))>
2.482 * * * * [progress]: [ 393 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))))))>
2.482 * * * * [progress]: [ 394 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))))))>
2.482 * * * * [progress]: [ 395 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))))>
2.482 * * * * [progress]: [ 396 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))))))>
2.482 * * * * [progress]: [ 397 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))))))>
2.482 * * * * [progress]: [ 398 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))))))>
2.483 * * * * [progress]: [ 399 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))))))>
2.483 * * * * [progress]: [ 400 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))))))>
2.483 * * * * [progress]: [ 401 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))))))>
2.483 * * * * [progress]: [ 402 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))))>
2.483 * * * * [progress]: [ 403 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))))))>
2.483 * * * * [progress]: [ 404 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))))))>
2.483 * * * * [progress]: [ 405 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))))))>
2.483 * * * * [progress]: [ 406 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))))))>
2.483 * * * * [progress]: [ 407 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))))))>
2.483 * * * * [progress]: [ 408 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))))>
2.483 * * * * [progress]: [ 409 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))))))>
2.483 * * * * [progress]: [ 410 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))))))>
2.483 * * * * [progress]: [ 411 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))))))>
2.483 * * * * [progress]: [ 412 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) (/ 1 1))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))))))>
2.483 * * * * [progress]: [ 413 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) 1)))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))))))>
2.483 * * * * [progress]: [ 414 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k)))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))))))>
2.483 * * * * [progress]: [ 415 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))))>
2.483 * * * * [progress]: [ 416 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))))))>
2.483 * * * * [progress]: [ 417 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))))))>
2.483 * * * * [progress]: [ 418 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))))))>
2.483 * * * * [progress]: [ 419 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))))))>
2.484 * * * * [progress]: [ 420 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))))))>
2.484 * * * * [progress]: [ 421 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))))>
2.484 * * * * [progress]: [ 422 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))))))>
2.484 * * * * [progress]: [ 423 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))))))>
2.484 * * * * [progress]: [ 424 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))))))>
2.484 * * * * [progress]: [ 425 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) (/ 1 1))))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))))))>
2.484 * * * * [progress]: [ 426 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k 2) 1)))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))))))>
2.484 * * * * [progress]: [ 427 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ 1 2) k)))) (/ (sqrt k) (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))))))>
2.484 * * * * [progress]: [ 428 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
2.484 * * * * [progress]: [ 429 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
2.484 * * * * [progress]: [ 430 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
2.484 * * * * [progress]: [ 431 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
2.484 * * * * [progress]: [ 432 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
2.484 * * * * [progress]: [ 433 / 445 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
2.484 * * * * [progress]: [ 434 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
2.484 * * * * [progress]: [ 435 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))>
2.484 * * * * [progress]: [ 436 / 445 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.484 * * * * [progress]: [ 437 / 445 ] 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)))>
2.484 * * * * [progress]: [ 438 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
2.484 * * * * [progress]: [ 439 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
2.484 * * * * [progress]: [ 440 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.484 * * * * [progress]: [ 441 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.485 * * * * [progress]: [ 442 / 445 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.485 * * * * [progress]: [ 443 / 445 ] 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)))))))))))))))))))))))>
2.485 * * * * [progress]: [ 444 / 445 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
2.485 * * * * [progress]: [ 445 / 445 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
2.495 * [simplify]: Simplifying (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))), (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))), (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))), (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))), (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))), (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))), (* 1 (- 1/2 (/ k 2))), (* 1 (- 1/2 (/ k 2))), (* 1 (- 1/2 (/ k 2))), (pow (* n (* 2 PI)) 1/2), (pow (* n (* 2 PI)) (/ k 2)), (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))), (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))), (pow (* n (* 2 PI)) 1), (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))), (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))), (pow (* n (* 2 PI)) 1), (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))), (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))), (pow (* n (* 2 PI)) (fma (* (cbrt 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1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))), (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))), (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
2.525 * * [simplify]: iteration 1: (695 enodes)
3.217 * * [simplify]: Extracting #0: cost 311 inf + 0
3.230 * * [simplify]: Extracting #1: cost 891 inf + 1
3.237 * * [simplify]: Extracting #2: cost 1121 inf + 507
3.246 * * [simplify]: Extracting #3: cost 1217 inf + 6860
3.260 * * [simplify]: Extracting #4: cost 1073 inf + 44343
3.287 * * [simplify]: Extracting #5: cost 734 inf + 182333
3.378 * * [simplify]: Extracting #6: cost 370 inf + 395273
3.490 * * [simplify]: Extracting #7: cost 112 inf + 571810
3.614 * * [simplify]: Extracting #8: cost 70 inf + 607747
3.695 * * [simplify]: Extracting #9: cost 58 inf + 620041
3.819 * * [simplify]: Extracting #10: cost 55 inf + 626674
3.912 * * [simplify]: Extracting #11: cost 47 inf + 634260
3.995 * * [simplify]: Extracting #12: cost 34 inf + 642997
4.102 * * [simplify]: Extracting #13: cost 27 inf + 650279
4.273 * * [simplify]: Extracting #14: cost 17 inf + 663059
4.430 * * [simplify]: Extracting #15: cost 3 inf + 684783
4.612 * * [simplify]: Extracting #16: cost 0 inf + 689641
4.766 * [simplify]: Simplified to (expm1 (pow (* (* PI 2) n) (- 1/2 (/ k 2)))), (log1p (pow (* (* PI 2) n) (- 1/2 (/ k 2)))), (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))), (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))), (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))), (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))), (- 1/2 (/ k 2)), (- 1/2 (/ k 2)), (- 1/2 (/ k 2)), (sqrt (* (* PI 2) n)), (pow (* (* PI 2) n) (/ k 2)), (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))), (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2)))), (* (* PI 2) n), (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2)))), (pow (* (* PI 2) n) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))), (* (* PI 2) n), (pow (* (* PI 2) n) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))), (pow (* (* PI 2) n) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2))))), (pow (* (* PI 2) n) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))), (pow (* 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4.863 * * * [progress]: adding candidates to table
11.716 * * [progress]: iteration 2 / 4
11.716 * * * [progress]: picking best candidate
11.766 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
11.766 * * * [progress]: localizing error
11.819 * * * [progress]: generating rewritten candidates
11.819 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
11.852 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1)
11.863 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1)
11.897 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
11.969 * * * [progress]: generating series expansions
11.969 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
11.970 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
11.970 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
11.970 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
11.970 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
11.970 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
11.970 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
11.970 * [taylor]: Taking taylor expansion of 1/2 in k
11.970 * [backup-simplify]: Simplify 1/2 into 1/2
11.970 * [taylor]: Taking taylor expansion of (- 1 k) in k
11.970 * [taylor]: Taking taylor expansion of 1 in k
11.970 * [backup-simplify]: Simplify 1 into 1
11.970 * [taylor]: Taking taylor expansion of k in k
11.970 * [backup-simplify]: Simplify 0 into 0
11.970 * [backup-simplify]: Simplify 1 into 1
11.971 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
11.971 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
11.971 * [taylor]: Taking taylor expansion of 2 in k
11.971 * [backup-simplify]: Simplify 2 into 2
11.971 * [taylor]: Taking taylor expansion of (* n PI) in k
11.971 * [taylor]: Taking taylor expansion of n in k
11.971 * [backup-simplify]: Simplify n into n
11.971 * [taylor]: Taking taylor expansion of PI in k
11.971 * [backup-simplify]: Simplify PI into PI
11.971 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.971 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
11.971 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
11.972 * [backup-simplify]: Simplify (- 0) into 0
11.972 * [backup-simplify]: Simplify (+ 1 0) into 1
11.973 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.973 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
11.973 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
11.973 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
11.973 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
11.973 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
11.973 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
11.973 * [taylor]: Taking taylor expansion of 1/2 in n
11.973 * [backup-simplify]: Simplify 1/2 into 1/2
11.973 * [taylor]: Taking taylor expansion of (- 1 k) in n
11.973 * [taylor]: Taking taylor expansion of 1 in n
11.973 * [backup-simplify]: Simplify 1 into 1
11.973 * [taylor]: Taking taylor expansion of k in n
11.973 * [backup-simplify]: Simplify k into k
11.973 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.973 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.973 * [taylor]: Taking taylor expansion of 2 in n
11.973 * [backup-simplify]: Simplify 2 into 2
11.973 * [taylor]: Taking taylor expansion of (* n PI) in n
11.973 * [taylor]: Taking taylor expansion of n in n
11.973 * [backup-simplify]: Simplify 0 into 0
11.973 * [backup-simplify]: Simplify 1 into 1
11.974 * [taylor]: Taking taylor expansion of PI in n
11.974 * [backup-simplify]: Simplify PI into PI
11.974 * [backup-simplify]: Simplify (* 0 PI) into 0
11.975 * [backup-simplify]: Simplify (* 2 0) into 0
11.976 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.978 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.979 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.980 * [backup-simplify]: Simplify (- k) into (- k)
11.980 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
11.980 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
11.981 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.982 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
11.984 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
11.984 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
11.984 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
11.984 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
11.984 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
11.984 * [taylor]: Taking taylor expansion of 1/2 in n
11.984 * [backup-simplify]: Simplify 1/2 into 1/2
11.984 * [taylor]: Taking taylor expansion of (- 1 k) in n
11.984 * [taylor]: Taking taylor expansion of 1 in n
11.984 * [backup-simplify]: Simplify 1 into 1
11.984 * [taylor]: Taking taylor expansion of k in n
11.984 * [backup-simplify]: Simplify k into k
11.984 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.984 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.984 * [taylor]: Taking taylor expansion of 2 in n
11.984 * [backup-simplify]: Simplify 2 into 2
11.984 * [taylor]: Taking taylor expansion of (* n PI) in n
11.984 * [taylor]: Taking taylor expansion of n in n
11.984 * [backup-simplify]: Simplify 0 into 0
11.984 * [backup-simplify]: Simplify 1 into 1
11.984 * [taylor]: Taking taylor expansion of PI in n
11.984 * [backup-simplify]: Simplify PI into PI
11.985 * [backup-simplify]: Simplify (* 0 PI) into 0
11.985 * [backup-simplify]: Simplify (* 2 0) into 0
11.987 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.989 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.990 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.990 * [backup-simplify]: Simplify (- k) into (- k)
11.990 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
11.990 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
11.992 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.993 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
11.994 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
11.994 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
11.994 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
11.994 * [taylor]: Taking taylor expansion of 1/2 in k
11.995 * [backup-simplify]: Simplify 1/2 into 1/2
11.995 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
11.995 * [taylor]: Taking taylor expansion of (- 1 k) in k
11.995 * [taylor]: Taking taylor expansion of 1 in k
11.995 * [backup-simplify]: Simplify 1 into 1
11.995 * [taylor]: Taking taylor expansion of k in k
11.995 * [backup-simplify]: Simplify 0 into 0
11.995 * [backup-simplify]: Simplify 1 into 1
11.995 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
11.995 * [taylor]: Taking taylor expansion of (log n) in k
11.995 * [taylor]: Taking taylor expansion of n in k
11.995 * [backup-simplify]: Simplify n into n
11.995 * [backup-simplify]: Simplify (log n) into (log n)
11.995 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
11.995 * [taylor]: Taking taylor expansion of (* 2 PI) in k
11.995 * [taylor]: Taking taylor expansion of 2 in k
11.995 * [backup-simplify]: Simplify 2 into 2
11.995 * [taylor]: Taking taylor expansion of PI in k
11.995 * [backup-simplify]: Simplify PI into PI
11.996 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.997 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.997 * [backup-simplify]: Simplify (- 0) into 0
11.997 * [backup-simplify]: Simplify (+ 1 0) into 1
11.999 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.000 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
12.001 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
12.002 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
12.003 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
12.004 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.005 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.007 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.008 * [backup-simplify]: Simplify (- 0) into 0
12.008 * [backup-simplify]: Simplify (+ 0 0) into 0
12.009 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
12.010 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.011 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
12.013 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.013 * [taylor]: Taking taylor expansion of 0 in k
12.013 * [backup-simplify]: Simplify 0 into 0
12.013 * [backup-simplify]: Simplify 0 into 0
12.014 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.015 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.017 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.017 * [backup-simplify]: Simplify (+ 0 0) into 0
12.018 * [backup-simplify]: Simplify (- 1) into -1
12.018 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.020 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
12.022 * [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)))))
12.028 * [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)))))))
12.030 * [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)))))))
12.031 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.031 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.033 * [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
12.034 * [backup-simplify]: Simplify (- 0) into 0
12.034 * [backup-simplify]: Simplify (+ 0 0) into 0
12.034 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
12.035 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.036 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.038 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.038 * [taylor]: Taking taylor expansion of 0 in k
12.038 * [backup-simplify]: Simplify 0 into 0
12.038 * [backup-simplify]: Simplify 0 into 0
12.038 * [backup-simplify]: Simplify 0 into 0
12.039 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.039 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.041 * [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
12.041 * [backup-simplify]: Simplify (+ 0 0) into 0
12.042 * [backup-simplify]: Simplify (- 0) into 0
12.042 * [backup-simplify]: Simplify (+ 0 0) into 0
12.043 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.045 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.047 * [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)))))
12.051 * [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)))))
12.056 * [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)))))
12.057 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
12.057 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
12.057 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
12.057 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.057 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.057 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
12.057 * [taylor]: Taking taylor expansion of 1/2 in k
12.057 * [backup-simplify]: Simplify 1/2 into 1/2
12.057 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
12.057 * [taylor]: Taking taylor expansion of 1 in k
12.057 * [backup-simplify]: Simplify 1 into 1
12.057 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.057 * [taylor]: Taking taylor expansion of k in k
12.057 * [backup-simplify]: Simplify 0 into 0
12.057 * [backup-simplify]: Simplify 1 into 1
12.057 * [backup-simplify]: Simplify (/ 1 1) into 1
12.057 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.057 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.057 * [taylor]: Taking taylor expansion of 2 in k
12.057 * [backup-simplify]: Simplify 2 into 2
12.057 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.057 * [taylor]: Taking taylor expansion of PI in k
12.057 * [backup-simplify]: Simplify PI into PI
12.057 * [taylor]: Taking taylor expansion of n in k
12.057 * [backup-simplify]: Simplify n into n
12.057 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.058 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.058 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.058 * [backup-simplify]: Simplify (- 1) into -1
12.058 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.058 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
12.059 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.059 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
12.059 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
12.059 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.059 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.059 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
12.059 * [taylor]: Taking taylor expansion of 1/2 in n
12.059 * [backup-simplify]: Simplify 1/2 into 1/2
12.059 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
12.059 * [taylor]: Taking taylor expansion of 1 in n
12.059 * [backup-simplify]: Simplify 1 into 1
12.059 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.059 * [taylor]: Taking taylor expansion of k in n
12.059 * [backup-simplify]: Simplify k into k
12.059 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.059 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.059 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.059 * [taylor]: Taking taylor expansion of 2 in n
12.059 * [backup-simplify]: Simplify 2 into 2
12.059 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.059 * [taylor]: Taking taylor expansion of PI in n
12.059 * [backup-simplify]: Simplify PI into PI
12.059 * [taylor]: Taking taylor expansion of n in n
12.059 * [backup-simplify]: Simplify 0 into 0
12.059 * [backup-simplify]: Simplify 1 into 1
12.059 * [backup-simplify]: Simplify (/ PI 1) into PI
12.060 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.060 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.060 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.060 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
12.060 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
12.061 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.062 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
12.063 * [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)))))
12.063 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
12.063 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.063 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.063 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
12.063 * [taylor]: Taking taylor expansion of 1/2 in n
12.063 * [backup-simplify]: Simplify 1/2 into 1/2
12.063 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
12.063 * [taylor]: Taking taylor expansion of 1 in n
12.063 * [backup-simplify]: Simplify 1 into 1
12.063 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.063 * [taylor]: Taking taylor expansion of k in n
12.063 * [backup-simplify]: Simplify k into k
12.064 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.064 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.064 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.064 * [taylor]: Taking taylor expansion of 2 in n
12.064 * [backup-simplify]: Simplify 2 into 2
12.064 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.064 * [taylor]: Taking taylor expansion of PI in n
12.064 * [backup-simplify]: Simplify PI into PI
12.064 * [taylor]: Taking taylor expansion of n in n
12.064 * [backup-simplify]: Simplify 0 into 0
12.064 * [backup-simplify]: Simplify 1 into 1
12.064 * [backup-simplify]: Simplify (/ PI 1) into PI
12.065 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.066 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.066 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.066 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
12.066 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
12.068 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.069 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
12.070 * [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)))))
12.070 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
12.070 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
12.070 * [taylor]: Taking taylor expansion of 1/2 in k
12.070 * [backup-simplify]: Simplify 1/2 into 1/2
12.070 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
12.070 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
12.070 * [taylor]: Taking taylor expansion of 1 in k
12.070 * [backup-simplify]: Simplify 1 into 1
12.070 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.070 * [taylor]: Taking taylor expansion of k in k
12.070 * [backup-simplify]: Simplify 0 into 0
12.070 * [backup-simplify]: Simplify 1 into 1
12.071 * [backup-simplify]: Simplify (/ 1 1) into 1
12.071 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
12.071 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.071 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.071 * [taylor]: Taking taylor expansion of 2 in k
12.071 * [backup-simplify]: Simplify 2 into 2
12.071 * [taylor]: Taking taylor expansion of PI in k
12.071 * [backup-simplify]: Simplify PI into PI
12.072 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.073 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.073 * [taylor]: Taking taylor expansion of (log n) in k
12.073 * [taylor]: Taking taylor expansion of n in k
12.073 * [backup-simplify]: Simplify n into n
12.073 * [backup-simplify]: Simplify (log n) into (log n)
12.073 * [backup-simplify]: Simplify (- 1) into -1
12.074 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.074 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.075 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
12.076 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
12.077 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
12.078 * [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)))))
12.080 * [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)))))
12.081 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.081 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.083 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.083 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.084 * [backup-simplify]: Simplify (- 0) into 0
12.084 * [backup-simplify]: Simplify (+ 0 0) into 0
12.085 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
12.086 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.087 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
12.089 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.089 * [taylor]: Taking taylor expansion of 0 in k
12.089 * [backup-simplify]: Simplify 0 into 0
12.089 * [backup-simplify]: Simplify 0 into 0
12.090 * [backup-simplify]: Simplify 0 into 0
12.091 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.092 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.095 * [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
12.095 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.096 * [backup-simplify]: Simplify (- 0) into 0
12.096 * [backup-simplify]: Simplify (+ 0 0) into 0
12.097 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
12.098 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.100 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
12.102 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.102 * [taylor]: Taking taylor expansion of 0 in k
12.102 * [backup-simplify]: Simplify 0 into 0
12.102 * [backup-simplify]: Simplify 0 into 0
12.102 * [backup-simplify]: Simplify 0 into 0
12.102 * [backup-simplify]: Simplify 0 into 0
12.104 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.105 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.110 * [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
12.111 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.111 * [backup-simplify]: Simplify (- 0) into 0
12.112 * [backup-simplify]: Simplify (+ 0 0) into 0
12.113 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
12.115 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.117 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
12.119 * [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
12.119 * [taylor]: Taking taylor expansion of 0 in k
12.119 * [backup-simplify]: Simplify 0 into 0
12.119 * [backup-simplify]: Simplify 0 into 0
12.121 * [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))))))
12.121 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
12.122 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
12.122 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
12.122 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
12.122 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
12.122 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
12.122 * [taylor]: Taking taylor expansion of 1/2 in k
12.122 * [backup-simplify]: Simplify 1/2 into 1/2
12.122 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
12.122 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.122 * [taylor]: Taking taylor expansion of k in k
12.122 * [backup-simplify]: Simplify 0 into 0
12.122 * [backup-simplify]: Simplify 1 into 1
12.122 * [backup-simplify]: Simplify (/ 1 1) into 1
12.122 * [taylor]: Taking taylor expansion of 1 in k
12.122 * [backup-simplify]: Simplify 1 into 1
12.122 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.122 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.122 * [taylor]: Taking taylor expansion of -2 in k
12.122 * [backup-simplify]: Simplify -2 into -2
12.123 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.123 * [taylor]: Taking taylor expansion of PI in k
12.123 * [backup-simplify]: Simplify PI into PI
12.123 * [taylor]: Taking taylor expansion of n in k
12.123 * [backup-simplify]: Simplify n into n
12.123 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.123 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.123 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.124 * [backup-simplify]: Simplify (+ 1 0) into 1
12.124 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.125 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
12.125 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
12.125 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
12.125 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
12.125 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
12.125 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
12.125 * [taylor]: Taking taylor expansion of 1/2 in n
12.125 * [backup-simplify]: Simplify 1/2 into 1/2
12.125 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.125 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.125 * [taylor]: Taking taylor expansion of k in n
12.125 * [backup-simplify]: Simplify k into k
12.125 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.125 * [taylor]: Taking taylor expansion of 1 in n
12.125 * [backup-simplify]: Simplify 1 into 1
12.125 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.125 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.125 * [taylor]: Taking taylor expansion of -2 in n
12.125 * [backup-simplify]: Simplify -2 into -2
12.125 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.125 * [taylor]: Taking taylor expansion of PI in n
12.125 * [backup-simplify]: Simplify PI into PI
12.125 * [taylor]: Taking taylor expansion of n in n
12.126 * [backup-simplify]: Simplify 0 into 0
12.126 * [backup-simplify]: Simplify 1 into 1
12.126 * [backup-simplify]: Simplify (/ PI 1) into PI
12.127 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.128 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.128 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.128 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
12.130 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.131 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.132 * [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)))))
12.132 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
12.132 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
12.132 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
12.132 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
12.132 * [taylor]: Taking taylor expansion of 1/2 in n
12.132 * [backup-simplify]: Simplify 1/2 into 1/2
12.132 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.132 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.132 * [taylor]: Taking taylor expansion of k in n
12.132 * [backup-simplify]: Simplify k into k
12.132 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.132 * [taylor]: Taking taylor expansion of 1 in n
12.132 * [backup-simplify]: Simplify 1 into 1
12.132 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.133 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.133 * [taylor]: Taking taylor expansion of -2 in n
12.133 * [backup-simplify]: Simplify -2 into -2
12.133 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.133 * [taylor]: Taking taylor expansion of PI in n
12.133 * [backup-simplify]: Simplify PI into PI
12.133 * [taylor]: Taking taylor expansion of n in n
12.133 * [backup-simplify]: Simplify 0 into 0
12.133 * [backup-simplify]: Simplify 1 into 1
12.133 * [backup-simplify]: Simplify (/ PI 1) into PI
12.134 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.135 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.135 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.135 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
12.137 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.138 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.139 * [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)))))
12.139 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
12.139 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
12.139 * [taylor]: Taking taylor expansion of 1/2 in k
12.139 * [backup-simplify]: Simplify 1/2 into 1/2
12.139 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
12.139 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
12.139 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.139 * [taylor]: Taking taylor expansion of k in k
12.139 * [backup-simplify]: Simplify 0 into 0
12.139 * [backup-simplify]: Simplify 1 into 1
12.140 * [backup-simplify]: Simplify (/ 1 1) into 1
12.140 * [taylor]: Taking taylor expansion of 1 in k
12.140 * [backup-simplify]: Simplify 1 into 1
12.140 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
12.140 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
12.140 * [taylor]: Taking taylor expansion of (* -2 PI) in k
12.140 * [taylor]: Taking taylor expansion of -2 in k
12.140 * [backup-simplify]: Simplify -2 into -2
12.140 * [taylor]: Taking taylor expansion of PI in k
12.140 * [backup-simplify]: Simplify PI into PI
12.140 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.141 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.141 * [taylor]: Taking taylor expansion of (log n) in k
12.141 * [taylor]: Taking taylor expansion of n in k
12.141 * [backup-simplify]: Simplify n into n
12.141 * [backup-simplify]: Simplify (log n) into (log n)
12.142 * [backup-simplify]: Simplify (+ 1 0) into 1
12.142 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.143 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
12.144 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
12.145 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
12.146 * [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)))))
12.147 * [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)))))
12.148 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.149 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.156 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
12.157 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.157 * [backup-simplify]: Simplify (+ 0 0) into 0
12.158 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
12.159 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.161 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
12.163 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.163 * [taylor]: Taking taylor expansion of 0 in k
12.163 * [backup-simplify]: Simplify 0 into 0
12.163 * [backup-simplify]: Simplify 0 into 0
12.163 * [backup-simplify]: Simplify 0 into 0
12.164 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.165 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.169 * [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
12.169 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.169 * [backup-simplify]: Simplify (+ 0 0) into 0
12.170 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
12.172 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.174 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
12.176 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.176 * [taylor]: Taking taylor expansion of 0 in k
12.176 * [backup-simplify]: Simplify 0 into 0
12.176 * [backup-simplify]: Simplify 0 into 0
12.177 * [backup-simplify]: Simplify 0 into 0
12.177 * [backup-simplify]: Simplify 0 into 0
12.178 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.179 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.185 * [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
12.186 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.186 * [backup-simplify]: Simplify (+ 0 0) into 0
12.187 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
12.189 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.191 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
12.193 * [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
12.194 * [taylor]: Taking taylor expansion of 0 in k
12.194 * [backup-simplify]: Simplify 0 into 0
12.194 * [backup-simplify]: Simplify 0 into 0
12.195 * [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))))))
12.195 * * * * [progress]: [ 2 / 4 ] generating series at (2 1)
12.195 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
12.195 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0
12.195 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.195 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.195 * [taylor]: Taking taylor expansion of k in k
12.195 * [backup-simplify]: Simplify 0 into 0
12.195 * [backup-simplify]: Simplify 1 into 1
12.196 * [backup-simplify]: Simplify (/ 1 1) into 1
12.196 * [backup-simplify]: Simplify (sqrt 0) into 0
12.198 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.198 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.198 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.198 * [taylor]: Taking taylor expansion of k in k
12.198 * [backup-simplify]: Simplify 0 into 0
12.198 * [backup-simplify]: Simplify 1 into 1
12.198 * [backup-simplify]: Simplify (/ 1 1) into 1
12.199 * [backup-simplify]: Simplify (sqrt 0) into 0
12.200 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.200 * [backup-simplify]: Simplify 0 into 0
12.200 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.201 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.204 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.204 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.205 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.209 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.209 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.209 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
12.209 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
12.209 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0
12.209 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.209 * [taylor]: Taking taylor expansion of k in k
12.209 * [backup-simplify]: Simplify 0 into 0
12.209 * [backup-simplify]: Simplify 1 into 1
12.210 * [backup-simplify]: Simplify (sqrt 0) into 0
12.211 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.211 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.211 * [taylor]: Taking taylor expansion of k in k
12.211 * [backup-simplify]: Simplify 0 into 0
12.211 * [backup-simplify]: Simplify 1 into 1
12.212 * [backup-simplify]: Simplify (sqrt 0) into 0
12.213 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.213 * [backup-simplify]: Simplify 0 into 0
12.213 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.216 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.216 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.220 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.220 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.221 * [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))))))))
12.221 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k)))
12.221 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0
12.221 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
12.221 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.221 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.221 * [taylor]: Taking taylor expansion of -1 in k
12.221 * [backup-simplify]: Simplify -1 into -1
12.221 * [taylor]: Taking taylor expansion of k in k
12.221 * [backup-simplify]: Simplify 0 into 0
12.221 * [backup-simplify]: Simplify 1 into 1
12.221 * [backup-simplify]: Simplify (/ -1 1) into -1
12.222 * [backup-simplify]: Simplify (sqrt 0) into 0
12.223 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.224 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
12.224 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
12.224 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.224 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.224 * [taylor]: Taking taylor expansion of -1 in k
12.224 * [backup-simplify]: Simplify -1 into -1
12.224 * [taylor]: Taking taylor expansion of k in k
12.224 * [backup-simplify]: Simplify 0 into 0
12.224 * [backup-simplify]: Simplify 1 into 1
12.224 * [backup-simplify]: Simplify (/ -1 1) into -1
12.225 * [backup-simplify]: Simplify (sqrt 0) into 0
12.226 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.227 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
12.227 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.228 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
12.231 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.233 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
12.233 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.234 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.238 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.242 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
12.243 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.244 * [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)))))
12.244 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1)
12.244 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
12.244 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
12.244 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.244 * [taylor]: Taking taylor expansion of 2 in n
12.244 * [backup-simplify]: Simplify 2 into 2
12.244 * [taylor]: Taking taylor expansion of (* n PI) in n
12.244 * [taylor]: Taking taylor expansion of n in n
12.244 * [backup-simplify]: Simplify 0 into 0
12.245 * [backup-simplify]: Simplify 1 into 1
12.245 * [taylor]: Taking taylor expansion of PI in n
12.245 * [backup-simplify]: Simplify PI into PI
12.245 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.245 * [taylor]: Taking taylor expansion of 2 in n
12.245 * [backup-simplify]: Simplify 2 into 2
12.245 * [taylor]: Taking taylor expansion of (* n PI) in n
12.245 * [taylor]: Taking taylor expansion of n in n
12.245 * [backup-simplify]: Simplify 0 into 0
12.245 * [backup-simplify]: Simplify 1 into 1
12.245 * [taylor]: Taking taylor expansion of PI in n
12.245 * [backup-simplify]: Simplify PI into PI
12.245 * [backup-simplify]: Simplify (* 0 PI) into 0
12.246 * [backup-simplify]: Simplify (* 2 0) into 0
12.246 * [backup-simplify]: Simplify 0 into 0
12.247 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.249 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.250 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.251 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.252 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.252 * [backup-simplify]: Simplify 0 into 0
12.253 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.255 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.255 * [backup-simplify]: Simplify 0 into 0
12.256 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.258 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.258 * [backup-simplify]: Simplify 0 into 0
12.260 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.261 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
12.261 * [backup-simplify]: Simplify 0 into 0
12.263 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.265 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
12.265 * [backup-simplify]: Simplify 0 into 0
12.267 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
12.269 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
12.269 * [backup-simplify]: Simplify 0 into 0
12.270 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
12.270 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
12.270 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
12.270 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.270 * [taylor]: Taking taylor expansion of 2 in n
12.270 * [backup-simplify]: Simplify 2 into 2
12.270 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.270 * [taylor]: Taking taylor expansion of PI in n
12.270 * [backup-simplify]: Simplify PI into PI
12.270 * [taylor]: Taking taylor expansion of n in n
12.271 * [backup-simplify]: Simplify 0 into 0
12.271 * [backup-simplify]: Simplify 1 into 1
12.271 * [backup-simplify]: Simplify (/ PI 1) into PI
12.271 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.271 * [taylor]: Taking taylor expansion of 2 in n
12.271 * [backup-simplify]: Simplify 2 into 2
12.271 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.271 * [taylor]: Taking taylor expansion of PI in n
12.271 * [backup-simplify]: Simplify PI into PI
12.271 * [taylor]: Taking taylor expansion of n in n
12.271 * [backup-simplify]: Simplify 0 into 0
12.271 * [backup-simplify]: Simplify 1 into 1
12.272 * [backup-simplify]: Simplify (/ PI 1) into PI
12.272 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.273 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.274 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.275 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.275 * [backup-simplify]: Simplify 0 into 0
12.276 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.277 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.277 * [backup-simplify]: Simplify 0 into 0
12.278 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.279 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.279 * [backup-simplify]: Simplify 0 into 0
12.281 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.282 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.282 * [backup-simplify]: Simplify 0 into 0
12.283 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.285 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.285 * [backup-simplify]: Simplify 0 into 0
12.286 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.288 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.288 * [backup-simplify]: Simplify 0 into 0
12.289 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
12.290 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n))
12.290 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
12.290 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.290 * [taylor]: Taking taylor expansion of -2 in n
12.290 * [backup-simplify]: Simplify -2 into -2
12.290 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.290 * [taylor]: Taking taylor expansion of PI in n
12.290 * [backup-simplify]: Simplify PI into PI
12.290 * [taylor]: Taking taylor expansion of n in n
12.290 * [backup-simplify]: Simplify 0 into 0
12.290 * [backup-simplify]: Simplify 1 into 1
12.291 * [backup-simplify]: Simplify (/ PI 1) into PI
12.291 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.291 * [taylor]: Taking taylor expansion of -2 in n
12.291 * [backup-simplify]: Simplify -2 into -2
12.291 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.291 * [taylor]: Taking taylor expansion of PI in n
12.291 * [backup-simplify]: Simplify PI into PI
12.291 * [taylor]: Taking taylor expansion of n in n
12.291 * [backup-simplify]: Simplify 0 into 0
12.291 * [backup-simplify]: Simplify 1 into 1
12.291 * [backup-simplify]: Simplify (/ PI 1) into PI
12.292 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.292 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.293 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.294 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.294 * [backup-simplify]: Simplify 0 into 0
12.295 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.296 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.296 * [backup-simplify]: Simplify 0 into 0
12.298 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.300 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.300 * [backup-simplify]: Simplify 0 into 0
12.301 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.303 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.303 * [backup-simplify]: Simplify 0 into 0
12.304 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.306 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.306 * [backup-simplify]: Simplify 0 into 0
12.307 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.308 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.309 * [backup-simplify]: Simplify 0 into 0
12.309 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
12.309 * * * * [progress]: [ 4 / 4 ] generating series at (2)
12.310 * [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)))
12.310 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0
12.310 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
12.310 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
12.310 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
12.310 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
12.310 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
12.310 * [taylor]: Taking taylor expansion of 1/2 in n
12.310 * [backup-simplify]: Simplify 1/2 into 1/2
12.310 * [taylor]: Taking taylor expansion of (- 1 k) in n
12.310 * [taylor]: Taking taylor expansion of 1 in n
12.310 * [backup-simplify]: Simplify 1 into 1
12.310 * [taylor]: Taking taylor expansion of k in n
12.310 * [backup-simplify]: Simplify k into k
12.310 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.310 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.310 * [taylor]: Taking taylor expansion of 2 in n
12.310 * [backup-simplify]: Simplify 2 into 2
12.310 * [taylor]: Taking taylor expansion of (* n PI) in n
12.310 * [taylor]: Taking taylor expansion of n in n
12.310 * [backup-simplify]: Simplify 0 into 0
12.311 * [backup-simplify]: Simplify 1 into 1
12.311 * [taylor]: Taking taylor expansion of PI in n
12.311 * [backup-simplify]: Simplify PI into PI
12.317 * [backup-simplify]: Simplify (* 0 PI) into 0
12.318 * [backup-simplify]: Simplify (* 2 0) into 0
12.320 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.322 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.323 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.323 * [backup-simplify]: Simplify (- k) into (- k)
12.323 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
12.323 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
12.325 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.326 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
12.327 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
12.327 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.327 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.327 * [taylor]: Taking taylor expansion of k in n
12.327 * [backup-simplify]: Simplify k into k
12.327 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.327 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.327 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.327 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.328 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
12.328 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
12.328 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
12.328 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
12.328 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
12.328 * [taylor]: Taking taylor expansion of 1/2 in k
12.328 * [backup-simplify]: Simplify 1/2 into 1/2
12.328 * [taylor]: Taking taylor expansion of (- 1 k) in k
12.328 * [taylor]: Taking taylor expansion of 1 in k
12.328 * [backup-simplify]: Simplify 1 into 1
12.328 * [taylor]: Taking taylor expansion of k in k
12.328 * [backup-simplify]: Simplify 0 into 0
12.328 * [backup-simplify]: Simplify 1 into 1
12.328 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.328 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.328 * [taylor]: Taking taylor expansion of 2 in k
12.328 * [backup-simplify]: Simplify 2 into 2
12.328 * [taylor]: Taking taylor expansion of (* n PI) in k
12.328 * [taylor]: Taking taylor expansion of n in k
12.328 * [backup-simplify]: Simplify n into n
12.328 * [taylor]: Taking taylor expansion of PI in k
12.328 * [backup-simplify]: Simplify PI into PI
12.328 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.328 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.328 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.329 * [backup-simplify]: Simplify (- 0) into 0
12.329 * [backup-simplify]: Simplify (+ 1 0) into 1
12.330 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.330 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
12.330 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
12.330 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.330 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.330 * [taylor]: Taking taylor expansion of k in k
12.330 * [backup-simplify]: Simplify 0 into 0
12.330 * [backup-simplify]: Simplify 1 into 1
12.331 * [backup-simplify]: Simplify (/ 1 1) into 1
12.331 * [backup-simplify]: Simplify (sqrt 0) into 0
12.333 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.333 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
12.333 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
12.333 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
12.333 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
12.333 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
12.333 * [taylor]: Taking taylor expansion of 1/2 in k
12.333 * [backup-simplify]: Simplify 1/2 into 1/2
12.333 * [taylor]: Taking taylor expansion of (- 1 k) in k
12.333 * [taylor]: Taking taylor expansion of 1 in k
12.333 * [backup-simplify]: Simplify 1 into 1
12.333 * [taylor]: Taking taylor expansion of k in k
12.333 * [backup-simplify]: Simplify 0 into 0
12.333 * [backup-simplify]: Simplify 1 into 1
12.333 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.333 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.333 * [taylor]: Taking taylor expansion of 2 in k
12.333 * [backup-simplify]: Simplify 2 into 2
12.333 * [taylor]: Taking taylor expansion of (* n PI) in k
12.333 * [taylor]: Taking taylor expansion of n in k
12.333 * [backup-simplify]: Simplify n into n
12.333 * [taylor]: Taking taylor expansion of PI in k
12.333 * [backup-simplify]: Simplify PI into PI
12.333 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.333 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.334 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.334 * [backup-simplify]: Simplify (- 0) into 0
12.334 * [backup-simplify]: Simplify (+ 1 0) into 1
12.335 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.335 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
12.335 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
12.335 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.335 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.335 * [taylor]: Taking taylor expansion of k in k
12.335 * [backup-simplify]: Simplify 0 into 0
12.335 * [backup-simplify]: Simplify 1 into 1
12.336 * [backup-simplify]: Simplify (/ 1 1) into 1
12.336 * [backup-simplify]: Simplify (sqrt 0) into 0
12.338 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.338 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0
12.338 * [taylor]: Taking taylor expansion of 0 in n
12.338 * [backup-simplify]: Simplify 0 into 0
12.338 * [backup-simplify]: Simplify 0 into 0
12.338 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
12.339 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
12.340 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
12.341 * [backup-simplify]: Simplify (- 1) into -1
12.341 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.342 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
12.343 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
12.343 * [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)))))
12.343 * [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)))))
12.343 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
12.343 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
12.344 * [taylor]: Taking taylor expansion of +nan.0 in n
12.344 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.344 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
12.344 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.344 * [taylor]: Taking taylor expansion of 2 in n
12.344 * [backup-simplify]: Simplify 2 into 2
12.344 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.345 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.345 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
12.345 * [taylor]: Taking taylor expansion of (* n PI) in n
12.345 * [taylor]: Taking taylor expansion of n in n
12.345 * [backup-simplify]: Simplify 0 into 0
12.345 * [backup-simplify]: Simplify 1 into 1
12.345 * [taylor]: Taking taylor expansion of PI in n
12.345 * [backup-simplify]: Simplify PI into PI
12.345 * [backup-simplify]: Simplify (* 0 PI) into 0
12.347 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.347 * [backup-simplify]: Simplify (sqrt 0) into 0
12.349 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
12.349 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
12.350 * [backup-simplify]: Simplify (* +nan.0 0) into 0
12.350 * [backup-simplify]: Simplify (- 0) into 0
12.350 * [backup-simplify]: Simplify 0 into 0
12.350 * [backup-simplify]: Simplify 0 into 0
12.351 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.354 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.355 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
12.356 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
12.357 * [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
12.358 * [backup-simplify]: Simplify (- 0) into 0
12.358 * [backup-simplify]: Simplify (+ 0 0) into 0
12.359 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
12.359 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
12.360 * [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)))
12.361 * [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)))))))
12.361 * [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
12.361 * [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
12.361 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
12.361 * [taylor]: Taking taylor expansion of +nan.0 in n
12.361 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.361 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
12.361 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
12.361 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.361 * [taylor]: Taking taylor expansion of 2 in n
12.361 * [backup-simplify]: Simplify 2 into 2
12.361 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.361 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.362 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.362 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.362 * [taylor]: Taking taylor expansion of 2 in n
12.362 * [backup-simplify]: Simplify 2 into 2
12.362 * [taylor]: Taking taylor expansion of (* n PI) in n
12.362 * [taylor]: Taking taylor expansion of n in n
12.362 * [backup-simplify]: Simplify 0 into 0
12.362 * [backup-simplify]: Simplify 1 into 1
12.362 * [taylor]: Taking taylor expansion of PI in n
12.362 * [backup-simplify]: Simplify PI into PI
12.362 * [backup-simplify]: Simplify (* 0 PI) into 0
12.362 * [backup-simplify]: Simplify (* 2 0) into 0
12.363 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.364 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.365 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.365 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
12.365 * [taylor]: Taking taylor expansion of (* n PI) in n
12.365 * [taylor]: Taking taylor expansion of n in n
12.365 * [backup-simplify]: Simplify 0 into 0
12.365 * [backup-simplify]: Simplify 1 into 1
12.365 * [taylor]: Taking taylor expansion of PI in n
12.365 * [backup-simplify]: Simplify PI into PI
12.365 * [backup-simplify]: Simplify (* 0 PI) into 0
12.366 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.367 * [backup-simplify]: Simplify (sqrt 0) into 0
12.367 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
12.367 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
12.367 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
12.367 * [taylor]: Taking taylor expansion of +nan.0 in n
12.367 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.367 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
12.367 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.367 * [taylor]: Taking taylor expansion of 2 in n
12.368 * [backup-simplify]: Simplify 2 into 2
12.368 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.368 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.368 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
12.368 * [taylor]: Taking taylor expansion of (* n PI) in n
12.368 * [taylor]: Taking taylor expansion of n in n
12.368 * [backup-simplify]: Simplify 0 into 0
12.368 * [backup-simplify]: Simplify 1 into 1
12.368 * [taylor]: Taking taylor expansion of PI in n
12.368 * [backup-simplify]: Simplify PI into PI
12.369 * [backup-simplify]: Simplify (* 0 PI) into 0
12.369 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.370 * [backup-simplify]: Simplify (sqrt 0) into 0
12.371 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
12.371 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.372 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
12.373 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
12.374 * [backup-simplify]: Simplify (* +nan.0 0) into 0
12.374 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
12.374 * [backup-simplify]: Simplify (* +nan.0 0) into 0
12.374 * [backup-simplify]: Simplify (- 0) into 0
12.375 * [backup-simplify]: Simplify (+ 0 0) into 0
12.375 * [backup-simplify]: Simplify (- 0) into 0
12.375 * [backup-simplify]: Simplify 0 into 0
12.377 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
12.380 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
12.382 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
12.383 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
12.383 * [backup-simplify]: Simplify 0 into 0
12.384 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.386 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.387 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.388 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
12.389 * [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
12.390 * [backup-simplify]: Simplify (- 0) into 0
12.390 * [backup-simplify]: Simplify (+ 0 0) into 0
12.391 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
12.391 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
12.393 * [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)))
12.393 * [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)))))))))
12.393 * [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
12.393 * [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
12.393 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
12.393 * [taylor]: Taking taylor expansion of +nan.0 in n
12.393 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.393 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
12.393 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
12.393 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.393 * [taylor]: Taking taylor expansion of 2 in n
12.393 * [backup-simplify]: Simplify 2 into 2
12.394 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.394 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.394 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.394 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.394 * [taylor]: Taking taylor expansion of 2 in n
12.394 * [backup-simplify]: Simplify 2 into 2
12.394 * [taylor]: Taking taylor expansion of (* n PI) in n
12.394 * [taylor]: Taking taylor expansion of n in n
12.394 * [backup-simplify]: Simplify 0 into 0
12.394 * [backup-simplify]: Simplify 1 into 1
12.394 * [taylor]: Taking taylor expansion of PI in n
12.394 * [backup-simplify]: Simplify PI into PI
12.395 * [backup-simplify]: Simplify (* 0 PI) into 0
12.395 * [backup-simplify]: Simplify (* 2 0) into 0
12.397 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.398 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.399 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.399 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
12.399 * [taylor]: Taking taylor expansion of (* n PI) in n
12.399 * [taylor]: Taking taylor expansion of n in n
12.399 * [backup-simplify]: Simplify 0 into 0
12.399 * [backup-simplify]: Simplify 1 into 1
12.399 * [taylor]: Taking taylor expansion of PI in n
12.399 * [backup-simplify]: Simplify PI into PI
12.400 * [backup-simplify]: Simplify (* 0 PI) into 0
12.402 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.402 * [backup-simplify]: Simplify (sqrt 0) into 0
12.404 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
12.404 * [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
12.404 * [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
12.404 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
12.404 * [taylor]: Taking taylor expansion of +nan.0 in n
12.404 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.404 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
12.404 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.404 * [taylor]: Taking taylor expansion of 2 in n
12.404 * [backup-simplify]: Simplify 2 into 2
12.404 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.405 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.405 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
12.405 * [taylor]: Taking taylor expansion of (* n PI) in n
12.405 * [taylor]: Taking taylor expansion of n in n
12.405 * [backup-simplify]: Simplify 0 into 0
12.405 * [backup-simplify]: Simplify 1 into 1
12.405 * [taylor]: Taking taylor expansion of PI in n
12.405 * [backup-simplify]: Simplify PI into PI
12.406 * [backup-simplify]: Simplify (* 0 PI) into 0
12.407 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.408 * [backup-simplify]: Simplify (sqrt 0) into 0
12.409 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
12.409 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n
12.409 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
12.409 * [taylor]: Taking taylor expansion of +nan.0 in n
12.409 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.409 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
12.409 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
12.409 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.409 * [taylor]: Taking taylor expansion of 2 in n
12.409 * [backup-simplify]: Simplify 2 into 2
12.410 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.410 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.410 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
12.410 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.410 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.410 * [taylor]: Taking taylor expansion of 2 in n
12.411 * [backup-simplify]: Simplify 2 into 2
12.411 * [taylor]: Taking taylor expansion of (* n PI) in n
12.411 * [taylor]: Taking taylor expansion of n in n
12.411 * [backup-simplify]: Simplify 0 into 0
12.411 * [backup-simplify]: Simplify 1 into 1
12.411 * [taylor]: Taking taylor expansion of PI in n
12.411 * [backup-simplify]: Simplify PI into PI
12.411 * [backup-simplify]: Simplify (* 0 PI) into 0
12.412 * [backup-simplify]: Simplify (* 2 0) into 0
12.413 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.415 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.416 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.417 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.417 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
12.417 * [taylor]: Taking taylor expansion of (* n PI) in n
12.417 * [taylor]: Taking taylor expansion of n in n
12.417 * [backup-simplify]: Simplify 0 into 0
12.417 * [backup-simplify]: Simplify 1 into 1
12.417 * [taylor]: Taking taylor expansion of PI in n
12.417 * [backup-simplify]: Simplify PI into PI
12.418 * [backup-simplify]: Simplify (* 0 PI) into 0
12.419 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.420 * [backup-simplify]: Simplify (sqrt 0) into 0
12.421 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
12.422 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.424 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
12.425 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
12.426 * [backup-simplify]: Simplify (* +nan.0 0) into 0
12.426 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
12.427 * [backup-simplify]: Simplify (* +nan.0 0) into 0
12.428 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.429 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.431 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
12.433 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
12.434 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
12.435 * [backup-simplify]: Simplify (* +nan.0 0) into 0
12.435 * [backup-simplify]: Simplify (- 0) into 0
12.436 * [backup-simplify]: Simplify (+ 0 0) into 0
12.436 * [backup-simplify]: Simplify (- 0) into 0
12.436 * [backup-simplify]: Simplify (+ 0 0) into 0
12.437 * [backup-simplify]: Simplify (- 0) into 0
12.437 * [backup-simplify]: Simplify 0 into 0
12.438 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.446 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.448 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.450 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.452 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
12.454 * [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))))))))
12.463 * [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))))))))
12.466 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
12.471 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
12.474 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
12.483 * [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))))))))))
12.491 * [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)))))))
12.499 * [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)))))))
12.500 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.504 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
12.505 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
12.511 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
12.520 * [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))))
12.524 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
12.528 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
12.542 * [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)))))))))))))
12.543 * [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))
12.543 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0
12.543 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
12.543 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
12.543 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.543 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.543 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
12.543 * [taylor]: Taking taylor expansion of 1/2 in n
12.543 * [backup-simplify]: Simplify 1/2 into 1/2
12.543 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
12.543 * [taylor]: Taking taylor expansion of 1 in n
12.543 * [backup-simplify]: Simplify 1 into 1
12.544 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.544 * [taylor]: Taking taylor expansion of k in n
12.544 * [backup-simplify]: Simplify k into k
12.544 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.544 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.544 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.544 * [taylor]: Taking taylor expansion of 2 in n
12.544 * [backup-simplify]: Simplify 2 into 2
12.544 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.544 * [taylor]: Taking taylor expansion of PI in n
12.544 * [backup-simplify]: Simplify PI into PI
12.544 * [taylor]: Taking taylor expansion of n in n
12.544 * [backup-simplify]: Simplify 0 into 0
12.544 * [backup-simplify]: Simplify 1 into 1
12.544 * [backup-simplify]: Simplify (/ PI 1) into PI
12.545 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.546 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.546 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.546 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
12.546 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
12.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.549 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
12.550 * [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)))))
12.550 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.550 * [taylor]: Taking taylor expansion of k in n
12.550 * [backup-simplify]: Simplify k into k
12.550 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.550 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.550 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
12.550 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
12.550 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.550 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.550 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
12.550 * [taylor]: Taking taylor expansion of 1/2 in k
12.550 * [backup-simplify]: Simplify 1/2 into 1/2
12.550 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
12.550 * [taylor]: Taking taylor expansion of 1 in k
12.550 * [backup-simplify]: Simplify 1 into 1
12.551 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.551 * [taylor]: Taking taylor expansion of k in k
12.551 * [backup-simplify]: Simplify 0 into 0
12.551 * [backup-simplify]: Simplify 1 into 1
12.551 * [backup-simplify]: Simplify (/ 1 1) into 1
12.551 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.551 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.551 * [taylor]: Taking taylor expansion of 2 in k
12.551 * [backup-simplify]: Simplify 2 into 2
12.551 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.551 * [taylor]: Taking taylor expansion of PI in k
12.551 * [backup-simplify]: Simplify PI into PI
12.551 * [taylor]: Taking taylor expansion of n in k
12.551 * [backup-simplify]: Simplify n into n
12.551 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.551 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.551 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.552 * [backup-simplify]: Simplify (- 1) into -1
12.552 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.553 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
12.553 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.553 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
12.553 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.553 * [taylor]: Taking taylor expansion of k in k
12.553 * [backup-simplify]: Simplify 0 into 0
12.553 * [backup-simplify]: Simplify 1 into 1
12.554 * [backup-simplify]: Simplify (sqrt 0) into 0
12.555 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.555 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
12.555 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
12.555 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.555 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.555 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
12.555 * [taylor]: Taking taylor expansion of 1/2 in k
12.555 * [backup-simplify]: Simplify 1/2 into 1/2
12.555 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
12.555 * [taylor]: Taking taylor expansion of 1 in k
12.555 * [backup-simplify]: Simplify 1 into 1
12.555 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.555 * [taylor]: Taking taylor expansion of k in k
12.555 * [backup-simplify]: Simplify 0 into 0
12.555 * [backup-simplify]: Simplify 1 into 1
12.555 * [backup-simplify]: Simplify (/ 1 1) into 1
12.555 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.555 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.555 * [taylor]: Taking taylor expansion of 2 in k
12.555 * [backup-simplify]: Simplify 2 into 2
12.555 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.555 * [taylor]: Taking taylor expansion of PI in k
12.555 * [backup-simplify]: Simplify PI into PI
12.555 * [taylor]: Taking taylor expansion of n in k
12.555 * [backup-simplify]: Simplify n into n
12.555 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.555 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.555 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.556 * [backup-simplify]: Simplify (- 1) into -1
12.556 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.556 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
12.556 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.556 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
12.556 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.556 * [taylor]: Taking taylor expansion of k in k
12.556 * [backup-simplify]: Simplify 0 into 0
12.557 * [backup-simplify]: Simplify 1 into 1
12.557 * [backup-simplify]: Simplify (sqrt 0) into 0
12.558 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.558 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0
12.558 * [taylor]: Taking taylor expansion of 0 in n
12.558 * [backup-simplify]: Simplify 0 into 0
12.558 * [backup-simplify]: Simplify 0 into 0
12.558 * [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))))))))
12.558 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
12.558 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
12.558 * [taylor]: Taking taylor expansion of +nan.0 in n
12.558 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.558 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
12.558 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
12.558 * [taylor]: Taking taylor expansion of 1/2 in n
12.558 * [backup-simplify]: Simplify 1/2 into 1/2
12.558 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
12.558 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
12.558 * [taylor]: Taking taylor expansion of 1 in n
12.558 * [backup-simplify]: Simplify 1 into 1
12.558 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.558 * [taylor]: Taking taylor expansion of k in n
12.558 * [backup-simplify]: Simplify k into k
12.558 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.559 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.559 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.559 * [taylor]: Taking taylor expansion of 2 in n
12.559 * [backup-simplify]: Simplify 2 into 2
12.559 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.559 * [taylor]: Taking taylor expansion of PI in n
12.559 * [backup-simplify]: Simplify PI into PI
12.559 * [taylor]: Taking taylor expansion of n in n
12.559 * [backup-simplify]: Simplify 0 into 0
12.559 * [backup-simplify]: Simplify 1 into 1
12.559 * [backup-simplify]: Simplify (/ PI 1) into PI
12.559 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.560 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.560 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.560 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
12.561 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.562 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
12.562 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
12.563 * [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)))))
12.564 * [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))))))
12.564 * [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)))))))
12.565 * [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)))))))
12.565 * [backup-simplify]: Simplify 0 into 0
12.567 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.567 * [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))))))))
12.568 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
12.568 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
12.568 * [taylor]: Taking taylor expansion of +nan.0 in n
12.568 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.568 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
12.568 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
12.568 * [taylor]: Taking taylor expansion of 1/2 in n
12.568 * [backup-simplify]: Simplify 1/2 into 1/2
12.568 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
12.568 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
12.568 * [taylor]: Taking taylor expansion of 1 in n
12.568 * [backup-simplify]: Simplify 1 into 1
12.568 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.568 * [taylor]: Taking taylor expansion of k in n
12.568 * [backup-simplify]: Simplify k into k
12.568 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.568 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.568 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.568 * [taylor]: Taking taylor expansion of 2 in n
12.568 * [backup-simplify]: Simplify 2 into 2
12.568 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.568 * [taylor]: Taking taylor expansion of PI in n
12.568 * [backup-simplify]: Simplify PI into PI
12.568 * [taylor]: Taking taylor expansion of n in n
12.568 * [backup-simplify]: Simplify 0 into 0
12.568 * [backup-simplify]: Simplify 1 into 1
12.568 * [backup-simplify]: Simplify (/ PI 1) into PI
12.569 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.569 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.569 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.569 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
12.570 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.571 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
12.572 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
12.572 * [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)))))
12.573 * [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))))))
12.574 * [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)))))))
12.575 * [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)))))))
12.580 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.580 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.582 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.582 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.582 * [backup-simplify]: Simplify (- 0) into 0
12.582 * [backup-simplify]: Simplify (+ 0 0) into 0
12.583 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.584 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
12.585 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
12.586 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.587 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
12.587 * [backup-simplify]: Simplify (- 0) into 0
12.587 * [backup-simplify]: Simplify 0 into 0
12.587 * [backup-simplify]: Simplify 0 into 0
12.590 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.590 * [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))))))))
12.590 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
12.590 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
12.590 * [taylor]: Taking taylor expansion of +nan.0 in n
12.590 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.591 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
12.591 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
12.591 * [taylor]: Taking taylor expansion of 1/2 in n
12.591 * [backup-simplify]: Simplify 1/2 into 1/2
12.591 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
12.591 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
12.591 * [taylor]: Taking taylor expansion of 1 in n
12.591 * [backup-simplify]: Simplify 1 into 1
12.591 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.591 * [taylor]: Taking taylor expansion of k in n
12.591 * [backup-simplify]: Simplify k into k
12.591 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.591 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.591 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.591 * [taylor]: Taking taylor expansion of 2 in n
12.591 * [backup-simplify]: Simplify 2 into 2
12.591 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.591 * [taylor]: Taking taylor expansion of PI in n
12.591 * [backup-simplify]: Simplify PI into PI
12.591 * [taylor]: Taking taylor expansion of n in n
12.591 * [backup-simplify]: Simplify 0 into 0
12.591 * [backup-simplify]: Simplify 1 into 1
12.591 * [backup-simplify]: Simplify (/ PI 1) into PI
12.591 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.592 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.592 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.592 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
12.593 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.594 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
12.595 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
12.595 * [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)))))
12.596 * [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))))))
12.597 * [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)))))))
12.598 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
12.600 * [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))))))))
12.601 * [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)))
12.601 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0
12.601 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
12.601 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
12.601 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
12.601 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
12.601 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
12.601 * [taylor]: Taking taylor expansion of 1/2 in n
12.601 * [backup-simplify]: Simplify 1/2 into 1/2
12.601 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.601 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.601 * [taylor]: Taking taylor expansion of k in n
12.601 * [backup-simplify]: Simplify k into k
12.601 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.601 * [taylor]: Taking taylor expansion of 1 in n
12.601 * [backup-simplify]: Simplify 1 into 1
12.601 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.601 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.601 * [taylor]: Taking taylor expansion of -2 in n
12.601 * [backup-simplify]: Simplify -2 into -2
12.601 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.601 * [taylor]: Taking taylor expansion of PI in n
12.601 * [backup-simplify]: Simplify PI into PI
12.601 * [taylor]: Taking taylor expansion of n in n
12.601 * [backup-simplify]: Simplify 0 into 0
12.601 * [backup-simplify]: Simplify 1 into 1
12.601 * [backup-simplify]: Simplify (/ PI 1) into PI
12.602 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.602 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.602 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.602 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
12.603 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.604 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.605 * [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)))))
12.605 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.605 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.605 * [taylor]: Taking taylor expansion of -1 in n
12.605 * [backup-simplify]: Simplify -1 into -1
12.605 * [taylor]: Taking taylor expansion of k in n
12.605 * [backup-simplify]: Simplify k into k
12.605 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.605 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.605 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.605 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.606 * [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)))
12.606 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
12.606 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
12.606 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
12.606 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
12.606 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
12.606 * [taylor]: Taking taylor expansion of 1/2 in k
12.606 * [backup-simplify]: Simplify 1/2 into 1/2
12.606 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
12.606 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.606 * [taylor]: Taking taylor expansion of k in k
12.606 * [backup-simplify]: Simplify 0 into 0
12.606 * [backup-simplify]: Simplify 1 into 1
12.606 * [backup-simplify]: Simplify (/ 1 1) into 1
12.606 * [taylor]: Taking taylor expansion of 1 in k
12.606 * [backup-simplify]: Simplify 1 into 1
12.606 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.606 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.606 * [taylor]: Taking taylor expansion of -2 in k
12.606 * [backup-simplify]: Simplify -2 into -2
12.606 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.606 * [taylor]: Taking taylor expansion of PI in k
12.606 * [backup-simplify]: Simplify PI into PI
12.606 * [taylor]: Taking taylor expansion of n in k
12.606 * [backup-simplify]: Simplify n into n
12.606 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.606 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.607 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.607 * [backup-simplify]: Simplify (+ 1 0) into 1
12.607 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.607 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
12.607 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
12.607 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.607 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.607 * [taylor]: Taking taylor expansion of -1 in k
12.607 * [backup-simplify]: Simplify -1 into -1
12.607 * [taylor]: Taking taylor expansion of k in k
12.607 * [backup-simplify]: Simplify 0 into 0
12.607 * [backup-simplify]: Simplify 1 into 1
12.608 * [backup-simplify]: Simplify (/ -1 1) into -1
12.608 * [backup-simplify]: Simplify (sqrt 0) into 0
12.609 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.609 * [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)))))
12.609 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
12.609 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
12.609 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
12.609 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
12.609 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
12.609 * [taylor]: Taking taylor expansion of 1/2 in k
12.609 * [backup-simplify]: Simplify 1/2 into 1/2
12.609 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
12.609 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.609 * [taylor]: Taking taylor expansion of k in k
12.609 * [backup-simplify]: Simplify 0 into 0
12.609 * [backup-simplify]: Simplify 1 into 1
12.609 * [backup-simplify]: Simplify (/ 1 1) into 1
12.610 * [taylor]: Taking taylor expansion of 1 in k
12.610 * [backup-simplify]: Simplify 1 into 1
12.610 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.610 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.610 * [taylor]: Taking taylor expansion of -2 in k
12.610 * [backup-simplify]: Simplify -2 into -2
12.610 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.610 * [taylor]: Taking taylor expansion of PI in k
12.610 * [backup-simplify]: Simplify PI into PI
12.610 * [taylor]: Taking taylor expansion of n in k
12.610 * [backup-simplify]: Simplify n into n
12.610 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.610 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.610 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.610 * [backup-simplify]: Simplify (+ 1 0) into 1
12.611 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.611 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
12.611 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
12.611 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.611 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.611 * [taylor]: Taking taylor expansion of -1 in k
12.611 * [backup-simplify]: Simplify -1 into -1
12.611 * [taylor]: Taking taylor expansion of k in k
12.611 * [backup-simplify]: Simplify 0 into 0
12.611 * [backup-simplify]: Simplify 1 into 1
12.611 * [backup-simplify]: Simplify (/ -1 1) into -1
12.611 * [backup-simplify]: Simplify (sqrt 0) into 0
12.612 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.612 * [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)))))
12.613 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
12.613 * [taylor]: Taking taylor expansion of +nan.0 in n
12.613 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.613 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
12.613 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
12.613 * [taylor]: Taking taylor expansion of 1/2 in n
12.613 * [backup-simplify]: Simplify 1/2 into 1/2
12.613 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
12.613 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.613 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.613 * [taylor]: Taking taylor expansion of -2 in n
12.613 * [backup-simplify]: Simplify -2 into -2
12.613 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.613 * [taylor]: Taking taylor expansion of PI in n
12.613 * [backup-simplify]: Simplify PI into PI
12.613 * [taylor]: Taking taylor expansion of n in n
12.613 * [backup-simplify]: Simplify 0 into 0
12.613 * [backup-simplify]: Simplify 1 into 1
12.613 * [backup-simplify]: Simplify (/ PI 1) into PI
12.613 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.614 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.614 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.614 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.614 * [taylor]: Taking taylor expansion of k in n
12.614 * [backup-simplify]: Simplify k into k
12.614 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.614 * [taylor]: Taking taylor expansion of 1 in n
12.614 * [backup-simplify]: Simplify 1 into 1
12.615 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.615 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.616 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
12.616 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.617 * [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)))))
12.618 * [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))))))
12.619 * [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))))))
12.619 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
12.621 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.622 * [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))))))
12.622 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
12.622 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
12.622 * [taylor]: Taking taylor expansion of +nan.0 in n
12.622 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.622 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
12.622 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
12.622 * [taylor]: Taking taylor expansion of 1/2 in n
12.622 * [backup-simplify]: Simplify 1/2 into 1/2
12.622 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
12.622 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.622 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.622 * [taylor]: Taking taylor expansion of -2 in n
12.622 * [backup-simplify]: Simplify -2 into -2
12.622 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.622 * [taylor]: Taking taylor expansion of PI in n
12.622 * [backup-simplify]: Simplify PI into PI
12.622 * [taylor]: Taking taylor expansion of n in n
12.622 * [backup-simplify]: Simplify 0 into 0
12.622 * [backup-simplify]: Simplify 1 into 1
12.623 * [backup-simplify]: Simplify (/ PI 1) into PI
12.623 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.624 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.624 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.624 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.624 * [taylor]: Taking taylor expansion of k in n
12.624 * [backup-simplify]: Simplify k into k
12.624 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.624 * [taylor]: Taking taylor expansion of 1 in n
12.624 * [backup-simplify]: Simplify 1 into 1
12.625 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.625 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.625 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
12.626 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.627 * [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)))))
12.628 * [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))))))
12.628 * [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)))))))
12.629 * [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)))))))
12.630 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.630 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.630 * [backup-simplify]: Simplify (+ 0 0) into 0
12.631 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.632 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.633 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
12.633 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
12.634 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
12.635 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.636 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
12.636 * [backup-simplify]: Simplify 0 into 0
12.637 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.641 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.642 * [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))))))
12.643 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
12.643 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
12.643 * [taylor]: Taking taylor expansion of +nan.0 in n
12.643 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.643 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
12.643 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
12.643 * [taylor]: Taking taylor expansion of 1/2 in n
12.643 * [backup-simplify]: Simplify 1/2 into 1/2
12.643 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
12.643 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.643 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.643 * [taylor]: Taking taylor expansion of -2 in n
12.643 * [backup-simplify]: Simplify -2 into -2
12.643 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.643 * [taylor]: Taking taylor expansion of PI in n
12.643 * [backup-simplify]: Simplify PI into PI
12.643 * [taylor]: Taking taylor expansion of n in n
12.643 * [backup-simplify]: Simplify 0 into 0
12.643 * [backup-simplify]: Simplify 1 into 1
12.644 * [backup-simplify]: Simplify (/ PI 1) into PI
12.644 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.646 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.646 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.646 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.646 * [taylor]: Taking taylor expansion of k in n
12.646 * [backup-simplify]: Simplify k into k
12.646 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.646 * [taylor]: Taking taylor expansion of 1 in n
12.646 * [backup-simplify]: Simplify 1 into 1
12.647 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.648 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.649 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
12.650 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.651 * [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)))))
12.652 * [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))))))
12.653 * [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)))))))
12.654 * [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)))))))
12.657 * [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))))))))))))
12.657 * * * [progress]: simplifying candidates
12.657 * * * * [progress]: [ 1 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (log1p (expm1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.657 * * * * [progress]: [ 2 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (expm1 (log1p (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.657 * * * * [progress]: [ 3 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
12.657 * * * * [progress]: [ 4 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
12.657 * * * * [progress]: [ 5 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
12.657 * * * * [progress]: [ 6 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
12.657 * * * * [progress]: [ 7 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
12.657 * * * * [progress]: [ 8 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
12.657 * * * * [progress]: [ 9 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
12.657 * * * * [progress]: [ 10 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))>
12.657 * * * * [progress]: [ 11 / 196 ] 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)))))>
12.657 * * * * [progress]: [ 12 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2)))))>
12.657 * * * * [progress]: [ 13 / 196 ] 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)))))>
12.657 * * * * [progress]: [ 14 / 196 ] 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)))))>
12.658 * * * * [progress]: [ 15 / 196 ] 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))))>
12.658 * * * * [progress]: [ 16 / 196 ] 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)))))>
12.658 * * * * [progress]: [ 17 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2)))))>
12.658 * * * * [progress]: [ 18 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2))))>
12.658 * * * * [progress]: [ 19 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
12.658 * * * * [progress]: [ 20 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
12.658 * * * * [progress]: [ 21 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
12.658 * * * * [progress]: [ 22 / 196 ] 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)))))>
12.658 * * * * [progress]: [ 23 / 196 ] 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)))))>
12.658 * * * * [progress]: [ 24 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2))))>
12.658 * * * * [progress]: [ 25 / 196 ] 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)))))>
12.658 * * * * [progress]: [ 26 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2)))))>
12.658 * * * * [progress]: [ 27 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))))>
12.658 * * * * [progress]: [ 28 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
12.658 * * * * [progress]: [ 29 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
12.658 * * * * [progress]: [ 30 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
12.658 * * * * [progress]: [ 31 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
12.658 * * * * [progress]: [ 32 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) (/ 1 2))))>
12.658 * * * * [progress]: [ 33 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))))>
12.658 * * * * [progress]: [ 34 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1)))>
12.658 * * * * [progress]: [ 35 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.658 * * * * [progress]: [ 36 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (log (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.658 * * * * [progress]: [ 37 / 196 ] 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))))))>
12.658 * * * * [progress]: [ 38 / 196 ] 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))))))>
12.659 * * * * [progress]: [ 39 / 196 ] 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))))))>
12.659 * * * * [progress]: [ 40 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.659 * * * * [progress]: [ 41 / 196 ] 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)))))>
12.659 * * * * [progress]: [ 42 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (posit16->real (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.659 * * * * [progress]: [ 43 / 196 ] simplifiying candidate #<alt (λ (k n) (* (log1p (expm1 (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 44 / 196 ] simplifiying candidate #<alt (λ (k n) (* (expm1 (log1p (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 45 / 196 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 46 / 196 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 47 / 196 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) (- 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 48 / 196 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- (/ 1 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 49 / 196 ] simplifiying candidate #<alt (λ (k n) (* (pow (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 50 / 196 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 51 / 196 ] simplifiying candidate #<alt (λ (k n) (* (exp (- 0 (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 52 / 196 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log 1) (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 53 / 196 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 54 / 196 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 55 / 196 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 56 / 196 ] 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))))>
12.659 * * * * [progress]: [ 57 / 196 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 58 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 59 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (- 1) (- (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 60 / 196 ] 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))))>
12.659 * * * * [progress]: [ 61 / 196 ] 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))))>
12.659 * * * * [progress]: [ 62 / 196 ] 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))))>
12.659 * * * * [progress]: [ 63 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.659 * * * * [progress]: [ 64 / 196 ] 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))))>
12.660 * * * * [progress]: [ 65 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 66 / 196 ] 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))))>
12.660 * * * * [progress]: [ 67 / 196 ] 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))))>
12.660 * * * * [progress]: [ 68 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 69 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 70 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 71 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 72 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 73 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 74 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 75 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt 1)) (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 76 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 77 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 1) (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 78 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 79 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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12.660 * * * * [progress]: [ 81 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 82 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 83 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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12.660 * * * * [progress]: [ 86 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 87 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (cbrt 1))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 88 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt k) (sqrt 1))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 89 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.660 * * * * [progress]: [ 90 / 196 ] simplifiying candidate #<alt (λ (k n) (* (posit16->real (real->posit16 (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 91 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (log1p (expm1 (* (* 2 PI) n))) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 92 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (expm1 (log1p (* (* 2 PI) n))) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 93 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 94 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 95 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 96 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (+ (log 2) (log PI)) (log n))) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 97 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (log (* 2 PI)) (log n))) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 98 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (log (* (* 2 PI) n))) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 99 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (log (exp (* (* 2 PI) n))) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 100 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 101 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 102 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) (cbrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 103 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 104 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 105 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 1 (* (* 2 PI) n)) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 106 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 107 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 108 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) 1) n) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 109 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 110 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (posit16->real (real->posit16 (* (* 2 PI) n))) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 111 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
12.661 * * * * [progress]: [ 112 / 196 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
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12.661 * * * * [progress]: [ 115 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
12.661 * * * * [progress]: [ 116 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
12.661 * * * * [progress]: [ 117 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
12.662 * * * * [progress]: [ 118 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
12.662 * * * * [progress]: [ 119 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.662 * * * * [progress]: [ 120 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
12.662 * * * * [progress]: [ 121 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
12.662 * * * * [progress]: [ 122 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
12.662 * * * * [progress]: [ 123 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
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12.662 * * * * [progress]: [ 125 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
12.662 * * * * [progress]: [ 126 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
12.662 * * * * [progress]: [ 127 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
12.662 * * * * [progress]: [ 128 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
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12.662 * * * * [progress]: [ 130 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
12.662 * * * * [progress]: [ 131 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
12.662 * * * * [progress]: [ 132 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
12.662 * * * * [progress]: [ 133 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
12.662 * * * * [progress]: [ 134 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.662 * * * * [progress]: [ 135 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.662 * * * * [progress]: [ 136 / 196 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.662 * * * * [progress]: [ 137 / 196 ] 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))))))>
12.662 * * * * [progress]: [ 138 / 196 ] 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))))))>
12.662 * * * * [progress]: [ 139 / 196 ] 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))))))>
12.662 * * * * [progress]: [ 140 / 196 ] 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))))))>
12.662 * * * * [progress]: [ 141 / 196 ] 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))))))>
12.662 * * * * [progress]: [ 142 / 196 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))))>
12.663 * * * * [progress]: [ 143 / 196 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.663 * * * * [progress]: [ 144 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.663 * * * * [progress]: [ 145 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
12.663 * * * * [progress]: [ 146 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.663 * * * * [progress]: [ 147 / 196 ] 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)))))>
12.663 * * * * [progress]: [ 148 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.663 * * * * [progress]: [ 149 / 196 ] 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)))))>
12.663 * * * * [progress]: [ 150 / 196 ] 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))))))>
12.663 * * * * [progress]: [ 151 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
12.663 * * * * [progress]: [ 152 / 196 ] 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))))))>
12.663 * * * * [progress]: [ 153 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
12.663 * * * * [progress]: [ 154 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))))>
12.663 * * * * [progress]: [ 155 / 196 ] 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)))))>
12.663 * * * * [progress]: [ 156 / 196 ] 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)))))>
12.663 * * * * [progress]: [ 157 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.663 * * * * [progress]: [ 158 / 196 ] 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))))>
12.663 * * * * [progress]: [ 159 / 196 ] 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)))))>
12.663 * * * * [progress]: [ 160 / 196 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.663 * * * * [progress]: [ 161 / 196 ] 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)))))>
12.663 * * * * [progress]: [ 162 / 196 ] 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)))))>
12.663 * * * * [progress]: [ 163 / 196 ] 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)))))>
12.663 * * * * [progress]: [ 164 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.663 * * * * [progress]: [ 165 / 196 ] 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)))))>
12.663 * * * * [progress]: [ 166 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) 1) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 167 / 196 ] 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)))))>
12.664 * * * * [progress]: [ 168 / 196 ] 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)))))>
12.664 * * * * [progress]: [ 169 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 170 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt 1)) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 171 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 172 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 173 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 174 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 175 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 176 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 177 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 178 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 179 / 196 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 180 / 196 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
12.664 * * * * [progress]: [ 181 / 196 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* (* 2 PI) n) (/ k 2))))>
12.664 * * * * [progress]: [ 182 / 196 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))>
12.664 * * * * [progress]: [ 183 / 196 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
12.664 * * * * [progress]: [ 184 / 196 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
12.664 * * * * [progress]: [ 185 / 196 ] 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)))))))>
12.664 * * * * [progress]: [ 186 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))>
12.664 * * * * [progress]: [ 187 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))>
12.664 * * * * [progress]: [ 188 / 196 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
12.664 * * * * [progress]: [ 189 / 196 ] 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))))>
12.664 * * * * [progress]: [ 190 / 196 ] 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))))>
12.665 * * * * [progress]: [ 191 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.665 * * * * [progress]: [ 192 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.665 * * * * [progress]: [ 193 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.665 * * * * [progress]: [ 194 / 196 ] 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))))))))))))))>
12.665 * * * * [progress]: [ 195 / 196 ] 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)))))))))>
12.665 * * * * [progress]: [ 196 / 196 ] 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)))))))))))))>
12.667 * [simplify]: Simplifying (expm1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (log1p (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (+ (+ (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 (* (* 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(* 2 PI) n) (/ (/ (- 1 k) 2) 2)), (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)), (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (expm1 (/ 1 (sqrt k))), (log1p (/ 1 (sqrt k))), (- 1/2), (- 1), (- (/ 1 2)), (- (log (sqrt k))), (- 0 (log (sqrt k))), (- (log 1) (log (sqrt k))), (log (/ 1 (sqrt k))), (exp (/ 1 (sqrt k))), (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))), (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))), (cbrt (/ 1 (sqrt k))), (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))), (sqrt (/ 1 (sqrt k))), (sqrt (/ 1 (sqrt k))), (- 1), (- (sqrt k)), (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (cbrt 1) (cbrt (sqrt k))), (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))), (/ (cbrt 1) (sqrt (cbrt k))), (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))), (/ (cbrt 1) (sqrt (sqrt k))), (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)), (/ (cbrt 1) (sqrt k)), (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))), (/ (cbrt 1) (sqrt (sqrt k))), (/ (* (cbrt 1) (cbrt 1)) 1), (/ (cbrt 1) (sqrt k)), (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ (sqrt 1) (cbrt (sqrt k))), (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))), (/ (sqrt 1) (sqrt (cbrt k))), (/ (sqrt 1) (sqrt (sqrt k))), (/ (sqrt 1) (sqrt (sqrt k))), (/ (sqrt 1) (sqrt 1)), (/ (sqrt 1) (sqrt k)), (/ (sqrt 1) (sqrt (sqrt k))), (/ (sqrt 1) (sqrt (sqrt k))), (/ (sqrt 1) 1), (/ (sqrt 1) (sqrt k)), (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ 1 (cbrt (sqrt k))), (/ 1 (sqrt (* (cbrt k) (cbrt k)))), (/ 1 (sqrt (cbrt k))), (/ 1 (sqrt (sqrt k))), (/ 1 (sqrt (sqrt k))), (/ 1 (sqrt 1)), (/ 1 (sqrt k)), (/ 1 (sqrt (sqrt k))), (/ 1 (sqrt (sqrt k))), (/ 1 1), (/ 1 (sqrt k)), (/ 1 (sqrt k)), (/ (sqrt k) 1), (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))), (/ 1 (sqrt (* (cbrt k) (cbrt k)))), (/ 1 (sqrt (sqrt k))), (/ 1 (sqrt 1)), (/ 1 (sqrt (sqrt k))), (/ 1 1), (/ (sqrt k) (cbrt 1)), (/ (sqrt k) (sqrt 1)), (/ (sqrt k) 1), (real->posit16 (/ 1 (sqrt k))), (expm1 (* (* 2 PI) n)), (log1p (* (* 2 PI) n)), (* (* 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)), (expm1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))), (log1p (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))), (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2))), (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))), (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))), (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))), (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))), (+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) 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(/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))), (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))), (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))), (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))), (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))), (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))), (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))), (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))), (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))), (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))), (* (/ 1 (sqrt k)) 1), (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))), (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))), (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))), (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))), (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))), (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))), (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))), (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))), (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))), (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))), (* 2 (* n PI)), (* 2 (* n PI)), (* 2 (* n PI)), (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))), (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))), (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
12.670 * * [simplify]: iteration 1: (353 enodes)
12.876 * * [simplify]: iteration 2: (1552 enodes)
13.374 * * [simplify]: Extracting #0: cost 104 inf + 0
13.376 * * [simplify]: Extracting #1: cost 563 inf + 3
13.382 * * [simplify]: Extracting #2: cost 956 inf + 8620
13.404 * * [simplify]: Extracting #3: cost 931 inf + 74129
13.467 * * [simplify]: Extracting #4: cost 464 inf + 256677
13.545 * * [simplify]: Extracting #5: cost 102 inf + 401683
13.648 * * [simplify]: Extracting #6: cost 9 inf + 444892
13.755 * * [simplify]: Extracting #7: cost 0 inf + 447130
13.845 * * [simplify]: Extracting #8: cost 0 inf + 445723
13.943 * * [simplify]: Extracting #9: cost 0 inf + 445498
14.034 * * [simplify]: Extracting #10: cost 0 inf + 445473
14.111 * [simplify]: Simplified to (expm1 (pow (* 2 (* n PI)) (/ (- 1 k) 2))), (log1p (pow (* 2 (* n PI)) (/ (- 1 k) 2))), (* (/ (- 1 k) 2) (log (* 2 (* n PI)))), (* (/ (- 1 k) 2) (log (* 2 (* n PI)))), (* (/ (- 1 k) 2) (log (* 2 (* n PI)))), (* (/ (- 1 k) 2) (log (* 2 (* n PI)))), (/ (- 1 k) 2), (/ (- 1 k) 2), (/ (- 1 k) 2), (sqrt (* 2 (* n PI))), (pow (* 2 (* n PI)) (/ k 2)), (pow (* 2 (* n PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))), (pow (* 2 (* n PI)) (sqrt (/ (- 1 k) 2))), (pow (* 2 (* n PI)) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2)))), (pow (* 2 (* n PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))), (pow (* 2 (* n PI)) (* (cbrt (- 1 k)) (cbrt (- 1 k)))), (pow (* 2 (* n PI)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2))), (pow (* 2 (* n PI)) (/ (sqrt (- 1 k)) (sqrt 2))), (pow (* 2 (* n PI)) (sqrt (- 1 k))), (pow (* 2 (* n PI)) (/ (/ 1 (cbrt 2)) (cbrt 2))), (pow (* 2 (* n PI)) (/ 1 (sqrt 2))), (* 2 (* n PI)), (pow (* 2 (* n PI)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2)))), (pow (* 2 (* n PI)) (/ (+ (sqrt k) 1) (sqrt 2))), (pow (* 2 (* n PI)) (+ (sqrt k) 1)), (pow (* 2 (* n PI)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2)))), (pow (* 2 (* n PI)) (/ (+ (sqrt k) 1) (sqrt 2))), (pow (* 2 (* n PI)) (+ (sqrt k) 1)), (pow (* 2 (* n PI)) (/ (/ 1 (cbrt 2)) (cbrt 2))), (pow (* 2 (* n PI)) (/ 1 (sqrt 2))), (* 2 (* n PI)), (* 2 (* n PI)), (pow (* 2 (* n PI)) (- 1 k)), (pow (* 2 PI) (/ (- 1 k) 2)), (pow n (/ (- 1 k) 2)), (* (/ (- 1 k) 2) (log (* 2 (* n PI)))), (exp (pow (* 2 (* n PI)) (/ (- 1 k) 2))), (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))), (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))), (pow (pow (* 2 (* n PI)) (/ (- 1 k) 2)) 3), (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))), (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))), (pow (* 2 (* n PI)) (- 1/4 (/ k 4))), (pow (* 2 (* n PI)) (- 1/4 (/ k 4))), (real->posit16 (pow (* 2 (* n PI)) (/ (- 1 k) 2))), (expm1 (/ 1 (sqrt k))), (log1p (/ 1 (sqrt k))), -1/2, -1, -1/2, (- (log (sqrt k))), (- (log (sqrt k))), (- (log (sqrt k))), (- (log (sqrt k))), (exp (/ 1 (sqrt k))), (/ 1 (* (sqrt k) k)), (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))), (cbrt (/ 1 (sqrt k))), (* (/ 1 (sqrt k)) (* (/ 1 (sqrt k)) (/ 1 (sqrt k)))), (sqrt (/ 1 (sqrt k))), (sqrt (/ 1 (sqrt k))), -1, (- (sqrt k)), (* (/ 1 (cbrt (sqrt k))) (/ 1 (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))) (/ 1 (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))) (/ 1 (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))) (/ 1 (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))), (expm1 (* 2 (* n PI))), (log1p (* 2 (* n PI))), (* 2 (* n PI)), (* 2 (* n PI)), (log (* 2 (* n PI))), (log (* 2 (* n PI))), (log (* 2 (* n PI))), (* (exp (* n PI)) (exp (* n PI))), (* n (* (* (* 8 PI) PI) (* PI (* n n)))), (* (* 2 PI) (* (* 2 PI) (* (* n (* n n)) (* 2 PI)))), (* (cbrt (* 2 (* n PI))) (cbrt (* 2 (* n PI)))), (cbrt (* 2 (* n PI))), (* (* 2 (* n PI)) (* (* (* n PI) (* n PI)) 4)), (sqrt (* 2 (* n PI))), (sqrt (* 2 (* n PI))), (* (* 2 PI) (* (cbrt n) (cbrt n))), (* (* (sqrt n) PI) 2), (* 2 PI), (* n PI), (real->posit16 (* 2 (* n PI))), (expm1 (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))), (log1p (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))), (exp (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))), (/ (/ (pow (pow (* 2 (* n PI)) (/ (- 1 k) 2)) 3) (sqrt k)) k), (* (* (pow (pow (* 2 (* n PI)) (/ (- 1 k) 2)) 3) (/ 1 (sqrt k))) (* (/ 1 (sqrt k)) (/ 1 (sqrt k)))), (* (cbrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))), (cbrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))), (* (* (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))), (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))), (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))), (sqrt (* 2 (* n PI))), (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))), (* (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))), (* (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))), (* (sqrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (- 1/4 (/ k 4)))), (* (sqrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (- 1/4 (/ k 4)))), (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (sqrt k))), (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (sqrt k))), (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (sqrt k))), (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (sqrt k))), (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)), (/ (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (sqrt k)), (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt k)), (/ 1 (sqrt k)), (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt k)), (* (cbrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))), (* (sqrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)), (/ (sqrt (* 2 (* n PI))) (sqrt k)), (pow (* 2 (* n PI)) (/ (- 1 k) 2)), (real->posit16 (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))), (- (fma (* (log (* 2 PI)) 1/4) (* (log n) (* (exp (* 1/2 (log (* 2 (* n PI))))) (* k k))) (fma 1/8 (* (exp (* 1/2 (log (* 2 (* n PI))))) (* (* (log n) k) (* (log n) k))) (fma (* (* (log (* 2 PI)) (log (* 2 PI))) 1/8) (* (exp (* 1/2 (log (* 2 (* n PI))))) (* k k)) (exp (* 1/2 (log (* 2 (* n PI)))))))) (* (* k (+ (* (log n) (exp (* 1/2 (log (* 2 (* n PI)))))) (* (exp (* 1/2 (log (* 2 (* n PI))))) (log (* 2 PI))))) 1/2)), (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))), (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* (- 1 k) 1/2))), (+ (- +nan.0 (* +nan.0 k)) (- (* (* +nan.0 k) k))), (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* (* k k) k)))), (+ (- (/ +nan.0 (* k k))) (- (/ +nan.0 k) +nan.0)), (* 2 (* n PI)), (* 2 (* n PI)), (* 2 (* n PI)), (+ (- (* (* (* n PI) k) (* +nan.0 (sqrt 2)))) (fma (* +nan.0 (sqrt 2)) (* n PI) (- (- (* (* (* (* n PI) k) (* +nan.0 (sqrt 2))) (log (* 2 PI))) (* (* +nan.0 (sqrt 2)) (- (* (* (log n) k) (* n PI)) (* (* n PI) (* n PI)))))))), (- (- (* +nan.0 (/ (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) k)) (- (/ (* +nan.0 (/ (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) k)) k) (* (/ (/ (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) k) (* k k)) +nan.0)))), (+ (* (- +nan.0) (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* (- 1 k) 1/2))) k)) (* +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))))))
14.124 * * * [progress]: adding candidates to table
16.358 * * [progress]: iteration 3 / 4
16.359 * * * [progress]: picking best candidate
16.411 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
16.411 * * * [progress]: localizing error
16.449 * * * [progress]: generating rewritten candidates
16.449 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1)
16.492 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1)
16.509 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1)
16.523 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1)
16.553 * * * [progress]: generating series expansions
16.553 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1)
16.555 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))
16.555 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
16.555 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
16.555 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
16.555 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
16.555 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
16.555 * [taylor]: Taking taylor expansion of 1/2 in k
16.555 * [backup-simplify]: Simplify 1/2 into 1/2
16.555 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
16.555 * [taylor]: Taking taylor expansion of 1/2 in k
16.555 * [backup-simplify]: Simplify 1/2 into 1/2
16.555 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
16.555 * [taylor]: Taking taylor expansion of 1/2 in k
16.555 * [backup-simplify]: Simplify 1/2 into 1/2
16.555 * [taylor]: Taking taylor expansion of k in k
16.555 * [backup-simplify]: Simplify 0 into 0
16.555 * [backup-simplify]: Simplify 1 into 1
16.555 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
16.555 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
16.555 * [taylor]: Taking taylor expansion of 2 in k
16.555 * [backup-simplify]: Simplify 2 into 2
16.555 * [taylor]: Taking taylor expansion of (* n PI) in k
16.555 * [taylor]: Taking taylor expansion of n in k
16.555 * [backup-simplify]: Simplify n into n
16.555 * [taylor]: Taking taylor expansion of PI in k
16.555 * [backup-simplify]: Simplify PI into PI
16.555 * [backup-simplify]: Simplify (* n PI) into (* n PI)
16.555 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
16.556 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
16.556 * [backup-simplify]: Simplify (* 1/2 0) into 0
16.556 * [backup-simplify]: Simplify (- 0) into 0
16.557 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.557 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
16.558 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
16.558 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
16.558 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
16.558 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
16.558 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
16.558 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
16.558 * [taylor]: Taking taylor expansion of 1/2 in n
16.558 * [backup-simplify]: Simplify 1/2 into 1/2
16.558 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
16.558 * [taylor]: Taking taylor expansion of 1/2 in n
16.558 * [backup-simplify]: Simplify 1/2 into 1/2
16.558 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
16.558 * [taylor]: Taking taylor expansion of 1/2 in n
16.558 * [backup-simplify]: Simplify 1/2 into 1/2
16.558 * [taylor]: Taking taylor expansion of k in n
16.558 * [backup-simplify]: Simplify k into k
16.558 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
16.558 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.558 * [taylor]: Taking taylor expansion of 2 in n
16.558 * [backup-simplify]: Simplify 2 into 2
16.558 * [taylor]: Taking taylor expansion of (* n PI) in n
16.558 * [taylor]: Taking taylor expansion of n in n
16.558 * [backup-simplify]: Simplify 0 into 0
16.558 * [backup-simplify]: Simplify 1 into 1
16.558 * [taylor]: Taking taylor expansion of PI in n
16.558 * [backup-simplify]: Simplify PI into PI
16.559 * [backup-simplify]: Simplify (* 0 PI) into 0
16.559 * [backup-simplify]: Simplify (* 2 0) into 0
16.561 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.562 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
16.563 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.563 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
16.563 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
16.564 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
16.564 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
16.565 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.566 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
16.567 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
16.567 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
16.568 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
16.568 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
16.568 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
16.568 * [taylor]: Taking taylor expansion of 1/2 in n
16.568 * [backup-simplify]: Simplify 1/2 into 1/2
16.568 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
16.568 * [taylor]: Taking taylor expansion of 1/2 in n
16.568 * [backup-simplify]: Simplify 1/2 into 1/2
16.568 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
16.568 * [taylor]: Taking taylor expansion of 1/2 in n
16.568 * [backup-simplify]: Simplify 1/2 into 1/2
16.568 * [taylor]: Taking taylor expansion of k in n
16.568 * [backup-simplify]: Simplify k into k
16.568 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
16.568 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.568 * [taylor]: Taking taylor expansion of 2 in n
16.568 * [backup-simplify]: Simplify 2 into 2
16.568 * [taylor]: Taking taylor expansion of (* n PI) in n
16.568 * [taylor]: Taking taylor expansion of n in n
16.568 * [backup-simplify]: Simplify 0 into 0
16.568 * [backup-simplify]: Simplify 1 into 1
16.568 * [taylor]: Taking taylor expansion of PI in n
16.568 * [backup-simplify]: Simplify PI into PI
16.569 * [backup-simplify]: Simplify (* 0 PI) into 0
16.569 * [backup-simplify]: Simplify (* 2 0) into 0
16.571 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.573 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
16.574 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.574 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
16.574 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
16.574 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
16.574 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
16.576 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.577 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
16.583 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
16.583 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
16.583 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
16.583 * [taylor]: Taking taylor expansion of 1/2 in k
16.583 * [backup-simplify]: Simplify 1/2 into 1/2
16.583 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
16.583 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
16.583 * [taylor]: Taking taylor expansion of 1/2 in k
16.583 * [backup-simplify]: Simplify 1/2 into 1/2
16.583 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
16.583 * [taylor]: Taking taylor expansion of 1/2 in k
16.583 * [backup-simplify]: Simplify 1/2 into 1/2
16.583 * [taylor]: Taking taylor expansion of k in k
16.583 * [backup-simplify]: Simplify 0 into 0
16.584 * [backup-simplify]: Simplify 1 into 1
16.584 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
16.584 * [taylor]: Taking taylor expansion of (log n) in k
16.584 * [taylor]: Taking taylor expansion of n in k
16.584 * [backup-simplify]: Simplify n into n
16.584 * [backup-simplify]: Simplify (log n) into (log n)
16.584 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
16.584 * [taylor]: Taking taylor expansion of (* 2 PI) in k
16.584 * [taylor]: Taking taylor expansion of 2 in k
16.584 * [backup-simplify]: Simplify 2 into 2
16.584 * [taylor]: Taking taylor expansion of PI in k
16.584 * [backup-simplify]: Simplify PI into PI
16.585 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.586 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.586 * [backup-simplify]: Simplify (* 1/2 0) into 0
16.587 * [backup-simplify]: Simplify (- 0) into 0
16.587 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.588 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.589 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
16.590 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
16.592 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
16.593 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
16.594 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.595 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
16.597 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.597 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
16.597 * [backup-simplify]: Simplify (- 0) into 0
16.598 * [backup-simplify]: Simplify (+ 0 0) into 0
16.598 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
16.600 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.601 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
16.603 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.603 * [taylor]: Taking taylor expansion of 0 in k
16.603 * [backup-simplify]: Simplify 0 into 0
16.603 * [backup-simplify]: Simplify 0 into 0
16.604 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
16.605 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
16.606 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.607 * [backup-simplify]: Simplify (+ 0 0) into 0
16.608 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
16.608 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.608 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.610 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
16.613 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
16.616 * [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)))))))
16.619 * [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)))))))
16.620 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
16.622 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
16.625 * [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
16.626 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
16.627 * [backup-simplify]: Simplify (- 0) into 0
16.627 * [backup-simplify]: Simplify (+ 0 0) into 0
16.629 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
16.631 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.632 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
16.635 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.635 * [taylor]: Taking taylor expansion of 0 in k
16.635 * [backup-simplify]: Simplify 0 into 0
16.635 * [backup-simplify]: Simplify 0 into 0
16.635 * [backup-simplify]: Simplify 0 into 0
16.637 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
16.638 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
16.641 * [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
16.642 * [backup-simplify]: Simplify (+ 0 0) into 0
16.643 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
16.643 * [backup-simplify]: Simplify (- 0) into 0
16.644 * [backup-simplify]: Simplify (+ 0 0) into 0
16.646 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
16.649 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0
16.653 * [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)))))
16.658 * [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)))))
16.664 * [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)))))))
16.665 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))))
16.665 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
16.665 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
16.665 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
16.665 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
16.665 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
16.665 * [taylor]: Taking taylor expansion of 1/2 in k
16.665 * [backup-simplify]: Simplify 1/2 into 1/2
16.665 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
16.665 * [taylor]: Taking taylor expansion of 1/2 in k
16.665 * [backup-simplify]: Simplify 1/2 into 1/2
16.665 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.665 * [taylor]: Taking taylor expansion of 1/2 in k
16.665 * [backup-simplify]: Simplify 1/2 into 1/2
16.665 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.665 * [taylor]: Taking taylor expansion of k in k
16.665 * [backup-simplify]: Simplify 0 into 0
16.665 * [backup-simplify]: Simplify 1 into 1
16.665 * [backup-simplify]: Simplify (/ 1 1) into 1
16.665 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
16.665 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
16.665 * [taylor]: Taking taylor expansion of 2 in k
16.665 * [backup-simplify]: Simplify 2 into 2
16.665 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.665 * [taylor]: Taking taylor expansion of PI in k
16.665 * [backup-simplify]: Simplify PI into PI
16.665 * [taylor]: Taking taylor expansion of n in k
16.665 * [backup-simplify]: Simplify n into n
16.665 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.665 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
16.665 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
16.666 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.666 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.666 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.667 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
16.667 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
16.667 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))))
16.667 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
16.667 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
16.667 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
16.667 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
16.667 * [taylor]: Taking taylor expansion of 1/2 in n
16.667 * [backup-simplify]: Simplify 1/2 into 1/2
16.667 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.667 * [taylor]: Taking taylor expansion of 1/2 in n
16.667 * [backup-simplify]: Simplify 1/2 into 1/2
16.667 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.667 * [taylor]: Taking taylor expansion of 1/2 in n
16.667 * [backup-simplify]: Simplify 1/2 into 1/2
16.667 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.667 * [taylor]: Taking taylor expansion of k in n
16.667 * [backup-simplify]: Simplify k into k
16.667 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.667 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
16.667 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.667 * [taylor]: Taking taylor expansion of 2 in n
16.667 * [backup-simplify]: Simplify 2 into 2
16.667 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.667 * [taylor]: Taking taylor expansion of PI in n
16.667 * [backup-simplify]: Simplify PI into PI
16.667 * [taylor]: Taking taylor expansion of n in n
16.667 * [backup-simplify]: Simplify 0 into 0
16.667 * [backup-simplify]: Simplify 1 into 1
16.667 * [backup-simplify]: Simplify (/ PI 1) into PI
16.668 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.668 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.668 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.669 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.669 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.669 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
16.670 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.670 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
16.671 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
16.671 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
16.671 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
16.671 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
16.671 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
16.671 * [taylor]: Taking taylor expansion of 1/2 in n
16.671 * [backup-simplify]: Simplify 1/2 into 1/2
16.671 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.671 * [taylor]: Taking taylor expansion of 1/2 in n
16.671 * [backup-simplify]: Simplify 1/2 into 1/2
16.671 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.671 * [taylor]: Taking taylor expansion of 1/2 in n
16.671 * [backup-simplify]: Simplify 1/2 into 1/2
16.671 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.671 * [taylor]: Taking taylor expansion of k in n
16.671 * [backup-simplify]: Simplify k into k
16.671 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.671 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
16.671 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.671 * [taylor]: Taking taylor expansion of 2 in n
16.671 * [backup-simplify]: Simplify 2 into 2
16.671 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.671 * [taylor]: Taking taylor expansion of PI in n
16.671 * [backup-simplify]: Simplify PI into PI
16.671 * [taylor]: Taking taylor expansion of n in n
16.671 * [backup-simplify]: Simplify 0 into 0
16.671 * [backup-simplify]: Simplify 1 into 1
16.672 * [backup-simplify]: Simplify (/ PI 1) into PI
16.672 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.673 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.673 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.673 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.673 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.673 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
16.674 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.674 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
16.675 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
16.675 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
16.675 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
16.675 * [taylor]: Taking taylor expansion of 1/2 in k
16.675 * [backup-simplify]: Simplify 1/2 into 1/2
16.675 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
16.675 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
16.675 * [taylor]: Taking taylor expansion of 1/2 in k
16.675 * [backup-simplify]: Simplify 1/2 into 1/2
16.675 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.675 * [taylor]: Taking taylor expansion of 1/2 in k
16.675 * [backup-simplify]: Simplify 1/2 into 1/2
16.675 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.676 * [taylor]: Taking taylor expansion of k in k
16.676 * [backup-simplify]: Simplify 0 into 0
16.676 * [backup-simplify]: Simplify 1 into 1
16.676 * [backup-simplify]: Simplify (/ 1 1) into 1
16.676 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
16.676 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
16.676 * [taylor]: Taking taylor expansion of (* 2 PI) in k
16.676 * [taylor]: Taking taylor expansion of 2 in k
16.676 * [backup-simplify]: Simplify 2 into 2
16.676 * [taylor]: Taking taylor expansion of PI in k
16.676 * [backup-simplify]: Simplify PI into PI
16.676 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.677 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.677 * [taylor]: Taking taylor expansion of (log n) in k
16.677 * [taylor]: Taking taylor expansion of n in k
16.677 * [backup-simplify]: Simplify n into n
16.677 * [backup-simplify]: Simplify (log n) into (log n)
16.678 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.678 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.678 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.678 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
16.679 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
16.679 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
16.680 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
16.681 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
16.682 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
16.682 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.683 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
16.684 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.684 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.684 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
16.684 * [backup-simplify]: Simplify (- 0) into 0
16.685 * [backup-simplify]: Simplify (+ 0 0) into 0
16.685 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
16.686 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.687 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
16.688 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.688 * [taylor]: Taking taylor expansion of 0 in k
16.688 * [backup-simplify]: Simplify 0 into 0
16.688 * [backup-simplify]: Simplify 0 into 0
16.688 * [backup-simplify]: Simplify 0 into 0
16.688 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.689 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
16.692 * [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
16.692 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.693 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
16.693 * [backup-simplify]: Simplify (- 0) into 0
16.693 * [backup-simplify]: Simplify (+ 0 0) into 0
16.695 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
16.696 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.698 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
16.700 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.700 * [taylor]: Taking taylor expansion of 0 in k
16.700 * [backup-simplify]: Simplify 0 into 0
16.700 * [backup-simplify]: Simplify 0 into 0
16.700 * [backup-simplify]: Simplify 0 into 0
16.700 * [backup-simplify]: Simplify 0 into 0
16.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.703 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.714 * [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
16.714 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.715 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
16.715 * [backup-simplify]: Simplify (- 0) into 0
16.716 * [backup-simplify]: Simplify (+ 0 0) into 0
16.717 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
16.717 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.719 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
16.721 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
16.721 * [taylor]: Taking taylor expansion of 0 in k
16.721 * [backup-simplify]: Simplify 0 into 0
16.721 * [backup-simplify]: Simplify 0 into 0
16.721 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))
16.722 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)))
16.722 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
16.722 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
16.722 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
16.722 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
16.722 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
16.722 * [taylor]: Taking taylor expansion of 1/2 in k
16.722 * [backup-simplify]: Simplify 1/2 into 1/2
16.722 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
16.722 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.722 * [taylor]: Taking taylor expansion of 1/2 in k
16.722 * [backup-simplify]: Simplify 1/2 into 1/2
16.722 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.722 * [taylor]: Taking taylor expansion of k in k
16.722 * [backup-simplify]: Simplify 0 into 0
16.722 * [backup-simplify]: Simplify 1 into 1
16.722 * [backup-simplify]: Simplify (/ 1 1) into 1
16.722 * [taylor]: Taking taylor expansion of 1/2 in k
16.722 * [backup-simplify]: Simplify 1/2 into 1/2
16.723 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
16.723 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
16.723 * [taylor]: Taking taylor expansion of -2 in k
16.723 * [backup-simplify]: Simplify -2 into -2
16.723 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.723 * [taylor]: Taking taylor expansion of PI in k
16.723 * [backup-simplify]: Simplify PI into PI
16.723 * [taylor]: Taking taylor expansion of n in k
16.723 * [backup-simplify]: Simplify n into n
16.723 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.723 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
16.723 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
16.723 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.723 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.724 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
16.724 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
16.724 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
16.724 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
16.724 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
16.724 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
16.724 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.724 * [taylor]: Taking taylor expansion of 1/2 in n
16.724 * [backup-simplify]: Simplify 1/2 into 1/2
16.724 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.724 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.724 * [taylor]: Taking taylor expansion of 1/2 in n
16.724 * [backup-simplify]: Simplify 1/2 into 1/2
16.724 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.724 * [taylor]: Taking taylor expansion of k in n
16.724 * [backup-simplify]: Simplify k into k
16.724 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.724 * [taylor]: Taking taylor expansion of 1/2 in n
16.724 * [backup-simplify]: Simplify 1/2 into 1/2
16.724 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
16.724 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.724 * [taylor]: Taking taylor expansion of -2 in n
16.724 * [backup-simplify]: Simplify -2 into -2
16.724 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.724 * [taylor]: Taking taylor expansion of PI in n
16.724 * [backup-simplify]: Simplify PI into PI
16.724 * [taylor]: Taking taylor expansion of n in n
16.724 * [backup-simplify]: Simplify 0 into 0
16.724 * [backup-simplify]: Simplify 1 into 1
16.725 * [backup-simplify]: Simplify (/ PI 1) into PI
16.725 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.725 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.726 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.726 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.726 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
16.727 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.727 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
16.728 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
16.728 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
16.728 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
16.728 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
16.728 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.728 * [taylor]: Taking taylor expansion of 1/2 in n
16.728 * [backup-simplify]: Simplify 1/2 into 1/2
16.728 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.728 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.728 * [taylor]: Taking taylor expansion of 1/2 in n
16.728 * [backup-simplify]: Simplify 1/2 into 1/2
16.728 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.728 * [taylor]: Taking taylor expansion of k in n
16.728 * [backup-simplify]: Simplify k into k
16.728 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.728 * [taylor]: Taking taylor expansion of 1/2 in n
16.728 * [backup-simplify]: Simplify 1/2 into 1/2
16.728 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
16.728 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.728 * [taylor]: Taking taylor expansion of -2 in n
16.728 * [backup-simplify]: Simplify -2 into -2
16.728 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.728 * [taylor]: Taking taylor expansion of PI in n
16.728 * [backup-simplify]: Simplify PI into PI
16.728 * [taylor]: Taking taylor expansion of n in n
16.728 * [backup-simplify]: Simplify 0 into 0
16.728 * [backup-simplify]: Simplify 1 into 1
16.729 * [backup-simplify]: Simplify (/ PI 1) into PI
16.729 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.730 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.730 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.730 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.730 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
16.731 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.731 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
16.732 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
16.732 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
16.732 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
16.732 * [taylor]: Taking taylor expansion of 1/2 in k
16.732 * [backup-simplify]: Simplify 1/2 into 1/2
16.732 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
16.732 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
16.732 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.732 * [taylor]: Taking taylor expansion of 1/2 in k
16.732 * [backup-simplify]: Simplify 1/2 into 1/2
16.732 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.732 * [taylor]: Taking taylor expansion of k in k
16.732 * [backup-simplify]: Simplify 0 into 0
16.732 * [backup-simplify]: Simplify 1 into 1
16.733 * [backup-simplify]: Simplify (/ 1 1) into 1
16.733 * [taylor]: Taking taylor expansion of 1/2 in k
16.733 * [backup-simplify]: Simplify 1/2 into 1/2
16.733 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
16.733 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
16.733 * [taylor]: Taking taylor expansion of (* -2 PI) in k
16.733 * [taylor]: Taking taylor expansion of -2 in k
16.733 * [backup-simplify]: Simplify -2 into -2
16.733 * [taylor]: Taking taylor expansion of PI in k
16.733 * [backup-simplify]: Simplify PI into PI
16.733 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.734 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.734 * [taylor]: Taking taylor expansion of (log n) in k
16.734 * [taylor]: Taking taylor expansion of n in k
16.734 * [backup-simplify]: Simplify n into n
16.734 * [backup-simplify]: Simplify (log n) into (log n)
16.734 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.734 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.735 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
16.735 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
16.736 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
16.737 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
16.737 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
16.738 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
16.739 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.739 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
16.740 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
16.740 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.741 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
16.741 * [backup-simplify]: Simplify (+ 0 0) into 0
16.741 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
16.742 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.743 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
16.745 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.745 * [taylor]: Taking taylor expansion of 0 in k
16.745 * [backup-simplify]: Simplify 0 into 0
16.745 * [backup-simplify]: Simplify 0 into 0
16.745 * [backup-simplify]: Simplify 0 into 0
16.747 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.748 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
16.751 * [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
16.751 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.752 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
16.753 * [backup-simplify]: Simplify (+ 0 0) into 0
16.754 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
16.755 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.757 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
16.760 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.760 * [taylor]: Taking taylor expansion of 0 in k
16.760 * [backup-simplify]: Simplify 0 into 0
16.760 * [backup-simplify]: Simplify 0 into 0
16.760 * [backup-simplify]: Simplify 0 into 0
16.760 * [backup-simplify]: Simplify 0 into 0
16.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.762 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.768 * [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
16.769 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.770 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
16.771 * [backup-simplify]: Simplify (+ 0 0) into 0
16.772 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
16.774 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.776 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
16.779 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
16.779 * [taylor]: Taking taylor expansion of 0 in k
16.779 * [backup-simplify]: Simplify 0 into 0
16.779 * [backup-simplify]: Simplify 0 into 0
16.780 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))
16.780 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1)
16.781 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))
16.781 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
16.781 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
16.781 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
16.781 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
16.781 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
16.781 * [taylor]: Taking taylor expansion of 1/2 in k
16.781 * [backup-simplify]: Simplify 1/2 into 1/2
16.781 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
16.781 * [taylor]: Taking taylor expansion of 1/2 in k
16.781 * [backup-simplify]: Simplify 1/2 into 1/2
16.781 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
16.781 * [taylor]: Taking taylor expansion of 1/2 in k
16.781 * [backup-simplify]: Simplify 1/2 into 1/2
16.781 * [taylor]: Taking taylor expansion of k in k
16.781 * [backup-simplify]: Simplify 0 into 0
16.781 * [backup-simplify]: Simplify 1 into 1
16.781 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
16.781 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
16.781 * [taylor]: Taking taylor expansion of 2 in k
16.781 * [backup-simplify]: Simplify 2 into 2
16.781 * [taylor]: Taking taylor expansion of (* n PI) in k
16.781 * [taylor]: Taking taylor expansion of n in k
16.781 * [backup-simplify]: Simplify n into n
16.781 * [taylor]: Taking taylor expansion of PI in k
16.782 * [backup-simplify]: Simplify PI into PI
16.782 * [backup-simplify]: Simplify (* n PI) into (* n PI)
16.782 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
16.782 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
16.782 * [backup-simplify]: Simplify (* 1/2 0) into 0
16.783 * [backup-simplify]: Simplify (- 0) into 0
16.783 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.783 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
16.784 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
16.784 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
16.784 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
16.784 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
16.784 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
16.784 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
16.784 * [taylor]: Taking taylor expansion of 1/2 in n
16.784 * [backup-simplify]: Simplify 1/2 into 1/2
16.784 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
16.784 * [taylor]: Taking taylor expansion of 1/2 in n
16.784 * [backup-simplify]: Simplify 1/2 into 1/2
16.784 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
16.784 * [taylor]: Taking taylor expansion of 1/2 in n
16.784 * [backup-simplify]: Simplify 1/2 into 1/2
16.784 * [taylor]: Taking taylor expansion of k in n
16.784 * [backup-simplify]: Simplify k into k
16.784 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
16.784 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.784 * [taylor]: Taking taylor expansion of 2 in n
16.784 * [backup-simplify]: Simplify 2 into 2
16.784 * [taylor]: Taking taylor expansion of (* n PI) in n
16.784 * [taylor]: Taking taylor expansion of n in n
16.784 * [backup-simplify]: Simplify 0 into 0
16.784 * [backup-simplify]: Simplify 1 into 1
16.784 * [taylor]: Taking taylor expansion of PI in n
16.784 * [backup-simplify]: Simplify PI into PI
16.785 * [backup-simplify]: Simplify (* 0 PI) into 0
16.785 * [backup-simplify]: Simplify (* 2 0) into 0
16.787 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.788 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
16.789 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.790 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
16.790 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
16.790 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
16.790 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
16.791 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.792 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
16.794 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
16.794 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
16.794 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
16.794 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
16.794 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
16.794 * [taylor]: Taking taylor expansion of 1/2 in n
16.794 * [backup-simplify]: Simplify 1/2 into 1/2
16.794 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
16.794 * [taylor]: Taking taylor expansion of 1/2 in n
16.794 * [backup-simplify]: Simplify 1/2 into 1/2
16.794 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
16.794 * [taylor]: Taking taylor expansion of 1/2 in n
16.794 * [backup-simplify]: Simplify 1/2 into 1/2
16.794 * [taylor]: Taking taylor expansion of k in n
16.794 * [backup-simplify]: Simplify k into k
16.794 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
16.794 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.794 * [taylor]: Taking taylor expansion of 2 in n
16.794 * [backup-simplify]: Simplify 2 into 2
16.794 * [taylor]: Taking taylor expansion of (* n PI) in n
16.794 * [taylor]: Taking taylor expansion of n in n
16.794 * [backup-simplify]: Simplify 0 into 0
16.794 * [backup-simplify]: Simplify 1 into 1
16.794 * [taylor]: Taking taylor expansion of PI in n
16.794 * [backup-simplify]: Simplify PI into PI
16.795 * [backup-simplify]: Simplify (* 0 PI) into 0
16.795 * [backup-simplify]: Simplify (* 2 0) into 0
16.796 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.798 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
16.799 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.799 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
16.799 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
16.799 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
16.799 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
16.801 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.802 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
16.803 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
16.803 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
16.803 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
16.803 * [taylor]: Taking taylor expansion of 1/2 in k
16.803 * [backup-simplify]: Simplify 1/2 into 1/2
16.803 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
16.803 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
16.803 * [taylor]: Taking taylor expansion of 1/2 in k
16.803 * [backup-simplify]: Simplify 1/2 into 1/2
16.803 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
16.803 * [taylor]: Taking taylor expansion of 1/2 in k
16.803 * [backup-simplify]: Simplify 1/2 into 1/2
16.803 * [taylor]: Taking taylor expansion of k in k
16.804 * [backup-simplify]: Simplify 0 into 0
16.804 * [backup-simplify]: Simplify 1 into 1
16.804 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
16.804 * [taylor]: Taking taylor expansion of (log n) in k
16.804 * [taylor]: Taking taylor expansion of n in k
16.804 * [backup-simplify]: Simplify n into n
16.804 * [backup-simplify]: Simplify (log n) into (log n)
16.804 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
16.804 * [taylor]: Taking taylor expansion of (* 2 PI) in k
16.804 * [taylor]: Taking taylor expansion of 2 in k
16.804 * [backup-simplify]: Simplify 2 into 2
16.804 * [taylor]: Taking taylor expansion of PI in k
16.804 * [backup-simplify]: Simplify PI into PI
16.804 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.805 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.806 * [backup-simplify]: Simplify (* 1/2 0) into 0
16.807 * [backup-simplify]: Simplify (- 0) into 0
16.807 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.808 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.809 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
16.810 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
16.811 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
16.813 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
16.814 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.815 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
16.817 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.817 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
16.818 * [backup-simplify]: Simplify (- 0) into 0
16.818 * [backup-simplify]: Simplify (+ 0 0) into 0
16.819 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
16.820 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.821 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
16.823 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.823 * [taylor]: Taking taylor expansion of 0 in k
16.823 * [backup-simplify]: Simplify 0 into 0
16.823 * [backup-simplify]: Simplify 0 into 0
16.824 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
16.825 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
16.827 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.827 * [backup-simplify]: Simplify (+ 0 0) into 0
16.828 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
16.828 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.829 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.830 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
16.833 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
16.837 * [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)))))))
16.840 * [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)))))))
16.841 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
16.842 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
16.852 * [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
16.853 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
16.854 * [backup-simplify]: Simplify (- 0) into 0
16.854 * [backup-simplify]: Simplify (+ 0 0) into 0
16.855 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
16.857 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.858 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
16.861 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.861 * [taylor]: Taking taylor expansion of 0 in k
16.861 * [backup-simplify]: Simplify 0 into 0
16.861 * [backup-simplify]: Simplify 0 into 0
16.861 * [backup-simplify]: Simplify 0 into 0
16.863 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
16.864 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
16.867 * [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
16.868 * [backup-simplify]: Simplify (+ 0 0) into 0
16.869 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
16.869 * [backup-simplify]: Simplify (- 0) into 0
16.870 * [backup-simplify]: Simplify (+ 0 0) into 0
16.872 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
16.875 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0
16.879 * [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)))))
16.884 * [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)))))
16.894 * [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)))))))
16.895 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))))
16.895 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
16.895 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
16.895 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
16.895 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
16.895 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
16.895 * [taylor]: Taking taylor expansion of 1/2 in k
16.895 * [backup-simplify]: Simplify 1/2 into 1/2
16.895 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
16.895 * [taylor]: Taking taylor expansion of 1/2 in k
16.895 * [backup-simplify]: Simplify 1/2 into 1/2
16.895 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.895 * [taylor]: Taking taylor expansion of 1/2 in k
16.895 * [backup-simplify]: Simplify 1/2 into 1/2
16.895 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.895 * [taylor]: Taking taylor expansion of k in k
16.895 * [backup-simplify]: Simplify 0 into 0
16.895 * [backup-simplify]: Simplify 1 into 1
16.896 * [backup-simplify]: Simplify (/ 1 1) into 1
16.896 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
16.896 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
16.896 * [taylor]: Taking taylor expansion of 2 in k
16.896 * [backup-simplify]: Simplify 2 into 2
16.896 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.896 * [taylor]: Taking taylor expansion of PI in k
16.896 * [backup-simplify]: Simplify PI into PI
16.896 * [taylor]: Taking taylor expansion of n in k
16.896 * [backup-simplify]: Simplify n into n
16.896 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.896 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
16.896 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
16.897 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.897 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.898 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.898 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
16.898 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
16.898 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))))
16.899 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
16.899 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
16.899 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
16.899 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
16.899 * [taylor]: Taking taylor expansion of 1/2 in n
16.899 * [backup-simplify]: Simplify 1/2 into 1/2
16.899 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.899 * [taylor]: Taking taylor expansion of 1/2 in n
16.899 * [backup-simplify]: Simplify 1/2 into 1/2
16.899 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.899 * [taylor]: Taking taylor expansion of 1/2 in n
16.899 * [backup-simplify]: Simplify 1/2 into 1/2
16.899 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.899 * [taylor]: Taking taylor expansion of k in n
16.899 * [backup-simplify]: Simplify k into k
16.899 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.899 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
16.899 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.899 * [taylor]: Taking taylor expansion of 2 in n
16.899 * [backup-simplify]: Simplify 2 into 2
16.899 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.899 * [taylor]: Taking taylor expansion of PI in n
16.899 * [backup-simplify]: Simplify PI into PI
16.899 * [taylor]: Taking taylor expansion of n in n
16.899 * [backup-simplify]: Simplify 0 into 0
16.899 * [backup-simplify]: Simplify 1 into 1
16.900 * [backup-simplify]: Simplify (/ PI 1) into PI
16.900 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.901 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.901 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.901 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.901 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.901 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
16.903 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.904 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
16.905 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
16.905 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
16.905 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
16.905 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
16.905 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
16.905 * [taylor]: Taking taylor expansion of 1/2 in n
16.905 * [backup-simplify]: Simplify 1/2 into 1/2
16.906 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.906 * [taylor]: Taking taylor expansion of 1/2 in n
16.906 * [backup-simplify]: Simplify 1/2 into 1/2
16.906 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.906 * [taylor]: Taking taylor expansion of 1/2 in n
16.906 * [backup-simplify]: Simplify 1/2 into 1/2
16.906 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.906 * [taylor]: Taking taylor expansion of k in n
16.906 * [backup-simplify]: Simplify k into k
16.906 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.906 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
16.906 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.906 * [taylor]: Taking taylor expansion of 2 in n
16.906 * [backup-simplify]: Simplify 2 into 2
16.906 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.906 * [taylor]: Taking taylor expansion of PI in n
16.906 * [backup-simplify]: Simplify PI into PI
16.906 * [taylor]: Taking taylor expansion of n in n
16.906 * [backup-simplify]: Simplify 0 into 0
16.906 * [backup-simplify]: Simplify 1 into 1
16.907 * [backup-simplify]: Simplify (/ PI 1) into PI
16.907 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.908 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.908 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.908 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.908 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.909 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
16.910 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.911 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
16.913 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
16.913 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
16.913 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
16.913 * [taylor]: Taking taylor expansion of 1/2 in k
16.913 * [backup-simplify]: Simplify 1/2 into 1/2
16.913 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
16.913 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
16.913 * [taylor]: Taking taylor expansion of 1/2 in k
16.913 * [backup-simplify]: Simplify 1/2 into 1/2
16.913 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.913 * [taylor]: Taking taylor expansion of 1/2 in k
16.913 * [backup-simplify]: Simplify 1/2 into 1/2
16.913 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.913 * [taylor]: Taking taylor expansion of k in k
16.913 * [backup-simplify]: Simplify 0 into 0
16.913 * [backup-simplify]: Simplify 1 into 1
16.914 * [backup-simplify]: Simplify (/ 1 1) into 1
16.914 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
16.914 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
16.914 * [taylor]: Taking taylor expansion of (* 2 PI) in k
16.914 * [taylor]: Taking taylor expansion of 2 in k
16.914 * [backup-simplify]: Simplify 2 into 2
16.914 * [taylor]: Taking taylor expansion of PI in k
16.914 * [backup-simplify]: Simplify PI into PI
16.914 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.915 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.915 * [taylor]: Taking taylor expansion of (log n) in k
16.915 * [taylor]: Taking taylor expansion of n in k
16.915 * [backup-simplify]: Simplify n into n
16.915 * [backup-simplify]: Simplify (log n) into (log n)
16.915 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.915 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.916 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.916 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
16.916 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
16.917 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
16.918 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
16.918 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
16.919 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
16.920 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.920 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
16.921 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.921 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.922 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
16.922 * [backup-simplify]: Simplify (- 0) into 0
16.922 * [backup-simplify]: Simplify (+ 0 0) into 0
16.922 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
16.923 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.924 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
16.925 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.925 * [taylor]: Taking taylor expansion of 0 in k
16.925 * [backup-simplify]: Simplify 0 into 0
16.925 * [backup-simplify]: Simplify 0 into 0
16.925 * [backup-simplify]: Simplify 0 into 0
16.926 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.927 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
16.929 * [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
16.929 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.929 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
16.930 * [backup-simplify]: Simplify (- 0) into 0
16.930 * [backup-simplify]: Simplify (+ 0 0) into 0
16.930 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
16.931 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.932 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
16.934 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.934 * [taylor]: Taking taylor expansion of 0 in k
16.934 * [backup-simplify]: Simplify 0 into 0
16.934 * [backup-simplify]: Simplify 0 into 0
16.934 * [backup-simplify]: Simplify 0 into 0
16.934 * [backup-simplify]: Simplify 0 into 0
16.935 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.935 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.938 * [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
16.939 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.939 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
16.940 * [backup-simplify]: Simplify (- 0) into 0
16.940 * [backup-simplify]: Simplify (+ 0 0) into 0
16.941 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
16.942 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.943 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
16.944 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
16.945 * [taylor]: Taking taylor expansion of 0 in k
16.945 * [backup-simplify]: Simplify 0 into 0
16.945 * [backup-simplify]: Simplify 0 into 0
16.945 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))
16.946 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)))
16.946 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
16.946 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
16.946 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
16.946 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
16.946 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
16.946 * [taylor]: Taking taylor expansion of 1/2 in k
16.946 * [backup-simplify]: Simplify 1/2 into 1/2
16.946 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
16.946 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.946 * [taylor]: Taking taylor expansion of 1/2 in k
16.946 * [backup-simplify]: Simplify 1/2 into 1/2
16.946 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.946 * [taylor]: Taking taylor expansion of k in k
16.946 * [backup-simplify]: Simplify 0 into 0
16.946 * [backup-simplify]: Simplify 1 into 1
16.946 * [backup-simplify]: Simplify (/ 1 1) into 1
16.946 * [taylor]: Taking taylor expansion of 1/2 in k
16.946 * [backup-simplify]: Simplify 1/2 into 1/2
16.946 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
16.947 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
16.947 * [taylor]: Taking taylor expansion of -2 in k
16.947 * [backup-simplify]: Simplify -2 into -2
16.947 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.947 * [taylor]: Taking taylor expansion of PI in k
16.947 * [backup-simplify]: Simplify PI into PI
16.947 * [taylor]: Taking taylor expansion of n in k
16.947 * [backup-simplify]: Simplify n into n
16.947 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.947 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
16.947 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
16.947 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.948 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.948 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
16.948 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
16.949 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
16.949 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
16.949 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
16.949 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
16.949 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.949 * [taylor]: Taking taylor expansion of 1/2 in n
16.949 * [backup-simplify]: Simplify 1/2 into 1/2
16.949 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.949 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.949 * [taylor]: Taking taylor expansion of 1/2 in n
16.949 * [backup-simplify]: Simplify 1/2 into 1/2
16.949 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.949 * [taylor]: Taking taylor expansion of k in n
16.949 * [backup-simplify]: Simplify k into k
16.949 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.949 * [taylor]: Taking taylor expansion of 1/2 in n
16.949 * [backup-simplify]: Simplify 1/2 into 1/2
16.949 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
16.949 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.949 * [taylor]: Taking taylor expansion of -2 in n
16.949 * [backup-simplify]: Simplify -2 into -2
16.949 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.949 * [taylor]: Taking taylor expansion of PI in n
16.949 * [backup-simplify]: Simplify PI into PI
16.949 * [taylor]: Taking taylor expansion of n in n
16.949 * [backup-simplify]: Simplify 0 into 0
16.949 * [backup-simplify]: Simplify 1 into 1
16.950 * [backup-simplify]: Simplify (/ PI 1) into PI
16.950 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.951 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.951 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.951 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.952 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
16.953 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.954 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
16.955 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
16.955 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
16.955 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
16.955 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
16.955 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.955 * [taylor]: Taking taylor expansion of 1/2 in n
16.955 * [backup-simplify]: Simplify 1/2 into 1/2
16.955 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.956 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.956 * [taylor]: Taking taylor expansion of 1/2 in n
16.956 * [backup-simplify]: Simplify 1/2 into 1/2
16.956 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.956 * [taylor]: Taking taylor expansion of k in n
16.956 * [backup-simplify]: Simplify k into k
16.956 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.956 * [taylor]: Taking taylor expansion of 1/2 in n
16.956 * [backup-simplify]: Simplify 1/2 into 1/2
16.956 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
16.956 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.956 * [taylor]: Taking taylor expansion of -2 in n
16.956 * [backup-simplify]: Simplify -2 into -2
16.956 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.956 * [taylor]: Taking taylor expansion of PI in n
16.956 * [backup-simplify]: Simplify PI into PI
16.956 * [taylor]: Taking taylor expansion of n in n
16.956 * [backup-simplify]: Simplify 0 into 0
16.956 * [backup-simplify]: Simplify 1 into 1
16.956 * [backup-simplify]: Simplify (/ PI 1) into PI
16.957 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.958 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.958 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.958 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.958 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
16.960 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.961 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
16.962 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
16.962 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
16.962 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
16.962 * [taylor]: Taking taylor expansion of 1/2 in k
16.962 * [backup-simplify]: Simplify 1/2 into 1/2
16.962 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
16.962 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
16.962 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.962 * [taylor]: Taking taylor expansion of 1/2 in k
16.962 * [backup-simplify]: Simplify 1/2 into 1/2
16.962 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.962 * [taylor]: Taking taylor expansion of k in k
16.962 * [backup-simplify]: Simplify 0 into 0
16.962 * [backup-simplify]: Simplify 1 into 1
16.963 * [backup-simplify]: Simplify (/ 1 1) into 1
16.963 * [taylor]: Taking taylor expansion of 1/2 in k
16.963 * [backup-simplify]: Simplify 1/2 into 1/2
16.963 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
16.963 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
16.963 * [taylor]: Taking taylor expansion of (* -2 PI) in k
16.963 * [taylor]: Taking taylor expansion of -2 in k
16.963 * [backup-simplify]: Simplify -2 into -2
16.963 * [taylor]: Taking taylor expansion of PI in k
16.963 * [backup-simplify]: Simplify PI into PI
16.964 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.965 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.965 * [taylor]: Taking taylor expansion of (log n) in k
16.965 * [taylor]: Taking taylor expansion of n in k
16.965 * [backup-simplify]: Simplify n into n
16.965 * [backup-simplify]: Simplify (log n) into (log n)
16.965 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.966 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.966 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
16.967 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
16.968 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
16.969 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
16.970 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
16.971 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
16.972 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.973 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
16.974 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
16.975 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.975 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
16.980 * [backup-simplify]: Simplify (+ 0 0) into 0
16.980 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
16.981 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.982 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
16.983 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.983 * [taylor]: Taking taylor expansion of 0 in k
16.983 * [backup-simplify]: Simplify 0 into 0
16.983 * [backup-simplify]: Simplify 0 into 0
16.983 * [backup-simplify]: Simplify 0 into 0
16.984 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.985 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
16.987 * [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
16.987 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.988 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
16.988 * [backup-simplify]: Simplify (+ 0 0) into 0
16.988 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
16.989 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.990 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
16.992 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.992 * [taylor]: Taking taylor expansion of 0 in k
16.992 * [backup-simplify]: Simplify 0 into 0
16.992 * [backup-simplify]: Simplify 0 into 0
16.992 * [backup-simplify]: Simplify 0 into 0
16.992 * [backup-simplify]: Simplify 0 into 0
16.993 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.993 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.997 * [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
16.997 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.998 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
16.998 * [backup-simplify]: Simplify (+ 0 0) into 0
16.999 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
17.001 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.003 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
17.006 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.006 * [taylor]: Taking taylor expansion of 0 in k
17.006 * [backup-simplify]: Simplify 0 into 0
17.006 * [backup-simplify]: Simplify 0 into 0
17.007 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))
17.007 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1)
17.008 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
17.008 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
17.008 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.008 * [taylor]: Taking taylor expansion of 2 in n
17.008 * [backup-simplify]: Simplify 2 into 2
17.008 * [taylor]: Taking taylor expansion of (* n PI) in n
17.008 * [taylor]: Taking taylor expansion of n in n
17.008 * [backup-simplify]: Simplify 0 into 0
17.008 * [backup-simplify]: Simplify 1 into 1
17.008 * [taylor]: Taking taylor expansion of PI in n
17.008 * [backup-simplify]: Simplify PI into PI
17.008 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.008 * [taylor]: Taking taylor expansion of 2 in n
17.008 * [backup-simplify]: Simplify 2 into 2
17.008 * [taylor]: Taking taylor expansion of (* n PI) in n
17.008 * [taylor]: Taking taylor expansion of n in n
17.008 * [backup-simplify]: Simplify 0 into 0
17.009 * [backup-simplify]: Simplify 1 into 1
17.009 * [taylor]: Taking taylor expansion of PI in n
17.009 * [backup-simplify]: Simplify PI into PI
17.009 * [backup-simplify]: Simplify (* 0 PI) into 0
17.010 * [backup-simplify]: Simplify (* 2 0) into 0
17.010 * [backup-simplify]: Simplify 0 into 0
17.011 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.013 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.013 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.014 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
17.016 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
17.016 * [backup-simplify]: Simplify 0 into 0
17.017 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
17.018 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
17.018 * [backup-simplify]: Simplify 0 into 0
17.020 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.021 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
17.021 * [backup-simplify]: Simplify 0 into 0
17.023 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.024 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
17.024 * [backup-simplify]: Simplify 0 into 0
17.026 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.028 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
17.028 * [backup-simplify]: Simplify 0 into 0
17.030 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
17.032 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
17.032 * [backup-simplify]: Simplify 0 into 0
17.033 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
17.033 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
17.033 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
17.033 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.033 * [taylor]: Taking taylor expansion of 2 in n
17.033 * [backup-simplify]: Simplify 2 into 2
17.034 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.034 * [taylor]: Taking taylor expansion of PI in n
17.034 * [backup-simplify]: Simplify PI into PI
17.034 * [taylor]: Taking taylor expansion of n in n
17.034 * [backup-simplify]: Simplify 0 into 0
17.034 * [backup-simplify]: Simplify 1 into 1
17.034 * [backup-simplify]: Simplify (/ PI 1) into PI
17.034 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.034 * [taylor]: Taking taylor expansion of 2 in n
17.034 * [backup-simplify]: Simplify 2 into 2
17.034 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.034 * [taylor]: Taking taylor expansion of PI in n
17.034 * [backup-simplify]: Simplify PI into PI
17.034 * [taylor]: Taking taylor expansion of n in n
17.034 * [backup-simplify]: Simplify 0 into 0
17.034 * [backup-simplify]: Simplify 1 into 1
17.035 * [backup-simplify]: Simplify (/ PI 1) into PI
17.035 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.036 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.037 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.038 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.038 * [backup-simplify]: Simplify 0 into 0
17.039 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.040 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.040 * [backup-simplify]: Simplify 0 into 0
17.041 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.043 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.043 * [backup-simplify]: Simplify 0 into 0
17.044 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.045 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.045 * [backup-simplify]: Simplify 0 into 0
17.046 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.047 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.047 * [backup-simplify]: Simplify 0 into 0
17.048 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.049 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.049 * [backup-simplify]: Simplify 0 into 0
17.049 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
17.050 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
17.050 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
17.050 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.050 * [taylor]: Taking taylor expansion of -2 in n
17.050 * [backup-simplify]: Simplify -2 into -2
17.050 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.050 * [taylor]: Taking taylor expansion of PI in n
17.050 * [backup-simplify]: Simplify PI into PI
17.050 * [taylor]: Taking taylor expansion of n in n
17.050 * [backup-simplify]: Simplify 0 into 0
17.050 * [backup-simplify]: Simplify 1 into 1
17.050 * [backup-simplify]: Simplify (/ PI 1) into PI
17.051 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.051 * [taylor]: Taking taylor expansion of -2 in n
17.051 * [backup-simplify]: Simplify -2 into -2
17.051 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.051 * [taylor]: Taking taylor expansion of PI in n
17.051 * [backup-simplify]: Simplify PI into PI
17.051 * [taylor]: Taking taylor expansion of n in n
17.051 * [backup-simplify]: Simplify 0 into 0
17.051 * [backup-simplify]: Simplify 1 into 1
17.051 * [backup-simplify]: Simplify (/ PI 1) into PI
17.051 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.052 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.052 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.053 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
17.053 * [backup-simplify]: Simplify 0 into 0
17.053 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.054 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
17.054 * [backup-simplify]: Simplify 0 into 0
17.055 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.055 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.055 * [backup-simplify]: Simplify 0 into 0
17.056 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.057 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.057 * [backup-simplify]: Simplify 0 into 0
17.058 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.058 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.058 * [backup-simplify]: Simplify 0 into 0
17.059 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.060 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.060 * [backup-simplify]: Simplify 0 into 0
17.061 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
17.061 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1)
17.061 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
17.061 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
17.061 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.061 * [taylor]: Taking taylor expansion of 2 in n
17.061 * [backup-simplify]: Simplify 2 into 2
17.061 * [taylor]: Taking taylor expansion of (* n PI) in n
17.061 * [taylor]: Taking taylor expansion of n in n
17.061 * [backup-simplify]: Simplify 0 into 0
17.061 * [backup-simplify]: Simplify 1 into 1
17.061 * [taylor]: Taking taylor expansion of PI in n
17.061 * [backup-simplify]: Simplify PI into PI
17.061 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.061 * [taylor]: Taking taylor expansion of 2 in n
17.061 * [backup-simplify]: Simplify 2 into 2
17.061 * [taylor]: Taking taylor expansion of (* n PI) in n
17.061 * [taylor]: Taking taylor expansion of n in n
17.061 * [backup-simplify]: Simplify 0 into 0
17.061 * [backup-simplify]: Simplify 1 into 1
17.061 * [taylor]: Taking taylor expansion of PI in n
17.061 * [backup-simplify]: Simplify PI into PI
17.062 * [backup-simplify]: Simplify (* 0 PI) into 0
17.062 * [backup-simplify]: Simplify (* 2 0) into 0
17.062 * [backup-simplify]: Simplify 0 into 0
17.063 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.064 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.064 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.065 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
17.065 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
17.065 * [backup-simplify]: Simplify 0 into 0
17.066 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
17.067 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
17.067 * [backup-simplify]: Simplify 0 into 0
17.068 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.068 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
17.068 * [backup-simplify]: Simplify 0 into 0
17.069 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.070 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
17.070 * [backup-simplify]: Simplify 0 into 0
17.071 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.072 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
17.072 * [backup-simplify]: Simplify 0 into 0
17.073 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
17.075 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
17.075 * [backup-simplify]: Simplify 0 into 0
17.075 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
17.075 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
17.075 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
17.075 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.075 * [taylor]: Taking taylor expansion of 2 in n
17.075 * [backup-simplify]: Simplify 2 into 2
17.075 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.075 * [taylor]: Taking taylor expansion of PI in n
17.076 * [backup-simplify]: Simplify PI into PI
17.076 * [taylor]: Taking taylor expansion of n in n
17.076 * [backup-simplify]: Simplify 0 into 0
17.076 * [backup-simplify]: Simplify 1 into 1
17.076 * [backup-simplify]: Simplify (/ PI 1) into PI
17.076 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.076 * [taylor]: Taking taylor expansion of 2 in n
17.076 * [backup-simplify]: Simplify 2 into 2
17.076 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.076 * [taylor]: Taking taylor expansion of PI in n
17.076 * [backup-simplify]: Simplify PI into PI
17.076 * [taylor]: Taking taylor expansion of n in n
17.076 * [backup-simplify]: Simplify 0 into 0
17.076 * [backup-simplify]: Simplify 1 into 1
17.076 * [backup-simplify]: Simplify (/ PI 1) into PI
17.077 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.077 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.078 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.078 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.078 * [backup-simplify]: Simplify 0 into 0
17.079 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.079 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.079 * [backup-simplify]: Simplify 0 into 0
17.080 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.081 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.081 * [backup-simplify]: Simplify 0 into 0
17.081 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.082 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.082 * [backup-simplify]: Simplify 0 into 0
17.083 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.084 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.084 * [backup-simplify]: Simplify 0 into 0
17.084 * [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
17.085 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.085 * [backup-simplify]: Simplify 0 into 0
17.086 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
17.086 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
17.086 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
17.086 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.086 * [taylor]: Taking taylor expansion of -2 in n
17.086 * [backup-simplify]: Simplify -2 into -2
17.086 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.086 * [taylor]: Taking taylor expansion of PI in n
17.086 * [backup-simplify]: Simplify PI into PI
17.086 * [taylor]: Taking taylor expansion of n in n
17.086 * [backup-simplify]: Simplify 0 into 0
17.086 * [backup-simplify]: Simplify 1 into 1
17.086 * [backup-simplify]: Simplify (/ PI 1) into PI
17.086 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.086 * [taylor]: Taking taylor expansion of -2 in n
17.086 * [backup-simplify]: Simplify -2 into -2
17.087 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.087 * [taylor]: Taking taylor expansion of PI in n
17.087 * [backup-simplify]: Simplify PI into PI
17.087 * [taylor]: Taking taylor expansion of n in n
17.087 * [backup-simplify]: Simplify 0 into 0
17.087 * [backup-simplify]: Simplify 1 into 1
17.087 * [backup-simplify]: Simplify (/ PI 1) into PI
17.087 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.088 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.088 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.089 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
17.089 * [backup-simplify]: Simplify 0 into 0
17.089 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.095 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
17.095 * [backup-simplify]: Simplify 0 into 0
17.096 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.097 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.097 * [backup-simplify]: Simplify 0 into 0
17.098 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.099 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.099 * [backup-simplify]: Simplify 0 into 0
17.101 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.102 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.102 * [backup-simplify]: Simplify 0 into 0
17.103 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.105 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.105 * [backup-simplify]: Simplify 0 into 0
17.106 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
17.106 * * * [progress]: simplifying candidates
17.106 * * * * [progress]: [ 1 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (log1p (expm1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
17.106 * * * * [progress]: [ 2 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (expm1 (log1p (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
17.106 * * * * [progress]: [ 3 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
17.106 * * * * [progress]: [ 4 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
17.106 * * * * [progress]: [ 5 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
17.106 * * * * [progress]: [ 6 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
17.106 * * * * [progress]: [ 7 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
17.107 * * * * [progress]: [ 8 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
17.107 * * * * [progress]: [ 9 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
17.107 * * * * [progress]: [ 10 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (/ (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2))) (sqrt k))))>
17.107 * * * * [progress]: [ 11 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (cbrt (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
17.107 * * * * [progress]: [ 12 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
17.107 * * * * [progress]: [ 13 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))) (sqrt k))))>
17.107 * * * * [progress]: [ 14 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2))) (sqrt k))))>
17.107 * * * * [progress]: [ 15 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (/ (cbrt (- 1/2 (/ k 2))) 2)) (sqrt k))))>
17.107 * * * * [progress]: [ 16 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2))) (sqrt k))))>
17.107 * * * * [progress]: [ 17 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (sqrt k))))>
17.107 * * * * [progress]: [ 18 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2)) (sqrt k))))>
17.107 * * * * [progress]: [ 19 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (sqrt k))))>
17.108 * * * * [progress]: [ 20 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (sqrt k))))>
17.108 * * * * [progress]: [ 21 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.108 * * * * [progress]: [ 22 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2))) (sqrt k))))>
17.108 * * * * [progress]: [ 23 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (sqrt k))))>
17.108 * * * * [progress]: [ 24 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (/ (- (sqrt 1/2) (sqrt (/ k 2))) 2)) (sqrt k))))>
17.108 * * * * [progress]: [ 25 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2))) (sqrt k))))>
17.108 * * * * [progress]: [ 26 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (sqrt k))))>
17.108 * * * * [progress]: [ 27 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 2)) (sqrt k))))>
17.108 * * * * [progress]: [ 28 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (sqrt k))))>
17.108 * * * * [progress]: [ 29 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (sqrt k))))>
17.108 * * * * [progress]: [ 30 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.109 * * * * [progress]: [ 31 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.109 * * * * [progress]: [ 32 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)) (sqrt k))))>
17.109 * * * * [progress]: [ 33 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
17.109 * * * * [progress]: [ 34 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (sqrt k))))>
17.109 * * * * [progress]: [ 35 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
17.109 * * * * [progress]: [ 36 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (log (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
17.109 * * * * [progress]: [ 37 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (* (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
17.109 * * * * [progress]: [ 38 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (cbrt (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
17.109 * * * * [progress]: [ 39 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (* (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
17.109 * * * * [progress]: [ 40 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (* 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
17.109 * * * * [progress]: [ 41 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2))) (sqrt k))))>
17.109 * * * * [progress]: [ 42 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
17.109 * * * * [progress]: [ 43 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (log1p (expm1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.109 * * * * [progress]: [ 44 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (expm1 (log1p (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 45 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 46 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 47 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 48 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 49 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 50 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 51 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 52 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 53 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (cbrt (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 54 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 55 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 56 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 57 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (/ (cbrt (- 1/2 (/ k 2))) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 58 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 59 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 60 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.110 * * * * [progress]: [ 61 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 62 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 63 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 64 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 65 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 66 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (/ (- (sqrt 1/2) (sqrt (/ k 2))) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 67 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 68 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 69 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 70 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 71 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 72 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 73 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 74 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 75 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 76 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 77 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 78 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (log (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 79 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 80 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (cbrt (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 81 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 82 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (* 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.111 * * * * [progress]: [ 83 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 84 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 85 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (log1p (expm1 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 86 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (expm1 (log1p (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 87 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 88 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 89 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 90 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 91 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 92 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (exp (log (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 93 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (log (exp (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 94 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 95 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 96 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 97 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 98 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 99 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 100 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 101 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 102 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 103 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 104 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 105 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* 2 PI) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 106 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (log1p (expm1 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.112 * * * * [progress]: [ 107 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (expm1 (log1p (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 108 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 109 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 110 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 111 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 112 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 113 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (exp (log (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 114 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (log (exp (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 115 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 116 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 117 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 118 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 119 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 120 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 121 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 122 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 123 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 124 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 125 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 126 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* 2 PI) n) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.113 * * * * [progress]: [ 127 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (sqrt k))))>
17.113 * * * * [progress]: [ 128 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k))))>
17.113 * * * * [progress]: [ 129 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))))>
17.114 * * * * [progress]: [ 130 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.114 * * * * [progress]: [ 131 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.114 * * * * [progress]: [ 132 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.114 * * * * [progress]: [ 133 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.114 * * * * [progress]: [ 134 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.114 * * * * [progress]: [ 135 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.114 * * * * [progress]: [ 136 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.114 * * * * [progress]: [ 137 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.114 * * * * [progress]: [ 138 / 138 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
17.115 * [simplify]: Simplifying (expm1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (log1p (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)), (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)), (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)), (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)), (* 1 (/ (- 1/2 (/ k 2)) 2)), (* 1 (/ (- 1/2 (/ k 2)) 2)), (* 1 (/ (- 1/2 (/ k 2)) 2)), (pow (* n (* 2 PI)) (/ 1/2 2)), (pow (* n (* 2 PI)) (/ (/ k 2) 2)), (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))), (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))), (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))), (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)), (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))), (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)), (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ 1 (sqrt 2))), (pow (* n (* 2 PI)) (/ 1 1)), (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))), (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)), (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))), (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)), (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ 1 (sqrt 2))), (pow (* n (* 2 PI)) (/ 1 1)), (pow (* n (* 2 PI)) 1), (pow (* n (* 2 PI)) (- 1/2 (/ k 2))), (pow n (/ (- 1/2 (/ k 2)) 2)), (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)), (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))), (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)), (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)), (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (expm1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (log1p (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)), (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)), (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)), (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)), (* 1 (/ (- 1/2 (/ k 2)) 2)), (* 1 (/ (- 1/2 (/ k 2)) 2)), (* 1 (/ (- 1/2 (/ k 2)) 2)), (pow (* n (* 2 PI)) (/ 1/2 2)), (pow (* n (* 2 PI)) (/ (/ k 2) 2)), (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))), (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))), (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))), (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)), (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))), (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)), (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ 1 (sqrt 2))), (pow (* n (* 2 PI)) (/ 1 1)), (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))), (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)), (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))), (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)), (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ 1 (sqrt 2))), (pow (* n (* 2 PI)) (/ 1 1)), (pow (* n (* 2 PI)) 1), (pow (* n (* 2 PI)) (- 1/2 (/ k 2))), (pow n (/ (- 1/2 (/ k 2)) 2)), (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)), (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))), (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)), (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)), (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (expm1 (* n (* 2 PI))), (log1p (* n (* 2 PI))), (* n (* 2 PI)), (* n (* 2 PI)), (+ (log n) (+ (log 2) (log PI))), (+ (log n) (log (* 2 PI))), (log (* n (* 2 PI))), (exp (* n (* 2 PI))), (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI))), (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI))), (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))), (cbrt (* n (* 2 PI))), (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI))), (sqrt (* n (* 2 PI))), (sqrt (* n (* 2 PI))), (* n 2), (* (cbrt n) (* 2 PI)), (* (sqrt n) (* 2 PI)), (* n (* 2 PI)), (real->posit16 (* n (* 2 PI))), (expm1 (* n (* 2 PI))), (log1p (* n (* 2 PI))), (* n (* 2 PI)), (* n (* 2 PI)), (+ (log n) (+ (log 2) (log PI))), (+ (log n) (log (* 2 PI))), (log (* n (* 2 PI))), (exp (* n (* 2 PI))), (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI))), (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI))), (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))), (cbrt (* n (* 2 PI))), (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI))), (sqrt (* n (* 2 PI))), (sqrt (* n (* 2 PI))), (* n 2), (* (cbrt n) (* 2 PI)), (* (sqrt n) (* 2 PI)), (* n (* 2 PI)), (real->posit16 (* n (* 2 PI))), (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))), (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))), (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))), (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))), (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))), (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))), (* 2 (* n PI)), (* 2 (* n PI)), (* 2 (* n PI)), (* 2 (* n PI)), (* 2 (* n PI)), (* 2 (* n PI))
17.117 * * [simplify]: iteration 1: (165 enodes)
17.180 * * [simplify]: iteration 2: (752 enodes)
17.429 * * [simplify]: iteration 3: (1966 enodes)
18.670 * * [simplify]: Extracting #0: cost 48 inf + 0
18.672 * * [simplify]: Extracting #1: cost 524 inf + 0
18.684 * * [simplify]: Extracting #2: cost 1524 inf + 10544
18.703 * * [simplify]: Extracting #3: cost 1840 inf + 58499
18.783 * * [simplify]: Extracting #4: cost 1030 inf + 300841
18.987 * * [simplify]: Extracting #5: cost 383 inf + 576598
19.208 * * [simplify]: Extracting #6: cost 110 inf + 700641
19.445 * * [simplify]: Extracting #7: cost 4 inf + 745570
19.664 * * [simplify]: Extracting #8: cost 0 inf + 748026
19.857 * [simplify]: Simplified to (expm1 (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (log1p (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))), (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))), (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))), (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))), (- 1/4 (* k 1/4)), (- 1/4 (* k 1/4)), (- 1/4 (* k 1/4)), (exp (* (log (* (* PI 2) n)) 1/4)), (pow (* (* PI 2) n) (* k 1/4)), (pow (* (* PI 2) n) (* (cbrt (- 1/4 (* k 1/4))) (cbrt (- 1/4 (* k 1/4))))), (pow (* (* PI 2) n) (sqrt (- 1/4 (* k 1/4)))), (pow (* (* PI 2) n) (* (/ (cbrt (fma k -1/2 1/2)) (cbrt 2)) (/ (cbrt (fma k -1/2 1/2)) (cbrt 2)))), (pow (* (* PI 2) n) (/ (* (cbrt (fma k -1/2 1/2)) (cbrt (fma k -1/2 1/2))) (sqrt 2))), (pow (* (* PI 2) n) (* (cbrt (fma k -1/2 1/2)) (cbrt (fma k -1/2 1/2)))), (pow (* (* PI 2) n) (/ (sqrt (fma k -1/2 1/2)) (* (cbrt 2) (cbrt 2)))), (pow (* (* PI 2) n) (/ (sqrt (fma k -1/2 1/2)) (sqrt 2))), (pow (* (* PI 2) n) (sqrt (fma k -1/2 1/2))), (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* (* PI 2) n) (/ 1 (sqrt 2))), (* (* PI 2) n), (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1/2) (sqrt (* 1/2 k))) (cbrt 2)) (cbrt 2))), (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (sqrt (* 1/2 k))) (sqrt 2))), (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (* 1/2 k)))), (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2)) (cbrt 2))), (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))), (pow (* (* PI 2) n) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))), (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* (* PI 2) n) (/ 1 (sqrt 2))), (* (* PI 2) n), (* (* PI 2) n), (exp (* (log (* (* PI 2) n)) (fma k -1/2 1/2))), (pow n (- 1/4 (* k 1/4))), (pow (* PI 2) (- 1/4 (* k 1/4))), (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))), (exp (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (* (cbrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (cbrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4)))))), (cbrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (* (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4)))) (exp (* (log (* (* PI 2) n)) (fma k -1/2 1/2)))), (sqrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (sqrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (pow (* (* PI 2) n) (- 1/8 (/ k 8))), (pow (* (* PI 2) n) (- 1/8 (/ k 8))), (real->posit16 (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (expm1 (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (log1p (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))), (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))), (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))), (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))), (- 1/4 (* k 1/4)), (- 1/4 (* k 1/4)), (- 1/4 (* k 1/4)), (exp (* (log (* (* PI 2) n)) 1/4)), (pow (* (* PI 2) n) (* k 1/4)), (pow (* (* PI 2) n) (* (cbrt (- 1/4 (* k 1/4))) (cbrt (- 1/4 (* k 1/4))))), (pow (* (* PI 2) n) (sqrt (- 1/4 (* k 1/4)))), (pow (* (* PI 2) n) (* (/ (cbrt (fma k -1/2 1/2)) (cbrt 2)) (/ (cbrt (fma k -1/2 1/2)) (cbrt 2)))), (pow (* (* PI 2) n) (/ (* (cbrt (fma k -1/2 1/2)) (cbrt (fma k -1/2 1/2))) (sqrt 2))), (pow (* (* PI 2) n) (* (cbrt (fma k -1/2 1/2)) (cbrt (fma k -1/2 1/2)))), (pow (* (* PI 2) n) (/ (sqrt (fma k -1/2 1/2)) (* (cbrt 2) (cbrt 2)))), (pow (* (* PI 2) n) (/ (sqrt (fma k -1/2 1/2)) (sqrt 2))), (pow (* (* PI 2) n) (sqrt (fma k -1/2 1/2))), (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* (* PI 2) n) (/ 1 (sqrt 2))), (* (* PI 2) n), (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1/2) (sqrt (* 1/2 k))) (cbrt 2)) (cbrt 2))), (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (sqrt (* 1/2 k))) (sqrt 2))), (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (* 1/2 k)))), (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2)) (cbrt 2))), (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))), (pow (* (* PI 2) n) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))), (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))), (pow (* (* PI 2) n) (/ 1 (sqrt 2))), (* (* PI 2) n), (* (* PI 2) n), (exp (* (log (* (* PI 2) n)) (fma k -1/2 1/2))), (pow n (- 1/4 (* k 1/4))), (pow (* PI 2) (- 1/4 (* k 1/4))), (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))), (exp (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (* (cbrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (cbrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4)))))), (cbrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (* (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4)))) (exp (* (log (* (* PI 2) n)) (fma k -1/2 1/2)))), (sqrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (sqrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (pow (* (* PI 2) n) (- 1/8 (/ k 8))), (pow (* (* PI 2) n) (- 1/8 (/ k 8))), (real->posit16 (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))), (expm1 (* (* PI 2) n)), (log1p (* (* PI 2) n)), (* (* PI 2) n), (* (* PI 2) n), (log (* (* PI 2) n)), (log (* (* PI 2) n)), (log (* (* PI 2) n)), (exp (+ (* n PI) (* n PI))), (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))), (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))), (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n))), (cbrt (* (* PI 2) n)), (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))), (sqrt (* (* PI 2) n)), (sqrt (* (* PI 2) n)), (* n 2), (* (cbrt n) (* PI 2)), (* PI (* 2 (sqrt n))), (* (* PI 2) n), (real->posit16 (* (* PI 2) n)), (expm1 (* (* PI 2) n)), (log1p (* (* PI 2) n)), (* (* PI 2) n), (* (* PI 2) n), (log (* (* PI 2) n)), (log (* (* PI 2) n)), (log (* (* PI 2) n)), (exp (+ (* n PI) (* n PI))), (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))), (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))), (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n))), (cbrt (* (* PI 2) n)), (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))), (sqrt (* (* PI 2) n)), (sqrt (* (* PI 2) n)), (* n 2), (* (cbrt n) (* PI 2)), (* PI (* 2 (sqrt n))), (* (* PI 2) n), (real->posit16 (* (* PI 2) n)), (fma -1/4 (* k (* (exp (* (log (* (* PI 2) n)) 1/4)) (log (* (* PI 2) n)))) (fma (* (log (* PI 2)) (* 1/16 (exp (* (log (* (* PI 2) n)) 1/4)))) (* k (* (log n) k)) (fma 1/32 (* (exp (* (log (* (* PI 2) n)) 1/4)) (+ (* (* k (log (* PI 2))) (* k (log (* PI 2)))) (* (* (log n) k) (* (log n) k)))) (exp (* (log (* (* PI 2) n)) 1/4))))), (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4)))), (exp (* (- 1/4 (* k 1/4)) (- (log (* PI -2)) (log (/ -1 n))))), (fma -1/4 (* k (* (exp (* (log (* (* PI 2) n)) 1/4)) (log (* (* PI 2) n)))) (fma (* (log (* PI 2)) (* 1/16 (exp (* (log (* (* PI 2) n)) 1/4)))) (* k (* (log n) k)) (fma 1/32 (* (exp (* (log (* (* PI 2) n)) 1/4)) (+ (* (* k (log (* PI 2))) (* k (log (* PI 2)))) (* (* (log n) k) (* (log n) k)))) (exp (* (log (* (* PI 2) n)) 1/4))))), (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4)))), (exp (* (- 1/4 (* k 1/4)) (- (log (* PI -2)) (log (/ -1 n))))), (* (* PI 2) n), (* (* PI 2) n), (* (* PI 2) n), (* (* PI 2) n), (* (* PI 2) n), (* (* PI 2) n)
19.870 * * * [progress]: adding candidates to table
21.745 * * [progress]: iteration 4 / 4
21.745 * * * [progress]: picking best candidate
21.769 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
21.769 * * * [progress]: localizing error
21.816 * * * [progress]: generating rewritten candidates
21.816 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1)
21.833 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1)
21.845 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1)
21.879 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
21.937 * * * [progress]: generating series expansions
21.937 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1)
21.938 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))
21.938 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
21.938 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
21.938 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
21.938 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
21.938 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
21.938 * [taylor]: Taking taylor expansion of 1/2 in k
21.938 * [backup-simplify]: Simplify 1/2 into 1/2
21.938 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
21.938 * [taylor]: Taking taylor expansion of 1/2 in k
21.938 * [backup-simplify]: Simplify 1/2 into 1/2
21.938 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
21.938 * [taylor]: Taking taylor expansion of 1/2 in k
21.938 * [backup-simplify]: Simplify 1/2 into 1/2
21.938 * [taylor]: Taking taylor expansion of k in k
21.938 * [backup-simplify]: Simplify 0 into 0
21.938 * [backup-simplify]: Simplify 1 into 1
21.938 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
21.938 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
21.938 * [taylor]: Taking taylor expansion of 2 in k
21.938 * [backup-simplify]: Simplify 2 into 2
21.938 * [taylor]: Taking taylor expansion of (* n PI) in k
21.938 * [taylor]: Taking taylor expansion of n in k
21.938 * [backup-simplify]: Simplify n into n
21.938 * [taylor]: Taking taylor expansion of PI in k
21.938 * [backup-simplify]: Simplify PI into PI
21.938 * [backup-simplify]: Simplify (* n PI) into (* n PI)
21.938 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
21.938 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
21.939 * [backup-simplify]: Simplify (* 1/2 0) into 0
21.939 * [backup-simplify]: Simplify (- 0) into 0
21.939 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
21.940 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
21.940 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
21.940 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
21.940 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
21.940 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
21.940 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
21.940 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
21.940 * [taylor]: Taking taylor expansion of 1/2 in n
21.940 * [backup-simplify]: Simplify 1/2 into 1/2
21.940 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
21.940 * [taylor]: Taking taylor expansion of 1/2 in n
21.940 * [backup-simplify]: Simplify 1/2 into 1/2
21.940 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
21.940 * [taylor]: Taking taylor expansion of 1/2 in n
21.940 * [backup-simplify]: Simplify 1/2 into 1/2
21.940 * [taylor]: Taking taylor expansion of k in n
21.940 * [backup-simplify]: Simplify k into k
21.940 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
21.940 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
21.940 * [taylor]: Taking taylor expansion of 2 in n
21.940 * [backup-simplify]: Simplify 2 into 2
21.940 * [taylor]: Taking taylor expansion of (* n PI) in n
21.940 * [taylor]: Taking taylor expansion of n in n
21.940 * [backup-simplify]: Simplify 0 into 0
21.940 * [backup-simplify]: Simplify 1 into 1
21.940 * [taylor]: Taking taylor expansion of PI in n
21.940 * [backup-simplify]: Simplify PI into PI
21.940 * [backup-simplify]: Simplify (* 0 PI) into 0
21.941 * [backup-simplify]: Simplify (* 2 0) into 0
21.942 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
21.943 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
21.943 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
21.943 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
21.943 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
21.943 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
21.943 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
21.944 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
21.945 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
21.946 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
21.946 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
21.946 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
21.946 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
21.946 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
21.946 * [taylor]: Taking taylor expansion of 1/2 in n
21.946 * [backup-simplify]: Simplify 1/2 into 1/2
21.946 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
21.946 * [taylor]: Taking taylor expansion of 1/2 in n
21.946 * [backup-simplify]: Simplify 1/2 into 1/2
21.946 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
21.946 * [taylor]: Taking taylor expansion of 1/2 in n
21.946 * [backup-simplify]: Simplify 1/2 into 1/2
21.946 * [taylor]: Taking taylor expansion of k in n
21.946 * [backup-simplify]: Simplify k into k
21.946 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
21.946 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
21.946 * [taylor]: Taking taylor expansion of 2 in n
21.946 * [backup-simplify]: Simplify 2 into 2
21.946 * [taylor]: Taking taylor expansion of (* n PI) in n
21.946 * [taylor]: Taking taylor expansion of n in n
21.946 * [backup-simplify]: Simplify 0 into 0
21.946 * [backup-simplify]: Simplify 1 into 1
21.946 * [taylor]: Taking taylor expansion of PI in n
21.946 * [backup-simplify]: Simplify PI into PI
21.946 * [backup-simplify]: Simplify (* 0 PI) into 0
21.947 * [backup-simplify]: Simplify (* 2 0) into 0
21.948 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
21.949 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
21.949 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
21.949 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
21.949 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
21.949 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
21.950 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
21.951 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
21.952 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
21.953 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
21.953 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
21.953 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
21.953 * [taylor]: Taking taylor expansion of 1/2 in k
21.953 * [backup-simplify]: Simplify 1/2 into 1/2
21.953 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
21.953 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
21.953 * [taylor]: Taking taylor expansion of 1/2 in k
21.953 * [backup-simplify]: Simplify 1/2 into 1/2
21.953 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
21.953 * [taylor]: Taking taylor expansion of 1/2 in k
21.954 * [backup-simplify]: Simplify 1/2 into 1/2
21.954 * [taylor]: Taking taylor expansion of k in k
21.954 * [backup-simplify]: Simplify 0 into 0
21.954 * [backup-simplify]: Simplify 1 into 1
21.954 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
21.954 * [taylor]: Taking taylor expansion of (log n) in k
21.954 * [taylor]: Taking taylor expansion of n in k
21.954 * [backup-simplify]: Simplify n into n
21.954 * [backup-simplify]: Simplify (log n) into (log n)
21.954 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
21.954 * [taylor]: Taking taylor expansion of (* 2 PI) in k
21.954 * [taylor]: Taking taylor expansion of 2 in k
21.954 * [backup-simplify]: Simplify 2 into 2
21.954 * [taylor]: Taking taylor expansion of PI in k
21.954 * [backup-simplify]: Simplify PI into PI
21.955 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
21.956 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
21.956 * [backup-simplify]: Simplify (* 1/2 0) into 0
21.957 * [backup-simplify]: Simplify (- 0) into 0
21.957 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
21.958 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
21.960 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
21.961 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
21.962 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
21.963 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
21.964 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
21.965 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
21.967 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
21.968 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
21.969 * [backup-simplify]: Simplify (- 0) into 0
21.969 * [backup-simplify]: Simplify (+ 0 0) into 0
21.978 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
21.980 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
21.981 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
21.983 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
21.984 * [taylor]: Taking taylor expansion of 0 in k
21.984 * [backup-simplify]: Simplify 0 into 0
21.984 * [backup-simplify]: Simplify 0 into 0
21.985 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
21.985 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
21.987 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
21.988 * [backup-simplify]: Simplify (+ 0 0) into 0
21.989 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
21.989 * [backup-simplify]: Simplify (- 1/2) into -1/2
21.989 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
21.991 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
21.994 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
21.997 * [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)))))))
22.000 * [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)))))))
22.002 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
22.003 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
22.006 * [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
22.008 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
22.008 * [backup-simplify]: Simplify (- 0) into 0
22.009 * [backup-simplify]: Simplify (+ 0 0) into 0
22.010 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
22.011 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
22.012 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
22.013 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
22.013 * [taylor]: Taking taylor expansion of 0 in k
22.013 * [backup-simplify]: Simplify 0 into 0
22.013 * [backup-simplify]: Simplify 0 into 0
22.013 * [backup-simplify]: Simplify 0 into 0
22.014 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
22.015 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
22.017 * [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
22.017 * [backup-simplify]: Simplify (+ 0 0) into 0
22.018 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
22.018 * [backup-simplify]: Simplify (- 0) into 0
22.018 * [backup-simplify]: Simplify (+ 0 0) into 0
22.020 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
22.022 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0
22.024 * [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)))))
22.027 * [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)))))
22.033 * [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)))))))
22.033 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))))
22.033 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
22.033 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
22.033 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
22.033 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
22.033 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
22.033 * [taylor]: Taking taylor expansion of 1/2 in k
22.033 * [backup-simplify]: Simplify 1/2 into 1/2
22.033 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
22.033 * [taylor]: Taking taylor expansion of 1/2 in k
22.033 * [backup-simplify]: Simplify 1/2 into 1/2
22.033 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.033 * [taylor]: Taking taylor expansion of 1/2 in k
22.033 * [backup-simplify]: Simplify 1/2 into 1/2
22.033 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.033 * [taylor]: Taking taylor expansion of k in k
22.033 * [backup-simplify]: Simplify 0 into 0
22.033 * [backup-simplify]: Simplify 1 into 1
22.034 * [backup-simplify]: Simplify (/ 1 1) into 1
22.034 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
22.034 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
22.034 * [taylor]: Taking taylor expansion of 2 in k
22.034 * [backup-simplify]: Simplify 2 into 2
22.034 * [taylor]: Taking taylor expansion of (/ PI n) in k
22.034 * [taylor]: Taking taylor expansion of PI in k
22.034 * [backup-simplify]: Simplify PI into PI
22.034 * [taylor]: Taking taylor expansion of n in k
22.034 * [backup-simplify]: Simplify n into n
22.034 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
22.034 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
22.034 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
22.034 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.035 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.035 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.035 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
22.035 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
22.035 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))))
22.035 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
22.035 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
22.035 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
22.035 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
22.036 * [taylor]: Taking taylor expansion of 1/2 in n
22.036 * [backup-simplify]: Simplify 1/2 into 1/2
22.036 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
22.036 * [taylor]: Taking taylor expansion of 1/2 in n
22.036 * [backup-simplify]: Simplify 1/2 into 1/2
22.036 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.036 * [taylor]: Taking taylor expansion of 1/2 in n
22.036 * [backup-simplify]: Simplify 1/2 into 1/2
22.036 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.036 * [taylor]: Taking taylor expansion of k in n
22.036 * [backup-simplify]: Simplify k into k
22.036 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.036 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
22.036 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
22.036 * [taylor]: Taking taylor expansion of 2 in n
22.036 * [backup-simplify]: Simplify 2 into 2
22.036 * [taylor]: Taking taylor expansion of (/ PI n) in n
22.036 * [taylor]: Taking taylor expansion of PI in n
22.036 * [backup-simplify]: Simplify PI into PI
22.036 * [taylor]: Taking taylor expansion of n in n
22.036 * [backup-simplify]: Simplify 0 into 0
22.036 * [backup-simplify]: Simplify 1 into 1
22.036 * [backup-simplify]: Simplify (/ PI 1) into PI
22.037 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.037 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.037 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.037 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
22.037 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
22.038 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
22.038 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
22.039 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
22.040 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
22.040 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
22.040 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
22.040 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
22.040 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
22.040 * [taylor]: Taking taylor expansion of 1/2 in n
22.040 * [backup-simplify]: Simplify 1/2 into 1/2
22.040 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
22.040 * [taylor]: Taking taylor expansion of 1/2 in n
22.040 * [backup-simplify]: Simplify 1/2 into 1/2
22.040 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.040 * [taylor]: Taking taylor expansion of 1/2 in n
22.040 * [backup-simplify]: Simplify 1/2 into 1/2
22.040 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.040 * [taylor]: Taking taylor expansion of k in n
22.040 * [backup-simplify]: Simplify k into k
22.040 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.040 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
22.040 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
22.040 * [taylor]: Taking taylor expansion of 2 in n
22.040 * [backup-simplify]: Simplify 2 into 2
22.040 * [taylor]: Taking taylor expansion of (/ PI n) in n
22.040 * [taylor]: Taking taylor expansion of PI in n
22.040 * [backup-simplify]: Simplify PI into PI
22.040 * [taylor]: Taking taylor expansion of n in n
22.040 * [backup-simplify]: Simplify 0 into 0
22.040 * [backup-simplify]: Simplify 1 into 1
22.041 * [backup-simplify]: Simplify (/ PI 1) into PI
22.041 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.042 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.042 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.042 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
22.042 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
22.042 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
22.043 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
22.044 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
22.044 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
22.044 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
22.044 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
22.044 * [taylor]: Taking taylor expansion of 1/2 in k
22.044 * [backup-simplify]: Simplify 1/2 into 1/2
22.044 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
22.044 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
22.044 * [taylor]: Taking taylor expansion of 1/2 in k
22.044 * [backup-simplify]: Simplify 1/2 into 1/2
22.045 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.045 * [taylor]: Taking taylor expansion of 1/2 in k
22.045 * [backup-simplify]: Simplify 1/2 into 1/2
22.045 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.045 * [taylor]: Taking taylor expansion of k in k
22.045 * [backup-simplify]: Simplify 0 into 0
22.045 * [backup-simplify]: Simplify 1 into 1
22.045 * [backup-simplify]: Simplify (/ 1 1) into 1
22.045 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
22.045 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
22.045 * [taylor]: Taking taylor expansion of (* 2 PI) in k
22.045 * [taylor]: Taking taylor expansion of 2 in k
22.045 * [backup-simplify]: Simplify 2 into 2
22.045 * [taylor]: Taking taylor expansion of PI in k
22.045 * [backup-simplify]: Simplify PI into PI
22.045 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.046 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.046 * [taylor]: Taking taylor expansion of (log n) in k
22.046 * [taylor]: Taking taylor expansion of n in k
22.046 * [backup-simplify]: Simplify n into n
22.046 * [backup-simplify]: Simplify (log n) into (log n)
22.046 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.047 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.047 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.047 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
22.048 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
22.048 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
22.049 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
22.050 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
22.050 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
22.051 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
22.052 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
22.054 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
22.054 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
22.054 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
22.055 * [backup-simplify]: Simplify (- 0) into 0
22.055 * [backup-simplify]: Simplify (+ 0 0) into 0
22.055 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
22.056 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
22.057 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
22.058 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
22.058 * [taylor]: Taking taylor expansion of 0 in k
22.058 * [backup-simplify]: Simplify 0 into 0
22.058 * [backup-simplify]: Simplify 0 into 0
22.058 * [backup-simplify]: Simplify 0 into 0
22.059 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.059 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
22.061 * [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
22.061 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.062 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
22.062 * [backup-simplify]: Simplify (- 0) into 0
22.063 * [backup-simplify]: Simplify (+ 0 0) into 0
22.063 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
22.064 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
22.065 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
22.067 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
22.067 * [taylor]: Taking taylor expansion of 0 in k
22.067 * [backup-simplify]: Simplify 0 into 0
22.067 * [backup-simplify]: Simplify 0 into 0
22.067 * [backup-simplify]: Simplify 0 into 0
22.067 * [backup-simplify]: Simplify 0 into 0
22.067 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.068 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
22.071 * [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
22.072 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.072 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
22.073 * [backup-simplify]: Simplify (- 0) into 0
22.073 * [backup-simplify]: Simplify (+ 0 0) into 0
22.074 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
22.075 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
22.076 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
22.078 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
22.078 * [taylor]: Taking taylor expansion of 0 in k
22.078 * [backup-simplify]: Simplify 0 into 0
22.078 * [backup-simplify]: Simplify 0 into 0
22.078 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))
22.079 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)))
22.079 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
22.079 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
22.079 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
22.079 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
22.079 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
22.079 * [taylor]: Taking taylor expansion of 1/2 in k
22.079 * [backup-simplify]: Simplify 1/2 into 1/2
22.079 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
22.079 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.079 * [taylor]: Taking taylor expansion of 1/2 in k
22.079 * [backup-simplify]: Simplify 1/2 into 1/2
22.079 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.079 * [taylor]: Taking taylor expansion of k in k
22.079 * [backup-simplify]: Simplify 0 into 0
22.079 * [backup-simplify]: Simplify 1 into 1
22.079 * [backup-simplify]: Simplify (/ 1 1) into 1
22.079 * [taylor]: Taking taylor expansion of 1/2 in k
22.079 * [backup-simplify]: Simplify 1/2 into 1/2
22.079 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
22.079 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
22.079 * [taylor]: Taking taylor expansion of -2 in k
22.079 * [backup-simplify]: Simplify -2 into -2
22.079 * [taylor]: Taking taylor expansion of (/ PI n) in k
22.079 * [taylor]: Taking taylor expansion of PI in k
22.080 * [backup-simplify]: Simplify PI into PI
22.080 * [taylor]: Taking taylor expansion of n in k
22.080 * [backup-simplify]: Simplify n into n
22.080 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
22.080 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
22.080 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
22.080 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.080 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
22.085 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
22.085 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
22.085 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
22.085 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
22.085 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
22.085 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
22.085 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
22.085 * [taylor]: Taking taylor expansion of 1/2 in n
22.085 * [backup-simplify]: Simplify 1/2 into 1/2
22.085 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
22.085 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.085 * [taylor]: Taking taylor expansion of 1/2 in n
22.085 * [backup-simplify]: Simplify 1/2 into 1/2
22.085 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.086 * [taylor]: Taking taylor expansion of k in n
22.086 * [backup-simplify]: Simplify k into k
22.086 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.086 * [taylor]: Taking taylor expansion of 1/2 in n
22.086 * [backup-simplify]: Simplify 1/2 into 1/2
22.086 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
22.086 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
22.086 * [taylor]: Taking taylor expansion of -2 in n
22.086 * [backup-simplify]: Simplify -2 into -2
22.086 * [taylor]: Taking taylor expansion of (/ PI n) in n
22.086 * [taylor]: Taking taylor expansion of PI in n
22.086 * [backup-simplify]: Simplify PI into PI
22.086 * [taylor]: Taking taylor expansion of n in n
22.086 * [backup-simplify]: Simplify 0 into 0
22.086 * [backup-simplify]: Simplify 1 into 1
22.086 * [backup-simplify]: Simplify (/ PI 1) into PI
22.087 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
22.087 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
22.087 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.087 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
22.087 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
22.088 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
22.089 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
22.090 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
22.090 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
22.090 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
22.090 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
22.090 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
22.090 * [taylor]: Taking taylor expansion of 1/2 in n
22.090 * [backup-simplify]: Simplify 1/2 into 1/2
22.090 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
22.090 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.090 * [taylor]: Taking taylor expansion of 1/2 in n
22.090 * [backup-simplify]: Simplify 1/2 into 1/2
22.090 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.090 * [taylor]: Taking taylor expansion of k in n
22.090 * [backup-simplify]: Simplify k into k
22.090 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.090 * [taylor]: Taking taylor expansion of 1/2 in n
22.090 * [backup-simplify]: Simplify 1/2 into 1/2
22.090 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
22.090 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
22.090 * [taylor]: Taking taylor expansion of -2 in n
22.090 * [backup-simplify]: Simplify -2 into -2
22.090 * [taylor]: Taking taylor expansion of (/ PI n) in n
22.090 * [taylor]: Taking taylor expansion of PI in n
22.090 * [backup-simplify]: Simplify PI into PI
22.090 * [taylor]: Taking taylor expansion of n in n
22.090 * [backup-simplify]: Simplify 0 into 0
22.090 * [backup-simplify]: Simplify 1 into 1
22.091 * [backup-simplify]: Simplify (/ PI 1) into PI
22.091 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
22.092 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
22.092 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.092 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
22.092 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
22.093 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
22.093 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
22.094 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
22.094 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
22.094 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
22.094 * [taylor]: Taking taylor expansion of 1/2 in k
22.094 * [backup-simplify]: Simplify 1/2 into 1/2
22.094 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
22.094 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
22.094 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.094 * [taylor]: Taking taylor expansion of 1/2 in k
22.094 * [backup-simplify]: Simplify 1/2 into 1/2
22.094 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.094 * [taylor]: Taking taylor expansion of k in k
22.094 * [backup-simplify]: Simplify 0 into 0
22.094 * [backup-simplify]: Simplify 1 into 1
22.095 * [backup-simplify]: Simplify (/ 1 1) into 1
22.095 * [taylor]: Taking taylor expansion of 1/2 in k
22.095 * [backup-simplify]: Simplify 1/2 into 1/2
22.095 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
22.095 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
22.095 * [taylor]: Taking taylor expansion of (* -2 PI) in k
22.095 * [taylor]: Taking taylor expansion of -2 in k
22.095 * [backup-simplify]: Simplify -2 into -2
22.095 * [taylor]: Taking taylor expansion of PI in k
22.095 * [backup-simplify]: Simplify PI into PI
22.095 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
22.096 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
22.096 * [taylor]: Taking taylor expansion of (log n) in k
22.096 * [taylor]: Taking taylor expansion of n in k
22.096 * [backup-simplify]: Simplify n into n
22.096 * [backup-simplify]: Simplify (log n) into (log n)
22.096 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.096 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
22.097 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
22.097 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
22.098 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
22.099 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
22.099 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
22.100 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
22.101 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
22.101 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
22.102 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
22.102 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
22.103 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
22.103 * [backup-simplify]: Simplify (+ 0 0) into 0
22.103 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
22.104 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
22.105 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
22.106 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
22.106 * [taylor]: Taking taylor expansion of 0 in k
22.106 * [backup-simplify]: Simplify 0 into 0
22.106 * [backup-simplify]: Simplify 0 into 0
22.106 * [backup-simplify]: Simplify 0 into 0
22.107 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.108 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
22.112 * [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
22.112 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.113 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
22.114 * [backup-simplify]: Simplify (+ 0 0) into 0
22.115 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
22.116 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
22.118 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
22.121 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
22.121 * [taylor]: Taking taylor expansion of 0 in k
22.121 * [backup-simplify]: Simplify 0 into 0
22.121 * [backup-simplify]: Simplify 0 into 0
22.121 * [backup-simplify]: Simplify 0 into 0
22.121 * [backup-simplify]: Simplify 0 into 0
22.122 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.123 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
22.129 * [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
22.129 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.131 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
22.131 * [backup-simplify]: Simplify (+ 0 0) into 0
22.132 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
22.134 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
22.136 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
22.139 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
22.139 * [taylor]: Taking taylor expansion of 0 in k
22.139 * [backup-simplify]: Simplify 0 into 0
22.139 * [backup-simplify]: Simplify 0 into 0
22.140 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))
22.140 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1)
22.140 * [backup-simplify]: Simplify (pow n (/ (- 1/2 (/ k 2)) 2)) into (pow n (* 1/2 (- 1/2 (* 1/2 k))))
22.140 * [approximate]: Taking taylor expansion of (pow n (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
22.140 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1/2 (* 1/2 k)))) in k
22.140 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log n))) in k
22.140 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log n)) in k
22.140 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
22.140 * [taylor]: Taking taylor expansion of 1/2 in k
22.140 * [backup-simplify]: Simplify 1/2 into 1/2
22.140 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
22.140 * [taylor]: Taking taylor expansion of 1/2 in k
22.141 * [backup-simplify]: Simplify 1/2 into 1/2
22.141 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
22.141 * [taylor]: Taking taylor expansion of 1/2 in k
22.141 * [backup-simplify]: Simplify 1/2 into 1/2
22.141 * [taylor]: Taking taylor expansion of k in k
22.141 * [backup-simplify]: Simplify 0 into 0
22.141 * [backup-simplify]: Simplify 1 into 1
22.141 * [taylor]: Taking taylor expansion of (log n) in k
22.141 * [taylor]: Taking taylor expansion of n in k
22.141 * [backup-simplify]: Simplify n into n
22.141 * [backup-simplify]: Simplify (log n) into (log n)
22.141 * [backup-simplify]: Simplify (* 1/2 0) into 0
22.142 * [backup-simplify]: Simplify (- 0) into 0
22.142 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
22.142 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
22.142 * [backup-simplify]: Simplify (* 1/4 (log n)) into (* 1/4 (log n))
22.143 * [backup-simplify]: Simplify (exp (* 1/4 (log n))) into (pow n 1/4)
22.143 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1/2 (* 1/2 k)))) in n
22.143 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log n))) in n
22.143 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log n)) in n
22.143 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
22.143 * [taylor]: Taking taylor expansion of 1/2 in n
22.143 * [backup-simplify]: Simplify 1/2 into 1/2
22.143 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
22.143 * [taylor]: Taking taylor expansion of 1/2 in n
22.143 * [backup-simplify]: Simplify 1/2 into 1/2
22.143 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
22.143 * [taylor]: Taking taylor expansion of 1/2 in n
22.143 * [backup-simplify]: Simplify 1/2 into 1/2
22.143 * [taylor]: Taking taylor expansion of k in n
22.143 * [backup-simplify]: Simplify k into k
22.143 * [taylor]: Taking taylor expansion of (log n) in n
22.143 * [taylor]: Taking taylor expansion of n in n
22.143 * [backup-simplify]: Simplify 0 into 0
22.143 * [backup-simplify]: Simplify 1 into 1
22.144 * [backup-simplify]: Simplify (log 1) into 0
22.144 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
22.144 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
22.144 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
22.144 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
22.144 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
22.145 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (log n)) into (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))
22.145 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n))))
22.145 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1/2 (* 1/2 k)))) in n
22.145 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log n))) in n
22.145 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log n)) in n
22.145 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
22.145 * [taylor]: Taking taylor expansion of 1/2 in n
22.145 * [backup-simplify]: Simplify 1/2 into 1/2
22.145 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
22.145 * [taylor]: Taking taylor expansion of 1/2 in n
22.145 * [backup-simplify]: Simplify 1/2 into 1/2
22.145 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
22.145 * [taylor]: Taking taylor expansion of 1/2 in n
22.145 * [backup-simplify]: Simplify 1/2 into 1/2
22.145 * [taylor]: Taking taylor expansion of k in n
22.145 * [backup-simplify]: Simplify k into k
22.145 * [taylor]: Taking taylor expansion of (log n) in n
22.145 * [taylor]: Taking taylor expansion of n in n
22.145 * [backup-simplify]: Simplify 0 into 0
22.145 * [backup-simplify]: Simplify 1 into 1
22.146 * [backup-simplify]: Simplify (log 1) into 0
22.146 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
22.146 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
22.146 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
22.146 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
22.147 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
22.147 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (log n)) into (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))
22.147 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n))))
22.147 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) in k
22.147 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (log n))) in k
22.147 * [taylor]: Taking taylor expansion of 1/2 in k
22.147 * [backup-simplify]: Simplify 1/2 into 1/2
22.147 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k
22.147 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
22.147 * [taylor]: Taking taylor expansion of 1/2 in k
22.147 * [backup-simplify]: Simplify 1/2 into 1/2
22.147 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
22.148 * [taylor]: Taking taylor expansion of 1/2 in k
22.148 * [backup-simplify]: Simplify 1/2 into 1/2
22.148 * [taylor]: Taking taylor expansion of k in k
22.148 * [backup-simplify]: Simplify 0 into 0
22.148 * [backup-simplify]: Simplify 1 into 1
22.148 * [taylor]: Taking taylor expansion of (log n) in k
22.148 * [taylor]: Taking taylor expansion of n in k
22.148 * [backup-simplify]: Simplify n into n
22.148 * [backup-simplify]: Simplify (log n) into (log n)
22.148 * [backup-simplify]: Simplify (* 1/2 0) into 0
22.149 * [backup-simplify]: Simplify (- 0) into 0
22.149 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
22.149 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
22.149 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (log n))) into (* 1/4 (log n))
22.149 * [backup-simplify]: Simplify (exp (* 1/4 (log n))) into (pow n 1/4)
22.149 * [backup-simplify]: Simplify (pow n 1/4) into (pow n 1/4)
22.151 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
22.151 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
22.152 * [backup-simplify]: Simplify (- 0) into 0
22.152 * [backup-simplify]: Simplify (+ 0 0) into 0
22.153 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
22.153 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
22.153 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (log n))) into 0
22.154 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
22.154 * [taylor]: Taking taylor expansion of 0 in k
22.154 * [backup-simplify]: Simplify 0 into 0
22.154 * [backup-simplify]: Simplify 0 into 0
22.155 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
22.156 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
22.156 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.157 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.157 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n)))
22.157 * [backup-simplify]: Simplify (+ (* 1/2 (- (* 1/2 (log n)))) (* 0 (* 1/2 (log n)))) into (- (* 1/4 (log n)))
22.158 * [backup-simplify]: Simplify (* (exp (* 1/4 (log n))) (+ (* (/ (pow (- (* 1/4 (log n))) 1) 1)))) into (* -1/4 (* (pow n 1/4) (log n)))
22.158 * [backup-simplify]: Simplify (* -1/4 (* (pow n 1/4) (log n))) into (* -1/4 (* (pow n 1/4) (log n)))
22.161 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
22.162 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
22.162 * [backup-simplify]: Simplify (- 0) into 0
22.162 * [backup-simplify]: Simplify (+ 0 0) into 0
22.163 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
22.164 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
22.164 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (log n)))) into 0
22.166 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
22.166 * [taylor]: Taking taylor expansion of 0 in k
22.166 * [backup-simplify]: Simplify 0 into 0
22.166 * [backup-simplify]: Simplify 0 into 0
22.166 * [backup-simplify]: Simplify 0 into 0
22.168 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
22.169 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
22.169 * [backup-simplify]: Simplify (- 0) into 0
22.169 * [backup-simplify]: Simplify (+ 0 0) into 0
22.170 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0
22.171 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (* 1/2 (log n)))) (* 0 (* 1/2 (log n))))) into 0
22.172 * [backup-simplify]: Simplify (* (exp (* 1/4 (log n))) (+ (* (/ (pow (- (* 1/4 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/32 (* (pow n 1/4) (pow (log n) 2)))
22.172 * [backup-simplify]: Simplify (* 1/32 (* (pow n 1/4) (pow (log n) 2))) into (* 1/32 (* (pow n 1/4) (pow (log n) 2)))
22.173 * [backup-simplify]: Simplify (+ (* (* 1/32 (* (pow n 1/4) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -1/4 (* (pow n 1/4) (log n))) (* k 1)) (pow n 1/4))) into (- (+ (pow n 1/4) (* 1/32 (* (pow n 1/4) (* (pow (log n) 2) (pow k 2))))) (* 1/4 (* (pow n 1/4) (* (log n) k))))
22.173 * [backup-simplify]: Simplify (pow (/ 1 n) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))))
22.173 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
22.173 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
22.173 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n)))) in k
22.173 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n))) in k
22.173 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
22.173 * [taylor]: Taking taylor expansion of 1/2 in k
22.173 * [backup-simplify]: Simplify 1/2 into 1/2
22.173 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
22.173 * [taylor]: Taking taylor expansion of 1/2 in k
22.173 * [backup-simplify]: Simplify 1/2 into 1/2
22.173 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.173 * [taylor]: Taking taylor expansion of 1/2 in k
22.174 * [backup-simplify]: Simplify 1/2 into 1/2
22.174 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.174 * [taylor]: Taking taylor expansion of k in k
22.174 * [backup-simplify]: Simplify 0 into 0
22.174 * [backup-simplify]: Simplify 1 into 1
22.174 * [backup-simplify]: Simplify (/ 1 1) into 1
22.174 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k
22.174 * [taylor]: Taking taylor expansion of (/ 1 n) in k
22.174 * [taylor]: Taking taylor expansion of n in k
22.174 * [backup-simplify]: Simplify n into n
22.174 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n)
22.174 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n))
22.175 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.175 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.175 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.176 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
22.176 * [backup-simplify]: Simplify (* -1/4 (log (/ 1 n))) into (* -1/4 (log (/ 1 n)))
22.176 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))))
22.176 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
22.176 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n)))) in n
22.176 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n))) in n
22.176 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
22.176 * [taylor]: Taking taylor expansion of 1/2 in n
22.176 * [backup-simplify]: Simplify 1/2 into 1/2
22.176 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
22.176 * [taylor]: Taking taylor expansion of 1/2 in n
22.176 * [backup-simplify]: Simplify 1/2 into 1/2
22.176 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.177 * [taylor]: Taking taylor expansion of 1/2 in n
22.177 * [backup-simplify]: Simplify 1/2 into 1/2
22.177 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.177 * [taylor]: Taking taylor expansion of k in n
22.177 * [backup-simplify]: Simplify k into k
22.177 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.177 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
22.177 * [taylor]: Taking taylor expansion of (/ 1 n) in n
22.177 * [taylor]: Taking taylor expansion of n in n
22.177 * [backup-simplify]: Simplify 0 into 0
22.177 * [backup-simplify]: Simplify 1 into 1
22.177 * [backup-simplify]: Simplify (/ 1 1) into 1
22.178 * [backup-simplify]: Simplify (log 1) into 0
22.178 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.178 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
22.178 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
22.178 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
22.178 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
22.179 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log n))) into (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))
22.179 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
22.179 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
22.179 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n)))) in n
22.179 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n))) in n
22.179 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
22.179 * [taylor]: Taking taylor expansion of 1/2 in n
22.179 * [backup-simplify]: Simplify 1/2 into 1/2
22.179 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
22.179 * [taylor]: Taking taylor expansion of 1/2 in n
22.179 * [backup-simplify]: Simplify 1/2 into 1/2
22.179 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.179 * [taylor]: Taking taylor expansion of 1/2 in n
22.179 * [backup-simplify]: Simplify 1/2 into 1/2
22.179 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.179 * [taylor]: Taking taylor expansion of k in n
22.180 * [backup-simplify]: Simplify k into k
22.180 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.180 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
22.180 * [taylor]: Taking taylor expansion of (/ 1 n) in n
22.180 * [taylor]: Taking taylor expansion of n in n
22.180 * [backup-simplify]: Simplify 0 into 0
22.180 * [backup-simplify]: Simplify 1 into 1
22.180 * [backup-simplify]: Simplify (/ 1 1) into 1
22.181 * [backup-simplify]: Simplify (log 1) into 0
22.181 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.181 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
22.181 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
22.181 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
22.181 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
22.182 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log n))) into (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))
22.182 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
22.182 * [taylor]: Taking taylor expansion of (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k
22.182 * [taylor]: Taking taylor expansion of (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k
22.182 * [taylor]: Taking taylor expansion of -1/2 in k
22.182 * [backup-simplify]: Simplify -1/2 into -1/2
22.182 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k
22.182 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
22.182 * [taylor]: Taking taylor expansion of 1/2 in k
22.182 * [backup-simplify]: Simplify 1/2 into 1/2
22.182 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.182 * [taylor]: Taking taylor expansion of 1/2 in k
22.182 * [backup-simplify]: Simplify 1/2 into 1/2
22.182 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.182 * [taylor]: Taking taylor expansion of k in k
22.182 * [backup-simplify]: Simplify 0 into 0
22.182 * [backup-simplify]: Simplify 1 into 1
22.183 * [backup-simplify]: Simplify (/ 1 1) into 1
22.183 * [taylor]: Taking taylor expansion of (log n) in k
22.183 * [taylor]: Taking taylor expansion of n in k
22.183 * [backup-simplify]: Simplify n into n
22.183 * [backup-simplify]: Simplify (log n) into (log n)
22.183 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.184 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.184 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.184 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n))
22.184 * [backup-simplify]: Simplify (* -1/2 (* -1/2 (log n))) into (* 1/4 (log n))
22.185 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
22.185 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
22.186 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
22.187 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
22.187 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
22.188 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
22.188 * [backup-simplify]: Simplify (- 0) into 0
22.189 * [backup-simplify]: Simplify (+ 0 0) into 0
22.189 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
22.190 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
22.190 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log n)))) into 0
22.191 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
22.191 * [taylor]: Taking taylor expansion of 0 in k
22.191 * [backup-simplify]: Simplify 0 into 0
22.191 * [backup-simplify]: Simplify 0 into 0
22.191 * [backup-simplify]: Simplify 0 into 0
22.192 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.195 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
22.195 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.196 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
22.197 * [backup-simplify]: Simplify (- 0) into 0
22.197 * [backup-simplify]: Simplify (+ 0 0) into 0
22.198 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
22.199 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
22.199 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0
22.201 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
22.201 * [taylor]: Taking taylor expansion of 0 in k
22.201 * [backup-simplify]: Simplify 0 into 0
22.201 * [backup-simplify]: Simplify 0 into 0
22.201 * [backup-simplify]: Simplify 0 into 0
22.201 * [backup-simplify]: Simplify 0 into 0
22.202 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.205 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
22.205 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.206 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
22.206 * [backup-simplify]: Simplify (- 0) into 0
22.206 * [backup-simplify]: Simplify (+ 0 0) into 0
22.207 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
22.207 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
22.208 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0
22.209 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
22.209 * [taylor]: Taking taylor expansion of 0 in k
22.209 * [backup-simplify]: Simplify 0 into 0
22.209 * [backup-simplify]: Simplify 0 into 0
22.209 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) into (exp (* -1/2 (* (- 1/2 (* 1/2 k)) (log (/ 1 n)))))
22.209 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)))
22.209 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
22.209 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
22.209 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n)))) in k
22.209 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n))) in k
22.209 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
22.209 * [taylor]: Taking taylor expansion of 1/2 in k
22.209 * [backup-simplify]: Simplify 1/2 into 1/2
22.209 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
22.209 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.209 * [taylor]: Taking taylor expansion of 1/2 in k
22.210 * [backup-simplify]: Simplify 1/2 into 1/2
22.210 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.210 * [taylor]: Taking taylor expansion of k in k
22.210 * [backup-simplify]: Simplify 0 into 0
22.210 * [backup-simplify]: Simplify 1 into 1
22.210 * [backup-simplify]: Simplify (/ 1 1) into 1
22.210 * [taylor]: Taking taylor expansion of 1/2 in k
22.210 * [backup-simplify]: Simplify 1/2 into 1/2
22.210 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k
22.210 * [taylor]: Taking taylor expansion of (/ -1 n) in k
22.210 * [taylor]: Taking taylor expansion of -1 in k
22.210 * [backup-simplify]: Simplify -1 into -1
22.210 * [taylor]: Taking taylor expansion of n in k
22.210 * [backup-simplify]: Simplify n into n
22.210 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n)
22.210 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n))
22.210 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.211 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
22.211 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
22.211 * [backup-simplify]: Simplify (* 1/4 (log (/ -1 n))) into (* 1/4 (log (/ -1 n)))
22.211 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n)))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))))
22.211 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
22.211 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n)))) in n
22.211 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n))) in n
22.211 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
22.211 * [taylor]: Taking taylor expansion of 1/2 in n
22.211 * [backup-simplify]: Simplify 1/2 into 1/2
22.211 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
22.211 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.211 * [taylor]: Taking taylor expansion of 1/2 in n
22.211 * [backup-simplify]: Simplify 1/2 into 1/2
22.211 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.211 * [taylor]: Taking taylor expansion of k in n
22.211 * [backup-simplify]: Simplify k into k
22.211 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.211 * [taylor]: Taking taylor expansion of 1/2 in n
22.211 * [backup-simplify]: Simplify 1/2 into 1/2
22.211 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
22.211 * [taylor]: Taking taylor expansion of (/ -1 n) in n
22.211 * [taylor]: Taking taylor expansion of -1 in n
22.211 * [backup-simplify]: Simplify -1 into -1
22.211 * [taylor]: Taking taylor expansion of n in n
22.211 * [backup-simplify]: Simplify 0 into 0
22.211 * [backup-simplify]: Simplify 1 into 1
22.212 * [backup-simplify]: Simplify (/ -1 1) into -1
22.212 * [backup-simplify]: Simplify (log -1) into (log -1)
22.212 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.212 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
22.212 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
22.213 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
22.213 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log -1) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
22.213 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))
22.213 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
22.213 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n)))) in n
22.213 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n))) in n
22.213 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
22.213 * [taylor]: Taking taylor expansion of 1/2 in n
22.213 * [backup-simplify]: Simplify 1/2 into 1/2
22.214 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
22.214 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.214 * [taylor]: Taking taylor expansion of 1/2 in n
22.214 * [backup-simplify]: Simplify 1/2 into 1/2
22.214 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.214 * [taylor]: Taking taylor expansion of k in n
22.214 * [backup-simplify]: Simplify k into k
22.214 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.214 * [taylor]: Taking taylor expansion of 1/2 in n
22.214 * [backup-simplify]: Simplify 1/2 into 1/2
22.214 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
22.214 * [taylor]: Taking taylor expansion of (/ -1 n) in n
22.214 * [taylor]: Taking taylor expansion of -1 in n
22.214 * [backup-simplify]: Simplify -1 into -1
22.214 * [taylor]: Taking taylor expansion of n in n
22.214 * [backup-simplify]: Simplify 0 into 0
22.214 * [backup-simplify]: Simplify 1 into 1
22.218 * [backup-simplify]: Simplify (/ -1 1) into -1
22.219 * [backup-simplify]: Simplify (log -1) into (log -1)
22.219 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.219 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
22.219 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
22.220 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
22.220 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log -1) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
22.221 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))
22.221 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) in k
22.221 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k
22.221 * [taylor]: Taking taylor expansion of 1/2 in k
22.221 * [backup-simplify]: Simplify 1/2 into 1/2
22.221 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k
22.221 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
22.221 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.221 * [taylor]: Taking taylor expansion of 1/2 in k
22.221 * [backup-simplify]: Simplify 1/2 into 1/2
22.221 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.221 * [taylor]: Taking taylor expansion of k in k
22.221 * [backup-simplify]: Simplify 0 into 0
22.221 * [backup-simplify]: Simplify 1 into 1
22.221 * [backup-simplify]: Simplify (/ 1 1) into 1
22.221 * [taylor]: Taking taylor expansion of 1/2 in k
22.221 * [backup-simplify]: Simplify 1/2 into 1/2
22.221 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k
22.221 * [taylor]: Taking taylor expansion of (log -1) in k
22.221 * [taylor]: Taking taylor expansion of -1 in k
22.221 * [backup-simplify]: Simplify -1 into -1
22.221 * [backup-simplify]: Simplify (log -1) into (log -1)
22.221 * [taylor]: Taking taylor expansion of (log n) in k
22.222 * [taylor]: Taking taylor expansion of n in k
22.222 * [backup-simplify]: Simplify n into n
22.222 * [backup-simplify]: Simplify (log n) into (log n)
22.222 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.222 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
22.222 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
22.223 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n))
22.223 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n)))
22.224 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log -1) (log n)))) into (* 1/4 (- (log -1) (log n)))
22.224 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))
22.225 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))
22.226 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
22.227 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0
22.227 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
22.228 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
22.228 * [backup-simplify]: Simplify (+ 0 0) into 0
22.229 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
22.230 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
22.230 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log -1) (log n)))) into 0
22.232 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
22.232 * [taylor]: Taking taylor expansion of 0 in k
22.232 * [backup-simplify]: Simplify 0 into 0
22.232 * [backup-simplify]: Simplify 0 into 0
22.232 * [backup-simplify]: Simplify 0 into 0
22.233 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.235 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0
22.235 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.236 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
22.237 * [backup-simplify]: Simplify (+ 0 0) into 0
22.237 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
22.238 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
22.239 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0
22.240 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
22.240 * [taylor]: Taking taylor expansion of 0 in k
22.240 * [backup-simplify]: Simplify 0 into 0
22.240 * [backup-simplify]: Simplify 0 into 0
22.240 * [backup-simplify]: Simplify 0 into 0
22.240 * [backup-simplify]: Simplify 0 into 0
22.241 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.244 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -1 1)))) 6) into 0
22.244 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.245 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
22.245 * [backup-simplify]: Simplify (+ 0 0) into 0
22.246 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
22.246 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
22.247 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0
22.249 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
22.249 * [taylor]: Taking taylor expansion of 0 in k
22.249 * [backup-simplify]: Simplify 0 into 0
22.249 * [backup-simplify]: Simplify 0 into 0
22.249 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))))
22.249 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1)
22.249 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
22.250 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
22.250 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
22.250 * [taylor]: Taking taylor expansion of 2 in n
22.250 * [backup-simplify]: Simplify 2 into 2
22.250 * [taylor]: Taking taylor expansion of (* n PI) in n
22.250 * [taylor]: Taking taylor expansion of n in n
22.250 * [backup-simplify]: Simplify 0 into 0
22.250 * [backup-simplify]: Simplify 1 into 1
22.250 * [taylor]: Taking taylor expansion of PI in n
22.250 * [backup-simplify]: Simplify PI into PI
22.250 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
22.250 * [taylor]: Taking taylor expansion of 2 in n
22.250 * [backup-simplify]: Simplify 2 into 2
22.250 * [taylor]: Taking taylor expansion of (* n PI) in n
22.250 * [taylor]: Taking taylor expansion of n in n
22.250 * [backup-simplify]: Simplify 0 into 0
22.250 * [backup-simplify]: Simplify 1 into 1
22.250 * [taylor]: Taking taylor expansion of PI in n
22.250 * [backup-simplify]: Simplify PI into PI
22.250 * [backup-simplify]: Simplify (* 0 PI) into 0
22.250 * [backup-simplify]: Simplify (* 2 0) into 0
22.250 * [backup-simplify]: Simplify 0 into 0
22.251 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
22.252 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
22.253 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.253 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
22.254 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
22.254 * [backup-simplify]: Simplify 0 into 0
22.255 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
22.255 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
22.255 * [backup-simplify]: Simplify 0 into 0
22.256 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
22.257 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
22.257 * [backup-simplify]: Simplify 0 into 0
22.258 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
22.259 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
22.259 * [backup-simplify]: Simplify 0 into 0
22.260 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
22.261 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
22.261 * [backup-simplify]: Simplify 0 into 0
22.262 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
22.263 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
22.263 * [backup-simplify]: Simplify 0 into 0
22.263 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
22.264 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
22.264 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
22.264 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
22.264 * [taylor]: Taking taylor expansion of 2 in n
22.264 * [backup-simplify]: Simplify 2 into 2
22.264 * [taylor]: Taking taylor expansion of (/ PI n) in n
22.264 * [taylor]: Taking taylor expansion of PI in n
22.264 * [backup-simplify]: Simplify PI into PI
22.264 * [taylor]: Taking taylor expansion of n in n
22.264 * [backup-simplify]: Simplify 0 into 0
22.264 * [backup-simplify]: Simplify 1 into 1
22.264 * [backup-simplify]: Simplify (/ PI 1) into PI
22.264 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
22.264 * [taylor]: Taking taylor expansion of 2 in n
22.264 * [backup-simplify]: Simplify 2 into 2
22.264 * [taylor]: Taking taylor expansion of (/ PI n) in n
22.264 * [taylor]: Taking taylor expansion of PI in n
22.264 * [backup-simplify]: Simplify PI into PI
22.264 * [taylor]: Taking taylor expansion of n in n
22.264 * [backup-simplify]: Simplify 0 into 0
22.264 * [backup-simplify]: Simplify 1 into 1
22.265 * [backup-simplify]: Simplify (/ PI 1) into PI
22.265 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.265 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.266 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
22.266 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
22.266 * [backup-simplify]: Simplify 0 into 0
22.267 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.268 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
22.268 * [backup-simplify]: Simplify 0 into 0
22.268 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.269 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
22.269 * [backup-simplify]: Simplify 0 into 0
22.270 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.271 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
22.271 * [backup-simplify]: Simplify 0 into 0
22.271 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.272 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
22.272 * [backup-simplify]: Simplify 0 into 0
22.273 * [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
22.274 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
22.274 * [backup-simplify]: Simplify 0 into 0
22.274 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
22.275 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
22.275 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
22.275 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
22.275 * [taylor]: Taking taylor expansion of -2 in n
22.275 * [backup-simplify]: Simplify -2 into -2
22.275 * [taylor]: Taking taylor expansion of (/ PI n) in n
22.275 * [taylor]: Taking taylor expansion of PI in n
22.275 * [backup-simplify]: Simplify PI into PI
22.275 * [taylor]: Taking taylor expansion of n in n
22.275 * [backup-simplify]: Simplify 0 into 0
22.275 * [backup-simplify]: Simplify 1 into 1
22.275 * [backup-simplify]: Simplify (/ PI 1) into PI
22.275 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
22.275 * [taylor]: Taking taylor expansion of -2 in n
22.275 * [backup-simplify]: Simplify -2 into -2
22.275 * [taylor]: Taking taylor expansion of (/ PI n) in n
22.275 * [taylor]: Taking taylor expansion of PI in n
22.275 * [backup-simplify]: Simplify PI into PI
22.275 * [taylor]: Taking taylor expansion of n in n
22.275 * [backup-simplify]: Simplify 0 into 0
22.275 * [backup-simplify]: Simplify 1 into 1
22.276 * [backup-simplify]: Simplify (/ PI 1) into PI
22.276 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
22.276 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
22.277 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
22.277 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
22.277 * [backup-simplify]: Simplify 0 into 0
22.278 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.279 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
22.279 * [backup-simplify]: Simplify 0 into 0
22.279 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.280 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
22.280 * [backup-simplify]: Simplify 0 into 0
22.281 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.282 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
22.282 * [backup-simplify]: Simplify 0 into 0
22.282 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.283 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
22.283 * [backup-simplify]: Simplify 0 into 0
22.284 * [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
22.285 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
22.285 * [backup-simplify]: Simplify 0 into 0
22.286 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
22.286 * * * * [progress]: [ 4 / 4 ] generating series at (2)
22.287 * [backup-simplify]: Simplify (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) into (* (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 k)))) (* (pow n (* 1/2 (- 1/2 (* 1/2 k)))) (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))))) (sqrt (/ 1 k)))
22.287 * [approximate]: Taking taylor expansion of (* (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 k)))) (* (pow n (* 1/2 (- 1/2 (* 1/2 k)))) (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))))) (sqrt (/ 1 k))) in (n k) around 0
22.287 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 k)))) (* (pow n (* 1/2 (- 1/2 (* 1/2 k)))) (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))))) (sqrt (/ 1 k))) in k
22.287 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 k)))) (* (pow n (* 1/2 (- 1/2 (* 1/2 k)))) (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))))) in k
22.287 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 k)))) in k
22.287 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 PI)))) in k
22.287 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 PI))) in k
22.287 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
22.287 * [taylor]: Taking taylor expansion of 1/2 in k
22.287 * [backup-simplify]: Simplify 1/2 into 1/2
22.287 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
22.287 * [taylor]: Taking taylor expansion of 1/2 in k
22.287 * [backup-simplify]: Simplify 1/2 into 1/2
22.287 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
22.287 * [taylor]: Taking taylor expansion of 1/2 in k
22.287 * [backup-simplify]: Simplify 1/2 into 1/2
22.287 * [taylor]: Taking taylor expansion of k in k
22.287 * [backup-simplify]: Simplify 0 into 0
22.287 * [backup-simplify]: Simplify 1 into 1
22.287 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
22.287 * [taylor]: Taking taylor expansion of (* 2 PI) in k
22.287 * [taylor]: Taking taylor expansion of 2 in k
22.287 * [backup-simplify]: Simplify 2 into 2
22.287 * [taylor]: Taking taylor expansion of PI in k
22.287 * [backup-simplify]: Simplify PI into PI
22.287 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.288 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.288 * [backup-simplify]: Simplify (* 1/2 0) into 0
22.288 * [backup-simplify]: Simplify (- 0) into 0
22.289 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
22.289 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
22.290 * [backup-simplify]: Simplify (* 1/4 (log (* 2 PI))) into (* 1/4 (log (* 2 PI)))
22.293 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 PI)))) into (pow (* 2 PI) 1/4)
22.293 * [taylor]: Taking taylor expansion of (* (pow n (* 1/2 (- 1/2 (* 1/2 k)))) (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))) in k
22.293 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1/2 (* 1/2 k)))) in k
22.293 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log n))) in k
22.293 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log n)) in k
22.293 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
22.293 * [taylor]: Taking taylor expansion of 1/2 in k
22.293 * [backup-simplify]: Simplify 1/2 into 1/2
22.293 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
22.293 * [taylor]: Taking taylor expansion of 1/2 in k
22.293 * [backup-simplify]: Simplify 1/2 into 1/2
22.293 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
22.293 * [taylor]: Taking taylor expansion of 1/2 in k
22.293 * [backup-simplify]: Simplify 1/2 into 1/2
22.294 * [taylor]: Taking taylor expansion of k in k
22.294 * [backup-simplify]: Simplify 0 into 0
22.294 * [backup-simplify]: Simplify 1 into 1
22.294 * [taylor]: Taking taylor expansion of (log n) in k
22.294 * [taylor]: Taking taylor expansion of n in k
22.294 * [backup-simplify]: Simplify n into n
22.294 * [backup-simplify]: Simplify (log n) into (log n)
22.294 * [backup-simplify]: Simplify (* 1/2 0) into 0
22.295 * [backup-simplify]: Simplify (- 0) into 0
22.295 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
22.295 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
22.295 * [backup-simplify]: Simplify (* 1/4 (log n)) into (* 1/4 (log n))
22.296 * [backup-simplify]: Simplify (exp (* 1/4 (log n))) into (pow n 1/4)
22.296 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
22.296 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
22.296 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
22.296 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
22.296 * [taylor]: Taking taylor expansion of 1/2 in k
22.296 * [backup-simplify]: Simplify 1/2 into 1/2
22.296 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
22.296 * [taylor]: Taking taylor expansion of 1/2 in k
22.296 * [backup-simplify]: Simplify 1/2 into 1/2
22.296 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
22.296 * [taylor]: Taking taylor expansion of 1/2 in k
22.296 * [backup-simplify]: Simplify 1/2 into 1/2
22.296 * [taylor]: Taking taylor expansion of k in k
22.296 * [backup-simplify]: Simplify 0 into 0
22.296 * [backup-simplify]: Simplify 1 into 1
22.296 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
22.296 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
22.296 * [taylor]: Taking taylor expansion of 2 in k
22.296 * [backup-simplify]: Simplify 2 into 2
22.296 * [taylor]: Taking taylor expansion of (* n PI) in k
22.296 * [taylor]: Taking taylor expansion of n in k
22.296 * [backup-simplify]: Simplify n into n
22.296 * [taylor]: Taking taylor expansion of PI in k
22.296 * [backup-simplify]: Simplify PI into PI
22.296 * [backup-simplify]: Simplify (* n PI) into (* n PI)
22.296 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
22.296 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
22.297 * [backup-simplify]: Simplify (* 1/2 0) into 0
22.297 * [backup-simplify]: Simplify (- 0) into 0
22.298 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
22.298 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
22.298 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
22.298 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
22.298 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
22.298 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.298 * [taylor]: Taking taylor expansion of k in k
22.298 * [backup-simplify]: Simplify 0 into 0
22.298 * [backup-simplify]: Simplify 1 into 1
22.299 * [backup-simplify]: Simplify (/ 1 1) into 1
22.299 * [backup-simplify]: Simplify (sqrt 0) into 0
22.301 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
22.301 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 k)))) (* (pow n (* 1/2 (- 1/2 (* 1/2 k)))) (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))))) (sqrt (/ 1 k))) in n
22.301 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 k)))) (* (pow n (* 1/2 (- 1/2 (* 1/2 k)))) (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))))) in n
22.301 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 k)))) in n
22.301 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 PI)))) in n
22.301 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 PI))) in n
22.301 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
22.301 * [taylor]: Taking taylor expansion of 1/2 in n
22.301 * [backup-simplify]: Simplify 1/2 into 1/2
22.301 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
22.301 * [taylor]: Taking taylor expansion of 1/2 in n
22.301 * [backup-simplify]: Simplify 1/2 into 1/2
22.301 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
22.301 * [taylor]: Taking taylor expansion of 1/2 in n
22.301 * [backup-simplify]: Simplify 1/2 into 1/2
22.301 * [taylor]: Taking taylor expansion of k in n
22.301 * [backup-simplify]: Simplify k into k
22.301 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
22.301 * [taylor]: Taking taylor expansion of (* 2 PI) in n
22.301 * [taylor]: Taking taylor expansion of 2 in n
22.301 * [backup-simplify]: Simplify 2 into 2
22.301 * [taylor]: Taking taylor expansion of PI in n
22.301 * [backup-simplify]: Simplify PI into PI
22.302 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.303 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.303 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
22.303 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
22.303 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
22.303 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
22.304 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 PI))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))
22.305 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))))
22.305 * [taylor]: Taking taylor expansion of (* (pow n (* 1/2 (- 1/2 (* 1/2 k)))) (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))) in n
22.306 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1/2 (* 1/2 k)))) in n
22.306 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log n))) in n
22.306 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log n)) in n
22.306 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
22.306 * [taylor]: Taking taylor expansion of 1/2 in n
22.306 * [backup-simplify]: Simplify 1/2 into 1/2
22.306 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
22.306 * [taylor]: Taking taylor expansion of 1/2 in n
22.306 * [backup-simplify]: Simplify 1/2 into 1/2
22.306 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
22.306 * [taylor]: Taking taylor expansion of 1/2 in n
22.306 * [backup-simplify]: Simplify 1/2 into 1/2
22.306 * [taylor]: Taking taylor expansion of k in n
22.306 * [backup-simplify]: Simplify k into k
22.306 * [taylor]: Taking taylor expansion of (log n) in n
22.306 * [taylor]: Taking taylor expansion of n in n
22.306 * [backup-simplify]: Simplify 0 into 0
22.306 * [backup-simplify]: Simplify 1 into 1
22.306 * [backup-simplify]: Simplify (log 1) into 0
22.306 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
22.307 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
22.307 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
22.307 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
22.307 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
22.307 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (log n)) into (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))
22.307 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n))))
22.307 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
22.308 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
22.308 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
22.308 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
22.308 * [taylor]: Taking taylor expansion of 1/2 in n
22.308 * [backup-simplify]: Simplify 1/2 into 1/2
22.308 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
22.308 * [taylor]: Taking taylor expansion of 1/2 in n
22.308 * [backup-simplify]: Simplify 1/2 into 1/2
22.308 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
22.308 * [taylor]: Taking taylor expansion of 1/2 in n
22.308 * [backup-simplify]: Simplify 1/2 into 1/2
22.308 * [taylor]: Taking taylor expansion of k in n
22.308 * [backup-simplify]: Simplify k into k
22.308 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
22.308 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
22.308 * [taylor]: Taking taylor expansion of 2 in n
22.308 * [backup-simplify]: Simplify 2 into 2
22.308 * [taylor]: Taking taylor expansion of (* n PI) in n
22.308 * [taylor]: Taking taylor expansion of n in n
22.308 * [backup-simplify]: Simplify 0 into 0
22.308 * [backup-simplify]: Simplify 1 into 1
22.308 * [taylor]: Taking taylor expansion of PI in n
22.308 * [backup-simplify]: Simplify PI into PI
22.309 * [backup-simplify]: Simplify (* 0 PI) into 0
22.309 * [backup-simplify]: Simplify (* 2 0) into 0
22.311 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
22.312 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
22.313 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.313 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
22.313 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
22.313 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
22.314 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
22.315 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
22.316 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
22.317 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
22.317 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
22.317 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.317 * [taylor]: Taking taylor expansion of k in n
22.317 * [backup-simplify]: Simplify k into k
22.317 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.317 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
22.318 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
22.318 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
22.318 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 k)))) (* (pow n (* 1/2 (- 1/2 (* 1/2 k)))) (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))))) (sqrt (/ 1 k))) in n
22.318 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 k)))) (* (pow n (* 1/2 (- 1/2 (* 1/2 k)))) (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))))) in n
22.318 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 k)))) in n
22.318 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 PI)))) in n
22.318 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 PI))) in n
22.318 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
22.318 * [taylor]: Taking taylor expansion of 1/2 in n
22.318 * [backup-simplify]: Simplify 1/2 into 1/2
22.318 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
22.318 * [taylor]: Taking taylor expansion of 1/2 in n
22.318 * [backup-simplify]: Simplify 1/2 into 1/2
22.318 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
22.318 * [taylor]: Taking taylor expansion of 1/2 in n
22.318 * [backup-simplify]: Simplify 1/2 into 1/2
22.318 * [taylor]: Taking taylor expansion of k in n
22.318 * [backup-simplify]: Simplify k into k
22.318 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
22.318 * [taylor]: Taking taylor expansion of (* 2 PI) in n
22.318 * [taylor]: Taking taylor expansion of 2 in n
22.318 * [backup-simplify]: Simplify 2 into 2
22.318 * [taylor]: Taking taylor expansion of PI in n
22.318 * [backup-simplify]: Simplify PI into PI
22.319 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.320 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.320 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
22.320 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
22.320 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
22.320 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
22.321 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 PI))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))
22.322 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))))
22.322 * [taylor]: Taking taylor expansion of (* (pow n (* 1/2 (- 1/2 (* 1/2 k)))) (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))) in n
22.323 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1/2 (* 1/2 k)))) in n
22.323 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log n))) in n
22.323 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log n)) in n
22.323 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
22.323 * [taylor]: Taking taylor expansion of 1/2 in n
22.323 * [backup-simplify]: Simplify 1/2 into 1/2
22.323 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
22.323 * [taylor]: Taking taylor expansion of 1/2 in n
22.323 * [backup-simplify]: Simplify 1/2 into 1/2
22.323 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
22.323 * [taylor]: Taking taylor expansion of 1/2 in n
22.323 * [backup-simplify]: Simplify 1/2 into 1/2
22.323 * [taylor]: Taking taylor expansion of k in n
22.323 * [backup-simplify]: Simplify k into k
22.323 * [taylor]: Taking taylor expansion of (log n) in n
22.323 * [taylor]: Taking taylor expansion of n in n
22.323 * [backup-simplify]: Simplify 0 into 0
22.323 * [backup-simplify]: Simplify 1 into 1
22.323 * [backup-simplify]: Simplify (log 1) into 0
22.323 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
22.324 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
22.324 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
22.324 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
22.324 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
22.324 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (log n)) into (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))
22.324 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n))))
22.325 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
22.325 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
22.325 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
22.325 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
22.325 * [taylor]: Taking taylor expansion of 1/2 in n
22.325 * [backup-simplify]: Simplify 1/2 into 1/2
22.325 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
22.325 * [taylor]: Taking taylor expansion of 1/2 in n
22.325 * [backup-simplify]: Simplify 1/2 into 1/2
22.325 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
22.325 * [taylor]: Taking taylor expansion of 1/2 in n
22.325 * [backup-simplify]: Simplify 1/2 into 1/2
22.325 * [taylor]: Taking taylor expansion of k in n
22.325 * [backup-simplify]: Simplify k into k
22.325 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
22.325 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
22.325 * [taylor]: Taking taylor expansion of 2 in n
22.325 * [backup-simplify]: Simplify 2 into 2
22.325 * [taylor]: Taking taylor expansion of (* n PI) in n
22.325 * [taylor]: Taking taylor expansion of n in n
22.325 * [backup-simplify]: Simplify 0 into 0
22.325 * [backup-simplify]: Simplify 1 into 1
22.325 * [taylor]: Taking taylor expansion of PI in n
22.325 * [backup-simplify]: Simplify PI into PI
22.326 * [backup-simplify]: Simplify (* 0 PI) into 0
22.326 * [backup-simplify]: Simplify (* 2 0) into 0
22.328 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
22.329 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
22.330 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.330 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
22.330 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
22.330 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
22.330 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
22.339 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
22.341 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
22.342 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
22.342 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
22.342 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.342 * [taylor]: Taking taylor expansion of k in n
22.342 * [backup-simplify]: Simplify k into k
22.342 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.342 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
22.343 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
22.343 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
22.344 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))
22.347 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))))))
22.349 * [backup-simplify]: Simplify (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))))) (sqrt (/ 1 k))) into (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) (sqrt (/ 1 k)))
22.349 * [taylor]: Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) (sqrt (/ 1 k))) in k
22.350 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) in k
22.350 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) in k
22.350 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (log n))) in k
22.350 * [taylor]: Taking taylor expansion of 1/2 in k
22.350 * [backup-simplify]: Simplify 1/2 into 1/2
22.350 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k
22.350 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
22.350 * [taylor]: Taking taylor expansion of 1/2 in k
22.350 * [backup-simplify]: Simplify 1/2 into 1/2
22.350 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
22.350 * [taylor]: Taking taylor expansion of 1/2 in k
22.350 * [backup-simplify]: Simplify 1/2 into 1/2
22.350 * [taylor]: Taking taylor expansion of k in k
22.350 * [backup-simplify]: Simplify 0 into 0
22.350 * [backup-simplify]: Simplify 1 into 1
22.350 * [taylor]: Taking taylor expansion of (log n) in k
22.350 * [taylor]: Taking taylor expansion of n in k
22.350 * [backup-simplify]: Simplify n into n
22.350 * [backup-simplify]: Simplify (log n) into (log n)
22.351 * [backup-simplify]: Simplify (* 1/2 0) into 0
22.351 * [backup-simplify]: Simplify (- 0) into 0
22.352 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
22.352 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
22.352 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (log n))) into (* 1/4 (log n))
22.352 * [backup-simplify]: Simplify (exp (* 1/4 (log n))) into (pow n 1/4)
22.352 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) in k
22.352 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) in k
22.352 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k
22.352 * [taylor]: Taking taylor expansion of 1/2 in k
22.352 * [backup-simplify]: Simplify 1/2 into 1/2
22.352 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k
22.352 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
22.352 * [taylor]: Taking taylor expansion of 1/2 in k
22.352 * [backup-simplify]: Simplify 1/2 into 1/2
22.352 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
22.352 * [taylor]: Taking taylor expansion of 1/2 in k
22.352 * [backup-simplify]: Simplify 1/2 into 1/2
22.352 * [taylor]: Taking taylor expansion of k in k
22.352 * [backup-simplify]: Simplify 0 into 0
22.352 * [backup-simplify]: Simplify 1 into 1
22.352 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
22.352 * [taylor]: Taking taylor expansion of (* 2 PI) in k
22.352 * [taylor]: Taking taylor expansion of 2 in k
22.352 * [backup-simplify]: Simplify 2 into 2
22.352 * [taylor]: Taking taylor expansion of PI in k
22.352 * [backup-simplify]: Simplify PI into PI
22.353 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.354 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.354 * [backup-simplify]: Simplify (* 1/2 0) into 0
22.355 * [backup-simplify]: Simplify (- 0) into 0
22.355 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
22.357 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
22.359 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (log (* 2 PI)))) into (* 1/4 (log (* 2 PI)))
22.362 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 PI)))) into (pow (* 2 PI) 1/4)
22.362 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
22.362 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
22.362 * [taylor]: Taking taylor expansion of 1/2 in k
22.362 * [backup-simplify]: Simplify 1/2 into 1/2
22.362 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
22.362 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
22.362 * [taylor]: Taking taylor expansion of 1/2 in k
22.362 * [backup-simplify]: Simplify 1/2 into 1/2
22.362 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
22.362 * [taylor]: Taking taylor expansion of 1/2 in k
22.362 * [backup-simplify]: Simplify 1/2 into 1/2
22.362 * [taylor]: Taking taylor expansion of k in k
22.363 * [backup-simplify]: Simplify 0 into 0
22.363 * [backup-simplify]: Simplify 1 into 1
22.363 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
22.363 * [taylor]: Taking taylor expansion of (log n) in k
22.363 * [taylor]: Taking taylor expansion of n in k
22.363 * [backup-simplify]: Simplify n into n
22.363 * [backup-simplify]: Simplify (log n) into (log n)
22.363 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
22.363 * [taylor]: Taking taylor expansion of (* 2 PI) in k
22.363 * [taylor]: Taking taylor expansion of 2 in k
22.363 * [backup-simplify]: Simplify 2 into 2
22.363 * [taylor]: Taking taylor expansion of PI in k
22.363 * [backup-simplify]: Simplify PI into PI
22.363 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.364 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.365 * [backup-simplify]: Simplify (* 1/2 0) into 0
22.365 * [backup-simplify]: Simplify (- 0) into 0
22.366 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
22.367 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
22.368 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
22.369 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
22.370 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
22.370 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
22.370 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.370 * [taylor]: Taking taylor expansion of k in k
22.370 * [backup-simplify]: Simplify 0 into 0
22.370 * [backup-simplify]: Simplify 1 into 1
22.370 * [backup-simplify]: Simplify (/ 1 1) into 1
22.371 * [backup-simplify]: Simplify (sqrt 0) into 0
22.372 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
22.375 * [backup-simplify]: Simplify (* (pow (* 2 PI) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) into (* (pow (* PI 2) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))
22.377 * [backup-simplify]: Simplify (* (pow n 1/4) (* (pow (* PI 2) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))
22.378 * [backup-simplify]: Simplify (* (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) 0) into 0
22.378 * [backup-simplify]: Simplify 0 into 0
22.379 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
22.380 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
22.382 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
22.382 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
22.383 * [backup-simplify]: Simplify (- 0) into 0
22.383 * [backup-simplify]: Simplify (+ 0 0) into 0
22.383 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
22.384 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
22.385 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
22.386 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
22.387 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
22.387 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
22.387 * [backup-simplify]: Simplify (- 0) into 0
22.388 * [backup-simplify]: Simplify (+ 0 0) into 0
22.388 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
22.388 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
22.388 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (log n))) into 0
22.389 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
22.390 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) 0) (* 0 (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
22.390 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
22.391 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
22.392 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
22.392 * [backup-simplify]: Simplify (- 0) into 0
22.392 * [backup-simplify]: Simplify (+ 0 0) into 0
22.393 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
22.393 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (log (* 2 PI)))) into 0
22.394 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
22.396 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) 0) (* 0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0
22.397 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
22.397 * [taylor]: Taking taylor expansion of 0 in k
22.397 * [backup-simplify]: Simplify 0 into 0
22.398 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
22.398 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
22.399 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
22.400 * [backup-simplify]: Simplify (+ 0 0) into 0
22.400 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
22.400 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.400 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.401 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
22.403 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
22.405 * [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)))))))
22.405 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
22.406 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
22.407 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
22.407 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.407 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.409 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI))))
22.416 * [backup-simplify]: Simplify (+ (* 1/2 (- (* 1/2 (log (* 2 PI))))) (* 0 (* 1/2 (log (* 2 PI))))) into (- (* 1/4 (log (* 2 PI))))
22.428 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/4 (log (* 2 PI)))) 1) 1)))) into (* -1/4 (* (pow (* PI 2) 1/4) (log (* 2 PI))))
22.437 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/4) (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) (* (* -1/4 (* (pow (* PI 2) 1/4) (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/2 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (* 1/4 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))))))
22.438 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
22.439 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
22.439 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.440 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.441 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n)))
22.441 * [backup-simplify]: Simplify (+ (* 1/2 (- (* 1/2 (log n)))) (* 0 (* 1/2 (log n)))) into (- (* 1/4 (log n)))
22.441 * [backup-simplify]: Simplify (* (exp (* 1/4 (log n))) (+ (* (/ (pow (- (* 1/4 (log n))) 1) 1)))) into (* -1/4 (* (pow n 1/4) (log n)))
22.447 * [backup-simplify]: Simplify (+ (* (pow n 1/4) (- (+ (* 1/2 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (* 1/4 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))))))) (* (* -1/4 (* (pow n 1/4) (log n))) (* (pow (* PI 2) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) into (- (+ (* 1/2 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (* 1/2 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))))))
22.450 * [backup-simplify]: Simplify (+ (* (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) +nan.0) (* (- (+ (* 1/2 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (* 1/2 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n)))))) 0)) into (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))))
22.451 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) into (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))))
22.451 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.451 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
22.452 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
22.453 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
22.459 * [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
22.460 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
22.461 * [backup-simplify]: Simplify (- 0) into 0
22.461 * [backup-simplify]: Simplify (+ 0 0) into 0
22.462 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
22.463 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
22.464 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
22.465 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
22.467 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
22.468 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
22.468 * [backup-simplify]: Simplify (- 0) into 0
22.468 * [backup-simplify]: Simplify (+ 0 0) into 0
22.469 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
22.469 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
22.469 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (log n)))) into 0
22.470 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
22.472 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0
22.473 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
22.476 * [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
22.477 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
22.477 * [backup-simplify]: Simplify (- 0) into 0
22.478 * [backup-simplify]: Simplify (+ 0 0) into 0
22.479 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
22.480 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0
22.482 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
22.485 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))))) into 0
22.488 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
22.488 * [taylor]: Taking taylor expansion of 0 in k
22.488 * [backup-simplify]: Simplify 0 into 0
22.488 * [backup-simplify]: Simplify 0 into 0
22.489 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
22.492 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
22.493 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
22.493 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
22.495 * [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
22.496 * [backup-simplify]: Simplify (+ 0 0) into 0
22.496 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
22.496 * [backup-simplify]: Simplify (- 0) into 0
22.497 * [backup-simplify]: Simplify (+ 0 0) into 0
22.498 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
22.500 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0
22.502 * [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)))))
22.503 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
22.505 * [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
22.505 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
22.506 * [backup-simplify]: Simplify (- 0) into 0
22.506 * [backup-simplify]: Simplify (+ 0 0) into 0
22.507 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0
22.508 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (* 1/2 (log (* 2 PI))))) (* 0 (* 1/2 (log (* 2 PI)))))) into 0
22.516 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/4 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/32 (* (pow (* PI 2) 1/4) (pow (log (* 2 PI)) 2)))
22.532 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/4) (* (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)))))) (+ (* (* -1/4 (* (pow (* PI 2) 1/4) (log (* 2 PI)))) (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) (* (* 1/32 (* (pow (* PI 2) 1/4) (pow (log (* 2 PI)) 2))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) into (+ (* 1/32 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (+ (* 1/8 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))) (* 1/8 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))))))
22.533 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
22.533 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
22.534 * [backup-simplify]: Simplify (- 0) into 0
22.534 * [backup-simplify]: Simplify (+ 0 0) into 0
22.534 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0
22.535 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (* 1/2 (log n)))) (* 0 (* 1/2 (log n))))) into 0
22.535 * [backup-simplify]: Simplify (* (exp (* 1/4 (log n))) (+ (* (/ (pow (- (* 1/4 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/32 (* (pow n 1/4) (pow (log n) 2)))
22.547 * [backup-simplify]: Simplify (+ (* (pow n 1/4) (+ (* 1/32 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (+ (* 1/8 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))) (* 1/8 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))))))) (+ (* (* -1/4 (* (pow n 1/4) (log n))) (- (+ (* 1/2 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (* 1/4 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))))))) (* (* 1/32 (* (pow n 1/4) (pow (log n) 2))) (* (pow (* PI 2) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/8 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (+ (* 1/8 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (* 1/4 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))))))
22.562 * [backup-simplify]: Simplify (+ (* (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) +nan.0) (+ (* (- (+ (* 1/2 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (* 1/2 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n)))))) +nan.0) (* (+ (* 1/8 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (+ (* 1/8 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (* 1/4 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) 0))) into (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n)))))))))
22.568 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))))))))) into (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n)))))))))
22.568 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.569 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
22.571 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
22.572 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
22.578 * [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
22.579 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
22.580 * [backup-simplify]: Simplify (- 0) into 0
22.580 * [backup-simplify]: Simplify (+ 0 0) into 0
22.581 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k)))))) into 0
22.583 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
22.585 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
22.587 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
22.593 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
22.595 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
22.595 * [backup-simplify]: Simplify (- 0) into 0
22.595 * [backup-simplify]: Simplify (+ 0 0) into 0
22.597 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k)))))) into 0
22.597 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
22.598 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0
22.600 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
22.602 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))))) into 0
22.603 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
22.609 * [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
22.610 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
22.611 * [backup-simplify]: Simplify (- 0) into 0
22.611 * [backup-simplify]: Simplify (+ 0 0) into 0
22.612 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k)))))) into 0
22.613 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
22.616 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
22.619 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))))) into 0
22.621 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log n)))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
22.621 * [taylor]: Taking taylor expansion of 0 in k
22.621 * [backup-simplify]: Simplify 0 into 0
22.621 * [backup-simplify]: Simplify 0 into 0
22.621 * [backup-simplify]: Simplify 0 into 0
22.622 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.624 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
22.626 * [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
22.626 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
22.629 * [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
22.630 * [backup-simplify]: Simplify (+ 0 0) into 0
22.630 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
22.631 * [backup-simplify]: Simplify (- 0) into 0
22.631 * [backup-simplify]: Simplify (+ 0 0) into 0
22.632 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
22.634 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))))) into 0
22.638 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/384 (pow (log n) 3)) (+ (* 1/128 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/128 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/384 (pow (log (* 2 PI)) 3)))))))
22.639 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
22.642 * [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
22.643 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
22.643 * [backup-simplify]: Simplify (- 0) into 0
22.644 * [backup-simplify]: Simplify (+ 0 0) into 0
22.645 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
22.646 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (* 1/2 (log (* 2 PI))))) (* 0 (* 1/2 (log (* 2 PI))))))) into 0
22.657 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/4 (log (* 2 PI)))) 3) 6)) (* (/ (pow (- (* 1/4 (log (* 2 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/384 (* (pow (* PI 2) 1/4) (pow (log (* 2 PI)) 3)))
22.700 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/4) (* -1 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/384 (pow (log n) 3)) (+ (* 1/128 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/128 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/384 (pow (log (* 2 PI)) 3)))))))) (+ (* (* -1/4 (* (pow (* PI 2) 1/4) (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)))))) (+ (* (* 1/32 (* (pow (* PI 2) 1/4) (pow (log (* 2 PI)) 2))) (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) (* (* -1/384 (* (pow (* PI 2) 1/4) (pow (log (* 2 PI)) 3))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* 1/32 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow (log (* 2 PI)) 2))))) (+ (* 1/384 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 3)))) (+ (* 1/64 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (log (* 2 PI)))))) (* 1/48 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 3))))))))
22.704 * [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
22.705 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
22.705 * [backup-simplify]: Simplify (- 0) into 0
22.706 * [backup-simplify]: Simplify (+ 0 0) into 0
22.707 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0
22.708 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (* 1/2 (log n)))) (* 0 (* 1/2 (log n)))))) into 0
22.710 * [backup-simplify]: Simplify (* (exp (* 1/4 (log n))) (+ (* (/ (pow (- (* 1/4 (log n))) 3) 6)) (* (/ (pow (- (* 1/4 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/384 (* (pow n 1/4) (pow (log n) 3)))
22.737 * [backup-simplify]: Simplify (+ (* (pow n 1/4) (- (+ (* 1/32 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow (log (* 2 PI)) 2))))) (+ (* 1/384 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 3)))) (+ (* 1/64 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (log (* 2 PI)))))) (* 1/48 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 3))))))))) (+ (* (* -1/4 (* (pow n 1/4) (log n))) (+ (* 1/32 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (+ (* 1/8 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))) (* 1/8 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))))))) (+ (* (* 1/32 (* (pow n 1/4) (pow (log n) 2))) (- (+ (* 1/2 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (* 1/4 (* (pow (* PI 2) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))))))) (* (* -1/384 (* (pow n 1/4) (pow (log n) 3))) (* (pow (* PI 2) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))))) into (- (+ (* 1/48 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 3)))) (+ (* 1/16 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow (log (* 2 PI)) 2))))) (+ (* 1/48 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 3)))) (* 1/16 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (log (* 2 PI))))))))))
22.752 * [backup-simplify]: Simplify (+ (* (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) +nan.0) (+ (* (- (+ (* 1/2 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (* 1/2 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n)))))) +nan.0) (+ (* (+ (* 1/8 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (+ (* 1/8 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (* 1/4 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) +nan.0) (* (- (+ (* 1/48 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 3)))) (+ (* 1/16 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow (log (* 2 PI)) 2))))) (+ (* 1/48 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 3)))) (* 1/16 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (log (* 2 PI)))))))))) 0)))) into (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))))
22.768 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))) into (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))))
22.790 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))) (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))))))))) (* k 1)) (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))))) into (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k)))) (- (+ (* +nan.0 (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log (* 2 PI)) (* (pow k 2) (log n)))) (pow (* PI (* n 2)) 1/4))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) k))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2))))) (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))))))))))))))))))))))
22.791 * [backup-simplify]: Simplify (* (/ (* (pow (/ 1 n) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ (/ 1 k) 2)) 2))) 1) (/ (pow (* (/ 1 n) (* 2 PI)) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) (sqrt (/ 1 k)))) into (* (* (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt k))
22.791 * [approximate]: Taking taylor expansion of (* (* (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt k)) in (n k) around 0
22.791 * [taylor]: Taking taylor expansion of (* (* (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt k)) in k
22.791 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))))) in k
22.791 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
22.791 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n)))) in k
22.791 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n))) in k
22.791 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
22.792 * [taylor]: Taking taylor expansion of 1/2 in k
22.792 * [backup-simplify]: Simplify 1/2 into 1/2
22.792 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
22.792 * [taylor]: Taking taylor expansion of 1/2 in k
22.792 * [backup-simplify]: Simplify 1/2 into 1/2
22.792 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.792 * [taylor]: Taking taylor expansion of 1/2 in k
22.792 * [backup-simplify]: Simplify 1/2 into 1/2
22.792 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.792 * [taylor]: Taking taylor expansion of k in k
22.792 * [backup-simplify]: Simplify 0 into 0
22.792 * [backup-simplify]: Simplify 1 into 1
22.792 * [backup-simplify]: Simplify (/ 1 1) into 1
22.792 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k
22.792 * [taylor]: Taking taylor expansion of (/ 1 n) in k
22.792 * [taylor]: Taking taylor expansion of n in k
22.792 * [backup-simplify]: Simplify n into n
22.792 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n)
22.792 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n))
22.796 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.797 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.797 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.797 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
22.798 * [backup-simplify]: Simplify (* -1/4 (log (/ 1 n))) into (* -1/4 (log (/ 1 n)))
22.798 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))))
22.798 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))))) in k
22.798 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
22.798 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 PI)))) in k
22.798 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 PI))) in k
22.798 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
22.798 * [taylor]: Taking taylor expansion of 1/2 in k
22.798 * [backup-simplify]: Simplify 1/2 into 1/2
22.798 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
22.798 * [taylor]: Taking taylor expansion of 1/2 in k
22.798 * [backup-simplify]: Simplify 1/2 into 1/2
22.798 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.798 * [taylor]: Taking taylor expansion of 1/2 in k
22.798 * [backup-simplify]: Simplify 1/2 into 1/2
22.798 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.798 * [taylor]: Taking taylor expansion of k in k
22.798 * [backup-simplify]: Simplify 0 into 0
22.798 * [backup-simplify]: Simplify 1 into 1
22.798 * [backup-simplify]: Simplify (/ 1 1) into 1
22.798 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
22.798 * [taylor]: Taking taylor expansion of (* 2 PI) in k
22.798 * [taylor]: Taking taylor expansion of 2 in k
22.798 * [backup-simplify]: Simplify 2 into 2
22.798 * [taylor]: Taking taylor expansion of PI in k
22.798 * [backup-simplify]: Simplify PI into PI
22.799 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.799 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.800 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.800 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.800 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.800 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
22.802 * [backup-simplify]: Simplify (* -1/4 (log (* 2 PI))) into (* -1/4 (log (* 2 PI)))
22.802 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))
22.802 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
22.802 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
22.802 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
22.802 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
22.802 * [taylor]: Taking taylor expansion of 1/2 in k
22.802 * [backup-simplify]: Simplify 1/2 into 1/2
22.802 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
22.802 * [taylor]: Taking taylor expansion of 1/2 in k
22.802 * [backup-simplify]: Simplify 1/2 into 1/2
22.802 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.802 * [taylor]: Taking taylor expansion of 1/2 in k
22.802 * [backup-simplify]: Simplify 1/2 into 1/2
22.802 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.802 * [taylor]: Taking taylor expansion of k in k
22.803 * [backup-simplify]: Simplify 0 into 0
22.803 * [backup-simplify]: Simplify 1 into 1
22.803 * [backup-simplify]: Simplify (/ 1 1) into 1
22.803 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
22.803 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
22.803 * [taylor]: Taking taylor expansion of 2 in k
22.803 * [backup-simplify]: Simplify 2 into 2
22.803 * [taylor]: Taking taylor expansion of (/ PI n) in k
22.803 * [taylor]: Taking taylor expansion of PI in k
22.803 * [backup-simplify]: Simplify PI into PI
22.803 * [taylor]: Taking taylor expansion of n in k
22.803 * [backup-simplify]: Simplify n into n
22.803 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
22.803 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
22.803 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
22.803 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.804 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.804 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.804 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
22.804 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
22.804 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))))
22.804 * [taylor]: Taking taylor expansion of (sqrt k) in k
22.804 * [taylor]: Taking taylor expansion of k in k
22.804 * [backup-simplify]: Simplify 0 into 0
22.804 * [backup-simplify]: Simplify 1 into 1
22.805 * [backup-simplify]: Simplify (sqrt 0) into 0
22.806 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
22.806 * [taylor]: Taking taylor expansion of (* (* (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt k)) in n
22.806 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))))) in n
22.806 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
22.806 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n)))) in n
22.806 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n))) in n
22.806 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
22.806 * [taylor]: Taking taylor expansion of 1/2 in n
22.806 * [backup-simplify]: Simplify 1/2 into 1/2
22.806 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
22.806 * [taylor]: Taking taylor expansion of 1/2 in n
22.806 * [backup-simplify]: Simplify 1/2 into 1/2
22.806 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.806 * [taylor]: Taking taylor expansion of 1/2 in n
22.806 * [backup-simplify]: Simplify 1/2 into 1/2
22.806 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.806 * [taylor]: Taking taylor expansion of k in n
22.806 * [backup-simplify]: Simplify k into k
22.806 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.806 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
22.806 * [taylor]: Taking taylor expansion of (/ 1 n) in n
22.806 * [taylor]: Taking taylor expansion of n in n
22.806 * [backup-simplify]: Simplify 0 into 0
22.806 * [backup-simplify]: Simplify 1 into 1
22.806 * [backup-simplify]: Simplify (/ 1 1) into 1
22.807 * [backup-simplify]: Simplify (log 1) into 0
22.807 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.807 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
22.807 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
22.807 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
22.807 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
22.807 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log n))) into (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))
22.807 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
22.807 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))))) in n
22.807 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
22.807 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 PI)))) in n
22.807 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 PI))) in n
22.807 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
22.808 * [taylor]: Taking taylor expansion of 1/2 in n
22.808 * [backup-simplify]: Simplify 1/2 into 1/2
22.808 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
22.808 * [taylor]: Taking taylor expansion of 1/2 in n
22.808 * [backup-simplify]: Simplify 1/2 into 1/2
22.808 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.808 * [taylor]: Taking taylor expansion of 1/2 in n
22.808 * [backup-simplify]: Simplify 1/2 into 1/2
22.808 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.808 * [taylor]: Taking taylor expansion of k in n
22.808 * [backup-simplify]: Simplify k into k
22.808 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.808 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
22.808 * [taylor]: Taking taylor expansion of (* 2 PI) in n
22.808 * [taylor]: Taking taylor expansion of 2 in n
22.808 * [backup-simplify]: Simplify 2 into 2
22.808 * [taylor]: Taking taylor expansion of PI in n
22.808 * [backup-simplify]: Simplify PI into PI
22.808 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.809 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.809 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.809 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
22.809 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
22.809 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
22.810 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 PI))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))
22.810 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))
22.810 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
22.810 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
22.810 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
22.810 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
22.810 * [taylor]: Taking taylor expansion of 1/2 in n
22.810 * [backup-simplify]: Simplify 1/2 into 1/2
22.810 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
22.811 * [taylor]: Taking taylor expansion of 1/2 in n
22.811 * [backup-simplify]: Simplify 1/2 into 1/2
22.811 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.811 * [taylor]: Taking taylor expansion of 1/2 in n
22.811 * [backup-simplify]: Simplify 1/2 into 1/2
22.811 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.811 * [taylor]: Taking taylor expansion of k in n
22.811 * [backup-simplify]: Simplify k into k
22.811 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.811 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
22.811 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
22.811 * [taylor]: Taking taylor expansion of 2 in n
22.811 * [backup-simplify]: Simplify 2 into 2
22.811 * [taylor]: Taking taylor expansion of (/ PI n) in n
22.811 * [taylor]: Taking taylor expansion of PI in n
22.811 * [backup-simplify]: Simplify PI into PI
22.811 * [taylor]: Taking taylor expansion of n in n
22.811 * [backup-simplify]: Simplify 0 into 0
22.811 * [backup-simplify]: Simplify 1 into 1
22.811 * [backup-simplify]: Simplify (/ PI 1) into PI
22.811 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.812 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.812 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.812 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
22.812 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
22.813 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
22.813 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
22.814 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
22.815 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
22.815 * [taylor]: Taking taylor expansion of (sqrt k) in n
22.815 * [taylor]: Taking taylor expansion of k in n
22.815 * [backup-simplify]: Simplify k into k
22.815 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
22.815 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
22.815 * [taylor]: Taking taylor expansion of (* (* (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt k)) in n
22.815 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))))) in n
22.815 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
22.815 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n)))) in n
22.815 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 1 n))) in n
22.815 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
22.815 * [taylor]: Taking taylor expansion of 1/2 in n
22.815 * [backup-simplify]: Simplify 1/2 into 1/2
22.815 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
22.815 * [taylor]: Taking taylor expansion of 1/2 in n
22.815 * [backup-simplify]: Simplify 1/2 into 1/2
22.815 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.815 * [taylor]: Taking taylor expansion of 1/2 in n
22.815 * [backup-simplify]: Simplify 1/2 into 1/2
22.815 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.815 * [taylor]: Taking taylor expansion of k in n
22.815 * [backup-simplify]: Simplify k into k
22.815 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.815 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
22.815 * [taylor]: Taking taylor expansion of (/ 1 n) in n
22.815 * [taylor]: Taking taylor expansion of n in n
22.815 * [backup-simplify]: Simplify 0 into 0
22.815 * [backup-simplify]: Simplify 1 into 1
22.816 * [backup-simplify]: Simplify (/ 1 1) into 1
22.816 * [backup-simplify]: Simplify (log 1) into 0
22.816 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.816 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
22.816 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
22.816 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
22.816 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
22.817 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log n))) into (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))
22.817 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
22.817 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))))) in n
22.817 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
22.817 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 PI)))) in n
22.817 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 PI))) in n
22.817 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
22.817 * [taylor]: Taking taylor expansion of 1/2 in n
22.817 * [backup-simplify]: Simplify 1/2 into 1/2
22.817 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
22.817 * [taylor]: Taking taylor expansion of 1/2 in n
22.817 * [backup-simplify]: Simplify 1/2 into 1/2
22.817 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.817 * [taylor]: Taking taylor expansion of 1/2 in n
22.817 * [backup-simplify]: Simplify 1/2 into 1/2
22.817 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.817 * [taylor]: Taking taylor expansion of k in n
22.817 * [backup-simplify]: Simplify k into k
22.817 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.817 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
22.817 * [taylor]: Taking taylor expansion of (* 2 PI) in n
22.817 * [taylor]: Taking taylor expansion of 2 in n
22.817 * [backup-simplify]: Simplify 2 into 2
22.817 * [taylor]: Taking taylor expansion of PI in n
22.817 * [backup-simplify]: Simplify PI into PI
22.817 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.818 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.818 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.818 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
22.818 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
22.818 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
22.819 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 PI))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))
22.820 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))
22.820 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
22.820 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
22.820 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
22.820 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
22.820 * [taylor]: Taking taylor expansion of 1/2 in n
22.820 * [backup-simplify]: Simplify 1/2 into 1/2
22.820 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
22.820 * [taylor]: Taking taylor expansion of 1/2 in n
22.820 * [backup-simplify]: Simplify 1/2 into 1/2
22.820 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
22.820 * [taylor]: Taking taylor expansion of 1/2 in n
22.820 * [backup-simplify]: Simplify 1/2 into 1/2
22.820 * [taylor]: Taking taylor expansion of (/ 1 k) in n
22.820 * [taylor]: Taking taylor expansion of k in n
22.820 * [backup-simplify]: Simplify k into k
22.820 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
22.820 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
22.820 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
22.820 * [taylor]: Taking taylor expansion of 2 in n
22.820 * [backup-simplify]: Simplify 2 into 2
22.820 * [taylor]: Taking taylor expansion of (/ PI n) in n
22.820 * [taylor]: Taking taylor expansion of PI in n
22.820 * [backup-simplify]: Simplify PI into PI
22.820 * [taylor]: Taking taylor expansion of n in n
22.820 * [backup-simplify]: Simplify 0 into 0
22.820 * [backup-simplify]: Simplify 1 into 1
22.820 * [backup-simplify]: Simplify (/ PI 1) into PI
22.821 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.821 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.821 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
22.821 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
22.822 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
22.822 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
22.823 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
22.823 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
22.824 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
22.824 * [taylor]: Taking taylor expansion of (sqrt k) in n
22.824 * [taylor]: Taking taylor expansion of k in n
22.824 * [backup-simplify]: Simplify k into k
22.824 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
22.824 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
22.826 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))
22.827 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) into (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))
22.829 * [backup-simplify]: Simplify (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) (sqrt k)) into (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) (sqrt k))
22.829 * [taylor]: Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) (sqrt k)) in k
22.829 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) in k
22.829 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
22.829 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
22.829 * [taylor]: Taking taylor expansion of 1/2 in k
22.829 * [backup-simplify]: Simplify 1/2 into 1/2
22.829 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
22.829 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
22.829 * [taylor]: Taking taylor expansion of 1/2 in k
22.829 * [backup-simplify]: Simplify 1/2 into 1/2
22.829 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.829 * [taylor]: Taking taylor expansion of 1/2 in k
22.829 * [backup-simplify]: Simplify 1/2 into 1/2
22.829 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.829 * [taylor]: Taking taylor expansion of k in k
22.829 * [backup-simplify]: Simplify 0 into 0
22.829 * [backup-simplify]: Simplify 1 into 1
22.829 * [backup-simplify]: Simplify (/ 1 1) into 1
22.829 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
22.829 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
22.829 * [taylor]: Taking taylor expansion of (* 2 PI) in k
22.829 * [taylor]: Taking taylor expansion of 2 in k
22.829 * [backup-simplify]: Simplify 2 into 2
22.829 * [taylor]: Taking taylor expansion of PI in k
22.829 * [backup-simplify]: Simplify PI into PI
22.830 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.830 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.830 * [taylor]: Taking taylor expansion of (log n) in k
22.830 * [taylor]: Taking taylor expansion of n in k
22.830 * [backup-simplify]: Simplify n into n
22.830 * [backup-simplify]: Simplify (log n) into (log n)
22.831 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.831 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.831 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.831 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
22.832 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
22.832 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
22.833 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
22.834 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
22.834 * [taylor]: Taking taylor expansion of (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))) in k
22.834 * [taylor]: Taking taylor expansion of (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k
22.834 * [taylor]: Taking taylor expansion of (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k
22.834 * [taylor]: Taking taylor expansion of -1/2 in k
22.834 * [backup-simplify]: Simplify -1/2 into -1/2
22.834 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k
22.834 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
22.834 * [taylor]: Taking taylor expansion of 1/2 in k
22.834 * [backup-simplify]: Simplify 1/2 into 1/2
22.834 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.834 * [taylor]: Taking taylor expansion of 1/2 in k
22.834 * [backup-simplify]: Simplify 1/2 into 1/2
22.834 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.834 * [taylor]: Taking taylor expansion of k in k
22.834 * [backup-simplify]: Simplify 0 into 0
22.834 * [backup-simplify]: Simplify 1 into 1
22.834 * [backup-simplify]: Simplify (/ 1 1) into 1
22.834 * [taylor]: Taking taylor expansion of (log n) in k
22.834 * [taylor]: Taking taylor expansion of n in k
22.834 * [backup-simplify]: Simplify n into n
22.834 * [backup-simplify]: Simplify (log n) into (log n)
22.835 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.835 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.835 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.835 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n))
22.835 * [backup-simplify]: Simplify (* -1/2 (* -1/2 (log n))) into (* 1/4 (log n))
22.836 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
22.836 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))) in k
22.836 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k
22.836 * [taylor]: Taking taylor expansion of 1/2 in k
22.836 * [backup-simplify]: Simplify 1/2 into 1/2
22.836 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k
22.836 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
22.836 * [taylor]: Taking taylor expansion of 1/2 in k
22.836 * [backup-simplify]: Simplify 1/2 into 1/2
22.836 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
22.836 * [taylor]: Taking taylor expansion of 1/2 in k
22.836 * [backup-simplify]: Simplify 1/2 into 1/2
22.836 * [taylor]: Taking taylor expansion of (/ 1 k) in k
22.836 * [taylor]: Taking taylor expansion of k in k
22.836 * [backup-simplify]: Simplify 0 into 0
22.836 * [backup-simplify]: Simplify 1 into 1
22.836 * [backup-simplify]: Simplify (/ 1 1) into 1
22.836 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
22.836 * [taylor]: Taking taylor expansion of (* 2 PI) in k
22.836 * [taylor]: Taking taylor expansion of 2 in k
22.836 * [backup-simplify]: Simplify 2 into 2
22.836 * [taylor]: Taking taylor expansion of PI in k
22.836 * [backup-simplify]: Simplify PI into PI
22.836 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
22.837 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
22.837 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
22.838 * [backup-simplify]: Simplify (- 1/2) into -1/2
22.838 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
22.839 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
22.841 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (log (* 2 PI)))) into (* -1/4 (log (* 2 PI)))
22.841 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))
22.841 * [taylor]: Taking taylor expansion of (sqrt k) in k
22.841 * [taylor]: Taking taylor expansion of k in k
22.841 * [backup-simplify]: Simplify 0 into 0
22.841 * [backup-simplify]: Simplify 1 into 1
22.842 * [backup-simplify]: Simplify (sqrt 0) into 0
22.843 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
22.844 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))) into (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))
22.845 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) into (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))
22.847 * [backup-simplify]: Simplify (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) 0) into 0
22.847 * [backup-simplify]: Simplify 0 into 0
22.847 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
22.848 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
22.849 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
22.849 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
22.849 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
22.850 * [backup-simplify]: Simplify (- 0) into 0
22.850 * [backup-simplify]: Simplify (+ 0 0) into 0
22.850 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
22.851 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
22.852 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
22.853 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
22.854 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
22.855 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
22.855 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
22.855 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
22.856 * [backup-simplify]: Simplify (- 0) into 0
22.856 * [backup-simplify]: Simplify (+ 0 0) into 0
22.856 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
22.857 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (log (* 2 PI)))) into 0
22.858 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
22.859 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))) 0) (* 0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
22.860 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
22.861 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
22.861 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
22.861 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
22.861 * [backup-simplify]: Simplify (- 0) into 0
22.862 * [backup-simplify]: Simplify (+ 0 0) into 0
22.862 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
22.862 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
22.862 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log n)))) into 0
22.863 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
22.865 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (* 0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))) into 0
22.866 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) 0) (* 0 (sqrt k))) into 0
22.866 * [taylor]: Taking taylor expansion of 0 in k
22.866 * [backup-simplify]: Simplify 0 into 0
22.866 * [backup-simplify]: Simplify 0 into 0
22.867 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (* 0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) into 0
22.869 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 0) (* 0 (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))) into 0
22.871 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))))
22.873 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))))
22.874 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
22.875 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.876 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
22.880 * [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
22.880 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.881 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
22.881 * [backup-simplify]: Simplify (- 0) into 0
22.882 * [backup-simplify]: Simplify (+ 0 0) into 0
22.883 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
22.884 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
22.886 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
22.888 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
22.889 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
22.893 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
22.893 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.894 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
22.894 * [backup-simplify]: Simplify (- 0) into 0
22.895 * [backup-simplify]: Simplify (+ 0 0) into 0
22.896 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
22.903 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0
22.906 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
22.909 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0
22.910 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.913 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
22.914 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.915 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
22.915 * [backup-simplify]: Simplify (- 0) into 0
22.916 * [backup-simplify]: Simplify (+ 0 0) into 0
22.917 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
22.917 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
22.918 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0
22.919 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
22.922 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))))) into 0
22.925 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
22.925 * [taylor]: Taking taylor expansion of 0 in k
22.925 * [backup-simplify]: Simplify 0 into 0
22.925 * [backup-simplify]: Simplify 0 into 0
22.925 * [backup-simplify]: Simplify 0 into 0
22.928 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
22.930 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))) into 0
22.933 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))))) into 0
22.936 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))))
22.938 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))))
22.939 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
22.940 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.942 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
22.947 * [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
22.948 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.949 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
22.949 * [backup-simplify]: Simplify (- 0) into 0
22.950 * [backup-simplify]: Simplify (+ 0 0) into 0
22.951 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
22.953 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
22.954 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
22.957 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
22.959 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
22.964 * [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
22.965 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.966 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
22.966 * [backup-simplify]: Simplify (- 0) into 0
22.967 * [backup-simplify]: Simplify (+ 0 0) into 0
22.968 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
22.969 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
22.972 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
22.975 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))))) into 0
22.976 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
22.979 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
22.979 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
22.980 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
22.980 * [backup-simplify]: Simplify (- 0) into 0
22.980 * [backup-simplify]: Simplify (+ 0 0) into 0
22.981 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
22.981 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
22.982 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0
22.983 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
22.985 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))))) into 0
22.987 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
22.987 * [taylor]: Taking taylor expansion of 0 in k
22.987 * [backup-simplify]: Simplify 0 into 0
22.987 * [backup-simplify]: Simplify 0 into 0
22.987 * [backup-simplify]: Simplify 0 into 0
22.987 * [backup-simplify]: Simplify 0 into 0
22.990 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
22.991 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))))) into 0
22.993 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))))) into 0
22.995 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))))
22.997 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))))))))
23.002 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (* 2 PI))))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (* 2 PI))))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) (* (exp (* -1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (* 2 PI))))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* -1/2 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))))) k)))))))
23.003 * [backup-simplify]: Simplify (* (/ (* (pow (/ 1 (- n)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2))) 1) (/ (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) (sqrt (/ 1 (- k))))) into (/ (* (pow (* 2 PI) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))))) (sqrt (/ -1 k)))
23.003 * [approximate]: Taking taylor expansion of (/ (* (pow (* 2 PI) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))))) (sqrt (/ -1 k))) in (n k) around 0
23.003 * [taylor]: Taking taylor expansion of (/ (* (pow (* 2 PI) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))))) (sqrt (/ -1 k))) in k
23.003 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))))) in k
23.003 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
23.003 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* 2 PI)))) in k
23.004 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* 2 PI))) in k
23.004 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
23.004 * [taylor]: Taking taylor expansion of 1/2 in k
23.004 * [backup-simplify]: Simplify 1/2 into 1/2
23.004 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
23.004 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
23.004 * [taylor]: Taking taylor expansion of 1/2 in k
23.004 * [backup-simplify]: Simplify 1/2 into 1/2
23.004 * [taylor]: Taking taylor expansion of (/ 1 k) in k
23.004 * [taylor]: Taking taylor expansion of k in k
23.004 * [backup-simplify]: Simplify 0 into 0
23.004 * [backup-simplify]: Simplify 1 into 1
23.004 * [backup-simplify]: Simplify (/ 1 1) into 1
23.004 * [taylor]: Taking taylor expansion of 1/2 in k
23.004 * [backup-simplify]: Simplify 1/2 into 1/2
23.004 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
23.004 * [taylor]: Taking taylor expansion of (* 2 PI) in k
23.004 * [taylor]: Taking taylor expansion of 2 in k
23.004 * [backup-simplify]: Simplify 2 into 2
23.004 * [taylor]: Taking taylor expansion of PI in k
23.004 * [backup-simplify]: Simplify PI into PI
23.004 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
23.005 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
23.005 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
23.006 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
23.006 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
23.007 * [backup-simplify]: Simplify (* 1/4 (log (* 2 PI))) into (* 1/4 (log (* 2 PI)))
23.008 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))))
23.008 * [taylor]: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)))) in k
23.008 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
23.008 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
23.008 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
23.008 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
23.008 * [taylor]: Taking taylor expansion of 1/2 in k
23.008 * [backup-simplify]: Simplify 1/2 into 1/2
23.008 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
23.008 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
23.008 * [taylor]: Taking taylor expansion of 1/2 in k
23.008 * [backup-simplify]: Simplify 1/2 into 1/2
23.008 * [taylor]: Taking taylor expansion of (/ 1 k) in k
23.008 * [taylor]: Taking taylor expansion of k in k
23.008 * [backup-simplify]: Simplify 0 into 0
23.008 * [backup-simplify]: Simplify 1 into 1
23.008 * [backup-simplify]: Simplify (/ 1 1) into 1
23.008 * [taylor]: Taking taylor expansion of 1/2 in k
23.008 * [backup-simplify]: Simplify 1/2 into 1/2
23.008 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
23.008 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
23.008 * [taylor]: Taking taylor expansion of -2 in k
23.008 * [backup-simplify]: Simplify -2 into -2
23.008 * [taylor]: Taking taylor expansion of (/ PI n) in k
23.008 * [taylor]: Taking taylor expansion of PI in k
23.008 * [backup-simplify]: Simplify PI into PI
23.009 * [taylor]: Taking taylor expansion of n in k
23.009 * [backup-simplify]: Simplify n into n
23.009 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
23.009 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
23.009 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
23.009 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
23.009 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
23.010 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
23.010 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
23.010 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
23.010 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
23.010 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n)))) in k
23.010 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n))) in k
23.010 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
23.010 * [taylor]: Taking taylor expansion of 1/2 in k
23.010 * [backup-simplify]: Simplify 1/2 into 1/2
23.010 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
23.010 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
23.010 * [taylor]: Taking taylor expansion of 1/2 in k
23.010 * [backup-simplify]: Simplify 1/2 into 1/2
23.010 * [taylor]: Taking taylor expansion of (/ 1 k) in k
23.010 * [taylor]: Taking taylor expansion of k in k
23.010 * [backup-simplify]: Simplify 0 into 0
23.010 * [backup-simplify]: Simplify 1 into 1
23.010 * [backup-simplify]: Simplify (/ 1 1) into 1
23.010 * [taylor]: Taking taylor expansion of 1/2 in k
23.010 * [backup-simplify]: Simplify 1/2 into 1/2
23.010 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k
23.010 * [taylor]: Taking taylor expansion of (/ -1 n) in k
23.010 * [taylor]: Taking taylor expansion of -1 in k
23.010 * [backup-simplify]: Simplify -1 into -1
23.010 * [taylor]: Taking taylor expansion of n in k
23.010 * [backup-simplify]: Simplify n into n
23.011 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n)
23.011 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n))
23.011 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
23.011 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
23.011 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
23.011 * [backup-simplify]: Simplify (* 1/4 (log (/ -1 n))) into (* 1/4 (log (/ -1 n)))
23.012 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n)))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))))
23.012 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
23.012 * [taylor]: Taking taylor expansion of (/ -1 k) in k
23.012 * [taylor]: Taking taylor expansion of -1 in k
23.012 * [backup-simplify]: Simplify -1 into -1
23.012 * [taylor]: Taking taylor expansion of k in k
23.012 * [backup-simplify]: Simplify 0 into 0
23.012 * [backup-simplify]: Simplify 1 into 1
23.012 * [backup-simplify]: Simplify (/ -1 1) into -1
23.012 * [backup-simplify]: Simplify (sqrt 0) into 0
23.013 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
23.013 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))))) into (* (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))))))
23.014 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (* (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))))))) into (* (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))))))
23.015 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))))))))
23.015 * [taylor]: Taking taylor expansion of (/ (* (pow (* 2 PI) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))))) (sqrt (/ -1 k))) in n
23.015 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))))) in n
23.015 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
23.015 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* 2 PI)))) in n
23.015 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* 2 PI))) in n
23.015 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
23.015 * [taylor]: Taking taylor expansion of 1/2 in n
23.015 * [backup-simplify]: Simplify 1/2 into 1/2
23.015 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
23.015 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
23.015 * [taylor]: Taking taylor expansion of 1/2 in n
23.015 * [backup-simplify]: Simplify 1/2 into 1/2
23.015 * [taylor]: Taking taylor expansion of (/ 1 k) in n
23.015 * [taylor]: Taking taylor expansion of k in n
23.016 * [backup-simplify]: Simplify k into k
23.016 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
23.016 * [taylor]: Taking taylor expansion of 1/2 in n
23.016 * [backup-simplify]: Simplify 1/2 into 1/2
23.016 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
23.016 * [taylor]: Taking taylor expansion of (* 2 PI) in n
23.016 * [taylor]: Taking taylor expansion of 2 in n
23.016 * [backup-simplify]: Simplify 2 into 2
23.016 * [taylor]: Taking taylor expansion of PI in n
23.016 * [backup-simplify]: Simplify PI into PI
23.020 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
23.021 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
23.021 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
23.021 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
23.021 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
23.022 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* 2 PI))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))
23.023 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))))
23.023 * [taylor]: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)))) in n
23.023 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
23.023 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
23.023 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
23.023 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
23.023 * [taylor]: Taking taylor expansion of 1/2 in n
23.023 * [backup-simplify]: Simplify 1/2 into 1/2
23.023 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
23.023 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
23.023 * [taylor]: Taking taylor expansion of 1/2 in n
23.023 * [backup-simplify]: Simplify 1/2 into 1/2
23.023 * [taylor]: Taking taylor expansion of (/ 1 k) in n
23.023 * [taylor]: Taking taylor expansion of k in n
23.023 * [backup-simplify]: Simplify k into k
23.023 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
23.023 * [taylor]: Taking taylor expansion of 1/2 in n
23.023 * [backup-simplify]: Simplify 1/2 into 1/2
23.023 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
23.023 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
23.023 * [taylor]: Taking taylor expansion of -2 in n
23.023 * [backup-simplify]: Simplify -2 into -2
23.023 * [taylor]: Taking taylor expansion of (/ PI n) in n
23.023 * [taylor]: Taking taylor expansion of PI in n
23.023 * [backup-simplify]: Simplify PI into PI
23.023 * [taylor]: Taking taylor expansion of n in n
23.023 * [backup-simplify]: Simplify 0 into 0
23.023 * [backup-simplify]: Simplify 1 into 1
23.024 * [backup-simplify]: Simplify (/ PI 1) into PI
23.024 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
23.025 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
23.025 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
23.025 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
23.025 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
23.026 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
23.027 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
23.027 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
23.027 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
23.027 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n)))) in n
23.027 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n))) in n
23.027 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
23.027 * [taylor]: Taking taylor expansion of 1/2 in n
23.027 * [backup-simplify]: Simplify 1/2 into 1/2
23.028 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
23.028 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
23.028 * [taylor]: Taking taylor expansion of 1/2 in n
23.028 * [backup-simplify]: Simplify 1/2 into 1/2
23.028 * [taylor]: Taking taylor expansion of (/ 1 k) in n
23.028 * [taylor]: Taking taylor expansion of k in n
23.028 * [backup-simplify]: Simplify k into k
23.028 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
23.028 * [taylor]: Taking taylor expansion of 1/2 in n
23.028 * [backup-simplify]: Simplify 1/2 into 1/2
23.028 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
23.028 * [taylor]: Taking taylor expansion of (/ -1 n) in n
23.028 * [taylor]: Taking taylor expansion of -1 in n
23.028 * [backup-simplify]: Simplify -1 into -1
23.028 * [taylor]: Taking taylor expansion of n in n
23.028 * [backup-simplify]: Simplify 0 into 0
23.028 * [backup-simplify]: Simplify 1 into 1
23.028 * [backup-simplify]: Simplify (/ -1 1) into -1
23.028 * [backup-simplify]: Simplify (log -1) into (log -1)
23.028 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
23.028 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
23.028 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
23.029 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
23.029 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log -1) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
23.030 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))
23.030 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
23.030 * [taylor]: Taking taylor expansion of (/ -1 k) in n
23.030 * [taylor]: Taking taylor expansion of -1 in n
23.030 * [backup-simplify]: Simplify -1 into -1
23.030 * [taylor]: Taking taylor expansion of k in n
23.030 * [backup-simplify]: Simplify k into k
23.030 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
23.030 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
23.030 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
23.030 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
23.031 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) into (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
23.033 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
23.035 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) (sqrt (/ -1 k))) into (/ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) (sqrt (/ -1 k)))
23.035 * [taylor]: Taking taylor expansion of (/ (* (pow (* 2 PI) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))))) (sqrt (/ -1 k))) in n
23.035 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))))) in n
23.035 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
23.035 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* 2 PI)))) in n
23.035 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* 2 PI))) in n
23.035 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
23.035 * [taylor]: Taking taylor expansion of 1/2 in n
23.035 * [backup-simplify]: Simplify 1/2 into 1/2
23.035 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
23.035 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
23.035 * [taylor]: Taking taylor expansion of 1/2 in n
23.035 * [backup-simplify]: Simplify 1/2 into 1/2
23.035 * [taylor]: Taking taylor expansion of (/ 1 k) in n
23.035 * [taylor]: Taking taylor expansion of k in n
23.035 * [backup-simplify]: Simplify k into k
23.035 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
23.035 * [taylor]: Taking taylor expansion of 1/2 in n
23.035 * [backup-simplify]: Simplify 1/2 into 1/2
23.035 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
23.035 * [taylor]: Taking taylor expansion of (* 2 PI) in n
23.035 * [taylor]: Taking taylor expansion of 2 in n
23.035 * [backup-simplify]: Simplify 2 into 2
23.035 * [taylor]: Taking taylor expansion of PI in n
23.035 * [backup-simplify]: Simplify PI into PI
23.035 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
23.036 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
23.036 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
23.036 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
23.036 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
23.037 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* 2 PI))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))
23.038 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))))
23.038 * [taylor]: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)))) in n
23.038 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
23.038 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
23.038 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
23.038 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
23.038 * [taylor]: Taking taylor expansion of 1/2 in n
23.038 * [backup-simplify]: Simplify 1/2 into 1/2
23.038 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
23.038 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
23.038 * [taylor]: Taking taylor expansion of 1/2 in n
23.038 * [backup-simplify]: Simplify 1/2 into 1/2
23.038 * [taylor]: Taking taylor expansion of (/ 1 k) in n
23.038 * [taylor]: Taking taylor expansion of k in n
23.038 * [backup-simplify]: Simplify k into k
23.038 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
23.038 * [taylor]: Taking taylor expansion of 1/2 in n
23.038 * [backup-simplify]: Simplify 1/2 into 1/2
23.038 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
23.038 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
23.038 * [taylor]: Taking taylor expansion of -2 in n
23.038 * [backup-simplify]: Simplify -2 into -2
23.038 * [taylor]: Taking taylor expansion of (/ PI n) in n
23.038 * [taylor]: Taking taylor expansion of PI in n
23.038 * [backup-simplify]: Simplify PI into PI
23.038 * [taylor]: Taking taylor expansion of n in n
23.038 * [backup-simplify]: Simplify 0 into 0
23.038 * [backup-simplify]: Simplify 1 into 1
23.038 * [backup-simplify]: Simplify (/ PI 1) into PI
23.039 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
23.039 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
23.039 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
23.039 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
23.040 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
23.040 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
23.041 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
23.042 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
23.042 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
23.042 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n)))) in n
23.042 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -1 n))) in n
23.042 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
23.042 * [taylor]: Taking taylor expansion of 1/2 in n
23.042 * [backup-simplify]: Simplify 1/2 into 1/2
23.042 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
23.042 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
23.042 * [taylor]: Taking taylor expansion of 1/2 in n
23.042 * [backup-simplify]: Simplify 1/2 into 1/2
23.042 * [taylor]: Taking taylor expansion of (/ 1 k) in n
23.042 * [taylor]: Taking taylor expansion of k in n
23.042 * [backup-simplify]: Simplify k into k
23.042 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
23.042 * [taylor]: Taking taylor expansion of 1/2 in n
23.042 * [backup-simplify]: Simplify 1/2 into 1/2
23.042 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
23.042 * [taylor]: Taking taylor expansion of (/ -1 n) in n
23.042 * [taylor]: Taking taylor expansion of -1 in n
23.042 * [backup-simplify]: Simplify -1 into -1
23.042 * [taylor]: Taking taylor expansion of n in n
23.042 * [backup-simplify]: Simplify 0 into 0
23.042 * [backup-simplify]: Simplify 1 into 1
23.043 * [backup-simplify]: Simplify (/ -1 1) into -1
23.043 * [backup-simplify]: Simplify (log -1) into (log -1)
23.043 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
23.043 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
23.043 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
23.044 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
23.044 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log -1) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
23.044 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))
23.044 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
23.044 * [taylor]: Taking taylor expansion of (/ -1 k) in n
23.044 * [taylor]: Taking taylor expansion of -1 in n
23.044 * [backup-simplify]: Simplify -1 into -1
23.044 * [taylor]: Taking taylor expansion of k in n
23.044 * [backup-simplify]: Simplify k into k
23.044 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
23.044 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
23.045 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
23.045 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
23.046 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) into (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
23.047 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
23.049 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) (sqrt (/ -1 k))) into (/ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) (sqrt (/ -1 k)))
23.049 * [taylor]: Taking taylor expansion of (/ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) (sqrt (/ -1 k))) in k
23.049 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) in k
23.050 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) in k
23.050 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k
23.050 * [taylor]: Taking taylor expansion of 1/2 in k
23.050 * [backup-simplify]: Simplify 1/2 into 1/2
23.050 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k
23.050 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
23.050 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
23.050 * [taylor]: Taking taylor expansion of 1/2 in k
23.050 * [backup-simplify]: Simplify 1/2 into 1/2
23.050 * [taylor]: Taking taylor expansion of (/ 1 k) in k
23.050 * [taylor]: Taking taylor expansion of k in k
23.050 * [backup-simplify]: Simplify 0 into 0
23.050 * [backup-simplify]: Simplify 1 into 1
23.050 * [backup-simplify]: Simplify (/ 1 1) into 1
23.050 * [taylor]: Taking taylor expansion of 1/2 in k
23.050 * [backup-simplify]: Simplify 1/2 into 1/2
23.050 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k
23.050 * [taylor]: Taking taylor expansion of (log -1) in k
23.050 * [taylor]: Taking taylor expansion of -1 in k
23.050 * [backup-simplify]: Simplify -1 into -1
23.050 * [backup-simplify]: Simplify (log -1) into (log -1)
23.050 * [taylor]: Taking taylor expansion of (log n) in k
23.050 * [taylor]: Taking taylor expansion of n in k
23.050 * [backup-simplify]: Simplify n into n
23.050 * [backup-simplify]: Simplify (log n) into (log n)
23.051 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
23.051 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
23.051 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
23.051 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n))
23.052 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n)))
23.052 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log -1) (log n)))) into (* 1/4 (- (log -1) (log n)))
23.052 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))
23.052 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) in k
23.052 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) in k
23.052 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k
23.052 * [taylor]: Taking taylor expansion of 1/2 in k
23.052 * [backup-simplify]: Simplify 1/2 into 1/2
23.052 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k
23.052 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
23.053 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
23.053 * [taylor]: Taking taylor expansion of 1/2 in k
23.053 * [backup-simplify]: Simplify 1/2 into 1/2
23.053 * [taylor]: Taking taylor expansion of (/ 1 k) in k
23.053 * [taylor]: Taking taylor expansion of k in k
23.053 * [backup-simplify]: Simplify 0 into 0
23.053 * [backup-simplify]: Simplify 1 into 1
23.053 * [backup-simplify]: Simplify (/ 1 1) into 1
23.053 * [taylor]: Taking taylor expansion of 1/2 in k
23.053 * [backup-simplify]: Simplify 1/2 into 1/2
23.053 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
23.053 * [taylor]: Taking taylor expansion of (* 2 PI) in k
23.053 * [taylor]: Taking taylor expansion of 2 in k
23.053 * [backup-simplify]: Simplify 2 into 2
23.053 * [taylor]: Taking taylor expansion of PI in k
23.053 * [backup-simplify]: Simplify PI into PI
23.053 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
23.054 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
23.054 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
23.054 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
23.056 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
23.057 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (log (* 2 PI)))) into (* 1/4 (log (* 2 PI)))
23.058 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))))
23.058 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
23.058 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
23.058 * [taylor]: Taking taylor expansion of 1/2 in k
23.058 * [backup-simplify]: Simplify 1/2 into 1/2
23.058 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
23.058 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
23.058 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
23.058 * [taylor]: Taking taylor expansion of 1/2 in k
23.058 * [backup-simplify]: Simplify 1/2 into 1/2
23.058 * [taylor]: Taking taylor expansion of (/ 1 k) in k
23.058 * [taylor]: Taking taylor expansion of k in k
23.058 * [backup-simplify]: Simplify 0 into 0
23.058 * [backup-simplify]: Simplify 1 into 1
23.058 * [backup-simplify]: Simplify (/ 1 1) into 1
23.058 * [taylor]: Taking taylor expansion of 1/2 in k
23.058 * [backup-simplify]: Simplify 1/2 into 1/2
23.058 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
23.058 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
23.058 * [taylor]: Taking taylor expansion of (* -2 PI) in k
23.058 * [taylor]: Taking taylor expansion of -2 in k
23.058 * [backup-simplify]: Simplify -2 into -2
23.058 * [taylor]: Taking taylor expansion of PI in k
23.058 * [backup-simplify]: Simplify PI into PI
23.059 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
23.059 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
23.059 * [taylor]: Taking taylor expansion of (log n) in k
23.059 * [taylor]: Taking taylor expansion of n in k
23.059 * [backup-simplify]: Simplify n into n
23.059 * [backup-simplify]: Simplify (log n) into (log n)
23.060 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
23.060 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
23.060 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
23.061 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
23.061 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
23.062 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
23.063 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
23.063 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
23.063 * [taylor]: Taking taylor expansion of (/ -1 k) in k
23.063 * [taylor]: Taking taylor expansion of -1 in k
23.063 * [backup-simplify]: Simplify -1 into -1
23.063 * [taylor]: Taking taylor expansion of k in k
23.063 * [backup-simplify]: Simplify 0 into 0
23.063 * [backup-simplify]: Simplify 1 into 1
23.063 * [backup-simplify]: Simplify (/ -1 1) into -1
23.063 * [backup-simplify]: Simplify (sqrt 0) into 0
23.064 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
23.066 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
23.067 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
23.069 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))))
23.071 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))))
23.072 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
23.074 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0
23.074 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
23.075 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
23.075 * [backup-simplify]: Simplify (+ 0 0) into 0
23.076 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
23.077 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
23.077 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log -1) (log n)))) into 0
23.078 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
23.079 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
23.080 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
23.082 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
23.082 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
23.083 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
23.083 * [backup-simplify]: Simplify (+ 0 0) into 0
23.084 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
23.086 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
23.087 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
23.089 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
23.090 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 0) (* 0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) into 0
23.091 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
23.093 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
23.093 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
23.094 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
23.094 * [backup-simplify]: Simplify (+ 0 0) into 0
23.095 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
23.095 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (log (* 2 PI)))) into 0
23.097 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
23.100 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) 0) (* 0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0
23.104 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
23.104 * [taylor]: Taking taylor expansion of 0 in k
23.104 * [backup-simplify]: Simplify 0 into 0
23.104 * [backup-simplify]: Simplify 0 into 0
23.106 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) 0) (* 0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into 0
23.109 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 0) (* 0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0
23.110 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
23.113 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
23.117 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))))
23.120 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))))
23.121 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
23.125 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0
23.125 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
23.126 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
23.126 * [backup-simplify]: Simplify (+ 0 0) into 0
23.127 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
23.128 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
23.129 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0
23.131 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
23.132 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
23.140 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
23.144 * [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
23.144 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
23.145 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
23.146 * [backup-simplify]: Simplify (+ 0 0) into 0
23.147 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
23.148 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
23.150 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
23.152 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
23.154 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))))) into 0
23.155 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
23.159 * [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
23.159 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
23.160 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
23.160 * [backup-simplify]: Simplify (+ 0 0) into 0
23.161 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
23.162 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0
23.165 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
23.168 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))))) into 0
23.168 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
23.169 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
23.172 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
23.172 * [taylor]: Taking taylor expansion of 0 in k
23.172 * [backup-simplify]: Simplify 0 into 0
23.172 * [backup-simplify]: Simplify 0 into 0
23.172 * [backup-simplify]: Simplify 0 into 0
23.175 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0
23.179 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))))) into 0
23.180 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
23.185 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
23.192 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))))
23.195 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))))
23.204 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n))))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n))))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n))))))) (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (log (* 2 PI))))) (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))))))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))))) k)) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))))) (pow k 2))))))))
23.204 * * * [progress]: simplifying candidates
23.204 * * * * [progress]: [ 1 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (log1p (expm1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
23.204 * * * * [progress]: [ 2 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (expm1 (log1p (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
23.204 * * * * [progress]: [ 3 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.204 * * * * [progress]: [ 4 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.204 * * * * [progress]: [ 5 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.204 * * * * [progress]: [ 6 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.204 * * * * [progress]: [ 7 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.204 * * * * [progress]: [ 8 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.204 * * * * [progress]: [ 9 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 10 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (/ (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 11 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (cbrt (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 12 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 13 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 14 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 15 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (/ (cbrt (- 1/2 (/ k 2))) 2)) (sqrt k))))>
23.205 * * * * [progress]: [ 16 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 17 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 18 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2)) (sqrt k))))>
23.205 * * * * [progress]: [ 19 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 20 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 21 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.205 * * * * [progress]: [ 22 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 23 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 24 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (/ (- (sqrt 1/2) (sqrt (/ k 2))) 2)) (sqrt k))))>
23.205 * * * * [progress]: [ 25 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 26 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 27 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 2)) (sqrt k))))>
23.205 * * * * [progress]: [ 28 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 29 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (sqrt k))))>
23.205 * * * * [progress]: [ 30 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.206 * * * * [progress]: [ 31 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.206 * * * * [progress]: [ 32 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)) (sqrt k))))>
23.206 * * * * [progress]: [ 33 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.206 * * * * [progress]: [ 34 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (sqrt k))))>
23.206 * * * * [progress]: [ 35 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
23.206 * * * * [progress]: [ 36 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (log (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
23.206 * * * * [progress]: [ 37 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
23.206 * * * * [progress]: [ 38 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (cbrt (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
23.206 * * * * [progress]: [ 39 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
23.206 * * * * [progress]: [ 40 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.206 * * * * [progress]: [ 41 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2))) (sqrt k))))>
23.206 * * * * [progress]: [ 42 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
23.206 * * * * [progress]: [ 43 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (log1p (expm1 (pow n (/ (- 1/2 (/ k 2)) 2)))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.206 * * * * [progress]: [ 44 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (expm1 (log1p (pow n (/ (- 1/2 (/ k 2)) 2)))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.206 * * * * [progress]: [ 45 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (exp (* (log n) (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.206 * * * * [progress]: [ 46 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (exp (* (log n) (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.206 * * * * [progress]: [ 47 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (* 1 (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.206 * * * * [progress]: [ 48 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (/ (pow n (/ 1/2 2)) (pow n (/ (/ k 2) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.206 * * * * [progress]: [ 49 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (cbrt (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.206 * * * * [progress]: [ 50 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.206 * * * * [progress]: [ 51 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 52 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 53 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (/ (cbrt (- 1/2 (/ k 2))) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 54 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 55 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 56 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 57 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 58 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 59 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 60 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 61 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 62 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (/ (- (sqrt 1/2) (sqrt (/ k 2))) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 63 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 64 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 65 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 66 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 67 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 68 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 69 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n 1) (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 70 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (- 1/2 (/ k 2))) (/ 1 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.207 * * * * [progress]: [ 71 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* (pow (* (cbrt n) (cbrt n)) (/ (- 1/2 (/ k 2)) 2)) (pow (cbrt n) (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 72 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* (pow (sqrt n) (/ (- 1/2 (/ k 2)) 2)) (pow (sqrt n) (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 73 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* (pow 1 (/ (- 1/2 (/ k 2)) 2)) (pow n (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 74 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow n (/ (- 1/2 (/ k 2)) 2)) 1) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 75 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (exp (log (pow n (/ (- 1/2 (/ k 2)) 2)))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 76 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (log (exp (pow n (/ (- 1/2 (/ k 2)) 2)))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 77 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* (* (cbrt (pow n (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow n (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow n (/ (- 1/2 (/ k 2)) 2)))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 78 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (* (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow n (/ (- 1/2 (/ k 2)) 2))) (pow n (/ (- 1/2 (/ k 2)) 2)))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 79 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* (sqrt (pow n (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow n (/ (- 1/2 (/ k 2)) 2)))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 80 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* 1 (pow n (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 81 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* (pow n (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow n (/ (/ (- 1/2 (/ k 2)) 2) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 82 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (posit16->real (real->posit16 (pow n (/ (- 1/2 (/ k 2)) 2)))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 83 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (log1p (expm1 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 84 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (expm1 (log1p (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 85 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 86 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 87 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 88 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 89 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 90 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (exp (log (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 91 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (log (exp (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 92 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 93 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.208 * * * * [progress]: [ 94 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.209 * * * * [progress]: [ 95 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.209 * * * * [progress]: [ 96 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.209 * * * * [progress]: [ 97 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.209 * * * * [progress]: [ 98 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.209 * * * * [progress]: [ 99 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.209 * * * * [progress]: [ 100 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.209 * * * * [progress]: [ 101 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.209 * * * * [progress]: [ 102 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.209 * * * * [progress]: [ 103 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* 2 PI) n) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.209 * * * * [progress]: [ 104 / 344 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.209 * * * * [progress]: [ 105 / 344 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.209 * * * * [progress]: [ 106 / 344 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) 1))>
23.209 * * * * [progress]: [ 107 / 344 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) 1))>
23.209 * * * * [progress]: [ 108 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.209 * * * * [progress]: [ 109 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.209 * * * * [progress]: [ 110 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.209 * * * * [progress]: [ 111 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.209 * * * * [progress]: [ 112 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.209 * * * * [progress]: [ 113 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.209 * * * * [progress]: [ 114 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.209 * * * * [progress]: [ 115 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.209 * * * * [progress]: [ 116 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 117 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 118 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 119 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
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23.210 * * * * [progress]: [ 121 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 122 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
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23.210 * * * * [progress]: [ 124 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 125 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.210 * * * * [progress]: [ 126 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 127 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 128 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 129 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 130 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 131 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.210 * * * * [progress]: [ 132 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 133 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 134 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 135 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.210 * * * * [progress]: [ 136 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 137 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.211 * * * * [progress]: [ 138 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 139 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 140 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 141 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 142 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 143 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.211 * * * * [progress]: [ 144 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 145 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 146 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 147 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 148 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 149 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.211 * * * * [progress]: [ 150 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 151 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 152 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 153 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 154 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.211 * * * * [progress]: [ 155 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.211 * * * * [progress]: [ 156 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 157 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 158 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 159 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 160 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 161 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.212 * * * * [progress]: [ 162 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 163 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 164 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 165 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 166 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 167 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.212 * * * * [progress]: [ 168 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 169 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 170 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 171 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 172 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 173 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.212 * * * * [progress]: [ 174 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 175 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.212 * * * * [progress]: [ 176 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 177 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 178 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 179 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.213 * * * * [progress]: [ 180 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 181 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 182 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 183 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 184 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 185 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.213 * * * * [progress]: [ 186 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 187 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 188 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 189 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 190 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 191 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.213 * * * * [progress]: [ 192 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 193 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 194 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 195 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 196 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.213 * * * * [progress]: [ 197 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.214 * * * * [progress]: [ 198 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 199 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 200 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 201 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 202 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 203 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (* (log n) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.214 * * * * [progress]: [ 204 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 205 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 206 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 207 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 208 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 209 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.214 * * * * [progress]: [ 210 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 211 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 212 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 213 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 214 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 215 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (+ (log 2) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.214 * * * * [progress]: [ 216 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.214 * * * * [progress]: [ 217 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 218 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 219 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 220 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 221 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.215 * * * * [progress]: [ 222 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 223 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 224 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 225 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 226 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 227 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.215 * * * * [progress]: [ 228 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 229 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 230 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 231 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 232 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 233 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.215 * * * * [progress]: [ 234 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 235 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 236 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.215 * * * * [progress]: [ 237 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 238 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 239 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (* (log (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.216 * * * * [progress]: [ 240 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 241 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 242 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 243 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 244 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 245 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.216 * * * * [progress]: [ 246 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 247 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 248 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 249 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 250 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 251 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (+ (log (pow n (/ (- 1/2 (/ k 2)) 2))) (log (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.216 * * * * [progress]: [ 252 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 253 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 254 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 255 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 256 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.216 * * * * [progress]: [ 257 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) 0) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.216 * * * * [progress]: [ 258 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.217 * * * * [progress]: [ 259 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.217 * * * * [progress]: [ 260 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.217 * * * * [progress]: [ 261 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.217 * * * * [progress]: [ 262 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.217 * * * * [progress]: [ 263 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (log 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.217 * * * * [progress]: [ 264 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.217 * * * * [progress]: [ 265 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.217 * * * * [progress]: [ 266 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.217 * * * * [progress]: [ 267 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (- (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
23.217 * * * * [progress]: [ 268 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (- (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
23.217 * * * * [progress]: [ 269 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (log (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.217 * * * * [progress]: [ 270 / 344 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.217 * * * * [progress]: [ 271 / 344 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.217 * * * * [progress]: [ 272 / 344 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow n (/ (- 1/2 (/ k 2)) 2))) (pow n (/ (- 1/2 (/ k 2)) 2))) (* (* (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (* (* 1 1) 1)) (/ (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
23.217 * * * * [progress]: [ 273 / 344 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow n (/ (- 1/2 (/ k 2)) 2))) (pow n (/ (- 1/2 (/ k 2)) 2))) (* (* (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (* (* 1 1) 1)) (* (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.217 * * * * [progress]: [ 274 / 344 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (* (* 1 1) 1)) (/ (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
23.217 * * * * [progress]: [ 275 / 344 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (* (* 1 1) 1)) (* (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.217 * * * * [progress]: [ 276 / 344 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
23.217 * * * * [progress]: [ 277 / 344 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (* (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.217 * * * * [progress]: [ 278 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))) (cbrt (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))) (cbrt (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.218 * * * * [progress]: [ 279 / 344 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.218 * * * * [progress]: [ 280 / 344 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))) (sqrt (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.218 * * * * [progress]: [ 281 / 344 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* 1 (sqrt k))))>
23.218 * * * * [progress]: [ 282 / 344 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
23.218 * * * * [progress]: [ 283 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))) (* (sqrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.218 * * * * [progress]: [ 284 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k)))) (* (sqrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k))))))>
23.218 * * * * [progress]: [ 285 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k)))) (* (sqrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k))))))>
23.218 * * * * [progress]: [ 286 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k)))) (* (sqrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k))))))>
23.218 * * * * [progress]: [ 287 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k)))) (* (sqrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k))))))>
23.218 * * * * [progress]: [ 288 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
23.218 * * * * [progress]: [ 289 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
23.218 * * * * [progress]: [ 290 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))>
23.218 * * * * [progress]: [ 291 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))>
23.218 * * * * [progress]: [ 292 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (/ (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
23.218 * * * * [progress]: [ 293 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))) (/ (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.218 * * * * [progress]: [ 294 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (/ (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
23.218 * * * * [progress]: [ 295 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow n (/ (- 1/2 (/ k 2)) 2)) 1)) (/ (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.218 * * * * [progress]: [ 296 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (sqrt k)))))>
23.218 * * * * [progress]: [ 297 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (cbrt k)))))>
23.218 * * * * [progress]: [ 298 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k)))))>
23.219 * * * * [progress]: [ 299 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt 1))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.219 * * * * [progress]: [ 300 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k)))))>
23.219 * * * * [progress]: [ 301 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) 1)) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.219 * * * * [progress]: [ 302 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (sqrt k)))))>
23.219 * * * * [progress]: [ 303 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (cbrt k)))))>
23.219 * * * * [progress]: [ 304 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k)))))>
23.219 * * * * [progress]: [ 305 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt 1))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.219 * * * * [progress]: [ 306 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k)))))>
23.219 * * * * [progress]: [ 307 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
23.219 * * * * [progress]: [ 308 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))>
23.219 * * * * [progress]: [ 309 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))>
23.219 * * * * [progress]: [ 310 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
23.219 * * * * [progress]: [ 311 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ 1 (sqrt 1))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.219 * * * * [progress]: [ 312 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
23.219 * * * * [progress]: [ 313 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ 1 1)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.219 * * * * [progress]: [ 314 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (cbrt (sqrt k)))))>
23.219 * * * * [progress]: [ 315 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (cbrt k)))))>
23.219 * * * * [progress]: [ 316 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k)))))>
23.219 * * * * [progress]: [ 317 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt 1))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt k))))>
23.219 * * * * [progress]: [ 318 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k)))))>
23.219 * * * * [progress]: [ 319 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt k))))>
23.220 * * * * [progress]: [ 320 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.220 * * * * [progress]: [ 321 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (/ 1 (sqrt k))))>
23.220 * * * * [progress]: [ 322 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (cbrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1))) (* (cbrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
23.220 * * * * [progress]: [ 323 / 344 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (* (sqrt (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
23.220 * * * * [progress]: [ 324 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (* (cbrt 1) (cbrt 1))) (* (/ (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt 1)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
23.220 * * * * [progress]: [ 325 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (* (/ (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
23.220 * * * * [progress]: [ 326 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1/2 (/ k 2)) 2)) 1) (* (/ (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
23.220 * * * * [progress]: [ 327 / 344 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
23.220 * * * * [progress]: [ 328 / 344 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (* (/ 1 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
23.220 * * * * [progress]: [ 329 / 344 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
23.220 * * * * [progress]: [ 330 / 344 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) 1))>
23.220 * * * * [progress]: [ 331 / 344 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
23.220 * * * * [progress]: [ 332 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)) (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1)))>
23.220 * * * * [progress]: [ 333 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (sqrt k))))>
23.220 * * * * [progress]: [ 334 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k))))>
23.220 * * * * [progress]: [ 335 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))))>
23.220 * * * * [progress]: [ 336 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (- (+ (pow n 1/4) (* 1/32 (* (pow n 1/4) (* (pow (log n) 2) (pow k 2))))) (* 1/4 (* (pow n 1/4) (* (log n) k)))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.220 * * * * [progress]: [ 337 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (exp (* -1/2 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.220 * * * * [progress]: [ 338 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n)))))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.220 * * * * [progress]: [ 339 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.220 * * * * [progress]: [ 340 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.220 * * * * [progress]: [ 341 / 344 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
23.221 * * * * [progress]: [ 342 / 344 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k)))) (- (+ (* +nan.0 (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log (* 2 PI)) (* (pow k 2) (log n)))) (pow (* PI (* n 2)) 1/4))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) k))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2))))) (- (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))))))))))))))))))))))))>
23.221 * * * * [progress]: [ 343 / 344 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* -1/2 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))))) k))))))))>
23.221 * * * * [progress]: [ 344 / 344 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))))))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))))) k)) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (log (* 2 PI))))))) (pow k 2)))))))))>
23.225 * [simplify]: Simplifying (expm1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (log1p (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))), (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)), (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)), (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)), (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)), (* 1 (/ (- 1/2 (/ k 2)) 2)), (* 1 (/ (- 1/2 (/ k 2)) 2)), (* 1 (/ (- 1/2 (/ k 2)) 2)), (pow (* n (* 2 PI)) (/ 1/2 2)), (pow (* n (* 2 PI)) (/ (/ k 2) 2)), (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))), (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))), (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))), (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)), (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))), (pow (* n (* 2 PI)) (/ (sqrt (- 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(log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))), (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))), (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))), (- (+ (pow n 1/4) (* 1/32 (* (pow n 1/4) (* (pow (log n) 2) (pow k 2))))) (* 1/4 (* (pow n 1/4) (* (log n) k)))), (exp (* -1/2 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))), (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n)))))), (* 2 (* n PI)), (* 2 (* n PI)), (* 2 (* n PI)), (- (+ (* +nan.0 (* (pow (* PI (* n 2)) 1/4) (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 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23.237 * * [simplify]: iteration 1: (523 enodes)
23.558 * * [simplify]: Extracting #0: cost 137 inf + 0
23.559 * * [simplify]: Extracting #1: cost 560 inf + 2
23.562 * * [simplify]: Extracting #2: cost 754 inf + 1464
23.565 * * [simplify]: Extracting #3: cost 772 inf + 12784
23.577 * * [simplify]: Extracting #4: cost 612 inf + 86368
23.628 * * [simplify]: Extracting #5: cost 360 inf + 255815
23.687 * * [simplify]: Extracting #6: cost 210 inf + 353074
23.757 * * [simplify]: Extracting #7: cost 120 inf + 413182
23.815 * * [simplify]: Extracting #8: cost 94 inf + 441744
23.920 * * [simplify]: Extracting #9: cost 78 inf + 462330
24.029 * * [simplify]: Extracting #10: cost 58 inf + 492874
24.143 * * [simplify]: Extracting #11: cost 46 inf + 511016
24.254 * * [simplify]: Extracting #12: cost 34 inf + 522976
24.366 * * [simplify]: Extracting #13: cost 25 inf + 535814
24.475 * * [simplify]: Extracting #14: cost 18 inf + 548591
24.599 * * [simplify]: Extracting #15: cost 8 inf + 570116
24.733 * * [simplify]: Extracting #16: cost 2 inf + 583672
24.896 * * [simplify]: Extracting #17: cost 0 inf + 588404
25.048 * * [simplify]: Extracting #18: cost 0 inf + 588374
25.184 * [simplify]: Simplified to (expm1 (pow (* (* PI 2) n) (- 1/4 (/ k 4)))), (log1p (pow (* (* PI 2) n) (- 1/4 (/ k 4)))), (* (log (* (* PI 2) n)) (- 1/4 (/ k 4))), (* (log (* (* PI 2) n)) (- 1/4 (/ k 4))), (* (log (* (* PI 2) n)) (- 1/4 (/ k 4))), (* (log (* (* PI 2) n)) (- 1/4 (/ k 4))), (- 1/4 (/ k 4)), (- 1/4 (/ k 4)), (- 1/4 (/ k 4)), (pow (* (* PI 2) n) 1/4), (pow (* (* PI 2) n) (/ k 4)), (pow (* (* PI 2) n) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4))))), (pow (* (* PI 2) n) (sqrt (- 1/4 (/ k 4)))), (pow (* (* PI 2) n) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)))), (pow (* (* PI 2) n) (/ (cbrt (- 1/2 (/ k 2))) (/ (sqrt 2) (cbrt (- 1/2 (/ k 2)))))), (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))), (pow (* (* PI 2) n) (/ (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2)) (cbrt 2))), (pow (* (* PI 2) n) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))), (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2)))), (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))), 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(/ (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (* (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))))) (sqrt (sqrt k))), (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (* (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))))), (/ (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (* (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))))) (sqrt (sqrt k))), (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (* (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (cbrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))))), (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (/ (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))), (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (/ (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (fabs (cbrt k)))), (/ (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4))))) (sqrt (sqrt k))), (* (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4))))), (/ (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4))))) (sqrt (sqrt k))), (* (sqrt (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4))))), (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))), (* (/ 1 (fabs (cbrt k))) (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4))))), (* (/ 1 (sqrt (sqrt k))) (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4))))), (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))), (* (/ 1 (sqrt (sqrt k))) (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4))))), (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))), (* (/ (pow (* (* PI 2) n) (/ (- 1/4 (/ k 4)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4))))), (/ (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (pow (* (* PI 2) n) (/ (- 1/4 (/ k 4)) 2))) (fabs (cbrt k))), (* (/ (pow (* (* PI 2) n) (/ (- 1/4 (/ k 4)) 2)) (sqrt (sqrt k))) (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4))))), (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (pow (* (* PI 2) n) (/ (- 1/4 (/ k 4)) 2))), (* (/ (pow (* (* PI 2) n) (/ (- 1/4 (/ k 4)) 2)) (sqrt (sqrt k))) (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4))))), (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (pow (* (* PI 2) n) (/ (- 1/4 (/ k 4)) 2))), (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))), (* (pow n (- 1/4 (/ k 4))) (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))), (* (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k)) (cbrt (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))))), (* (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k)) (sqrt (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))))), (* (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k)) (pow (* PI 2) (- 1/4 (/ k 4)))), (* (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k)) (pow (* PI 2) (- 1/4 (/ k 4)))), (* (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k)) (pow (* PI 2) (- 1/4 (/ k 4)))), (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k))), (* (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k)) 1), (* (pow n (- 1/4 (/ k 4))) (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))), (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k))), (real->posit16 (* (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow n (- 1/4 (/ k 4)))) (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k)))), (- (fma 1/16 (* (* (* (log (* PI 2)) (* k k)) (log n)) (exp (* (log (* (* PI 2) n)) 1/4))) (+ (exp (* (log (* (* PI 2) n)) 1/4)) (* 1/32 (+ (* (exp (* (log (* (* PI 2) n)) 1/4)) (* (* (log n) (log n)) (* k k))) (* (* (exp (* (log (* (* PI 2) n)) 1/4)) (* k k)) (* (log (* PI 2)) (log (* PI 2)))))))) (* 1/4 (+ (* (* (log n) k) (exp (* (log (* (* PI 2) n)) 1/4))) (* k (* (log (* PI 2)) (exp (* (log (* (* PI 2) n)) 1/4))))))), (exp (* (* (- 1/2 (* 1/2 k)) (- (log (* PI 2)) (- (log n)))) 1/2)), (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n)))))), (- (+ (* (* (pow n 1/4) (* (* (log n) (log n)) (* k k))) 1/32) (pow n 1/4)) (* (* 1/4 (pow n 1/4)) (* (log n) k))), (exp (* (* (- (log n)) (- 1/2 (* 1/2 k))) -1/2)), (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) (- 1/2 (* 1/2 k))))), (* (* PI 2) n), (* (* PI 2) n), (* (* PI 2) n), (- (- (* (* +nan.0 (pow (* (* PI 2) n) 1/4)) (* (* (exp (* (log (* (* PI 2) n)) 1/4)) (* k k)) (* (log (* PI 2)) (log (* PI 2))))) (- (* (* +nan.0 (pow (* (* PI 2) n) 1/4)) (exp (* (log (* (* PI 2) n)) 1/4))) (- (* (* +nan.0 (pow (* (* PI 2) n) 1/4)) (* (* (exp (* (log (* (* PI 2) n)) 1/4)) (* k k)) (log (* PI 2)))) (- (* (* (* k (* (log (* PI 2)) (exp (* (log (* (* PI 2) n)) 1/4)))) (pow (* (* PI 2) n) 1/4)) +nan.0) (- (* +nan.0 (* (* (* (log n) k) (exp (* (log (* (* PI 2) n)) 1/4))) (pow (* (* PI 2) n) 1/4))) (- (* +nan.0 (* (pow (* (* PI 2) n) 1/4) (* (* (* (log (* PI 2)) (* k k)) (log n)) (exp (* (log (* (* PI 2) n)) 1/4))))) (- (* +nan.0 (* (* k (exp (* (log (* (* PI 2) n)) 1/4))) (pow (* (* PI 2) n) 1/4))) (- (* +nan.0 (* (pow (* (* PI 2) n) 1/4) (* (exp (* (log (* (* PI 2) n)) 1/4)) (* k k)))) (- (* +nan.0 (* (pow (* (* PI 2) n) 1/4) (* (exp (* (log (* (* PI 2) n)) 1/4)) (* (* (log n) (log n)) (* k k))))) (* (* +nan.0 (pow (* (* PI 2) n) 1/4)) (* (exp (* (log (* (* PI 2) n)) 1/4)) (* (* k k) (log n)))))))))))))), (- (- (* (/ (exp (* (* (log (* PI 2)) (- 1/2 (* 1/2 k))) 1/2)) (/ (* (* k k) k) (exp (+ (* (* (- 1/2 (* 1/2 k)) (- (log (* PI 2)) (- (log n)))) 1/2) (* (* (- (log n)) (- 1/2 (* 1/2 k))) -1/2))))) +nan.0) (- (/ (* +nan.0 (* (exp (* (* (log (* PI 2)) (- 1/2 (* 1/2 k))) 1/2)) (* (exp (* (* (- 1/2 (* 1/2 k)) (- (log (* PI 2)) (- (log n)))) 1/2)) (exp (* (* (- (log n)) (- 1/2 (* 1/2 k))) -1/2))))) (* k k)) (* (/ (* (exp (* (* (log (* PI 2)) (- 1/2 (* 1/2 k))) 1/2)) (* (exp (* (* (- 1/2 (* 1/2 k)) (- (log (* PI 2)) (- (log n)))) 1/2)) (exp (* (* (- (log n)) (- 1/2 (* 1/2 k))) -1/2)))) k) +nan.0)))), (- (- (* (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))))) (exp (+ (* 1/2 (* (- (log -1) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (* (* (log (* PI 2)) (- 1/2 (* 1/2 k))) 1/2)))) (- (/ (* (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))))) (exp (+ (* 1/2 (* (- (log -1) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (* (* (log (* PI 2)) (- 1/2 (* 1/2 k))) 1/2)))) k) (/ (* (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))))) (exp (+ (* 1/2 (* (- (log -1) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (* (* (log (* PI 2)) (- 1/2 (* 1/2 k))) 1/2)))) (* k k)))))
25.226 * * * [progress]: adding candidates to table
30.257 * [progress]: [Phase 3 of 3] Extracting.
30.257 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> #<alt (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (- (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (/ (/ (sqrt (* 2 (* n PI))) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))> #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k))) (sqrt (cbrt k))))>)
30.260 * * * [regime-changes]: Trying 4 branch expressions: (n (* (* 2 PI) n) k (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
30.260 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> #<alt (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (- (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (/ (/ (sqrt (* 2 (* n PI))) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))> #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k))) (sqrt (cbrt k))))>)
30.357 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> #<alt (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (- (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (/ (/ (sqrt (* 2 (* n PI))) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))> #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k))) (sqrt (cbrt k))))>)
30.425 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> #<alt (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (- (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (/ (/ (sqrt (* 2 (* n PI))) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))> #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k))) (sqrt (cbrt k))))>)
30.498 * * * * [regimes]: Trying to branch on (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) from (#<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> #<alt (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (- (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (/ (/ (sqrt (* 2 (* n PI))) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))> #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k))) (sqrt (cbrt k))))>)
30.583 * * * [regime]: Found split indices: #<option (#s(si 3 255))>
30.583 * [simplify]: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
30.583 * * [simplify]: iteration 1: (13 enodes)
30.585 * * [simplify]: iteration 2: (18 enodes)
30.586 * * [simplify]: Extracting #0: cost 1 inf + 0
30.586 * * [simplify]: Extracting #1: cost 3 inf + 0
30.586 * * [simplify]: Extracting #2: cost 7 inf + 0
30.586 * * [simplify]: Extracting #3: cost 11 inf + 1
30.586 * * [simplify]: Extracting #4: cost 5 inf + 252
30.587 * * [simplify]: Extracting #5: cost 4 inf + 253
30.587 * * [simplify]: Extracting #6: cost 1 inf + 753
30.587 * * [simplify]: Extracting #7: cost 0 inf + 1248
30.587 * [simplify]: Simplified to (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
39.212 * [regime-testing]: Baseline error score: 0.355475915601184
39.217 * [regime-testing]: Oracle error score: 0.05495305810598163
39.226 * [regime-testing]: End program error score: 0.355475915601184