72.947 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.207 * * * [progress]: [2/2] Setting up program.
0.212 * [progress]: [Phase 2 of 3] Improving.
0.212 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.212 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.213 * * [simplify]: iteration 1: (13 enodes)
0.219 * * [simplify]: iteration 2: (29 enodes)
0.230 * * [simplify]: iteration 3: (60 enodes)
0.254 * * [simplify]: iteration 4: (123 enodes)
0.376 * * [simplify]: iteration 5: (322 enodes)
0.648 * * [simplify]: iteration 6: (817 enodes)
1.670 * * [simplify]: Extracting #0: cost 1 inf + 0
1.670 * * [simplify]: Extracting #1: cost 58 inf + 0
1.672 * * [simplify]: Extracting #2: cost 198 inf + 1
1.675 * * [simplify]: Extracting #3: cost 265 inf + 46
1.679 * * [simplify]: Extracting #4: cost 245 inf + 1713
1.687 * * [simplify]: Extracting #5: cost 180 inf + 14173
1.729 * * [simplify]: Extracting #6: cost 61 inf + 110645
1.780 * * [simplify]: Extracting #7: cost 0 inf + 167860
1.828 * * [simplify]: Extracting #8: cost 0 inf + 164570
1.877 * [simplify]: Simplified to:
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
1.890 * * [progress]: iteration 1 / 4
1.890 * * * [progress]: picking best candidate
1.902 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))>
1.902 * * * [progress]: localizing error
1.928 * * * [progress]: generating rewritten candidates
1.928 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
1.949 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
1.975 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
1.999 * * * [progress]: generating series expansions
1.999 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
2.000 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
2.000 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
2.000 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
2.000 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
2.000 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
2.000 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.000 * [taylor]: Taking taylor expansion of 1/2 in k
2.000 * [backup-simplify]: Simplify 1/2 into 1/2
2.000 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.000 * [taylor]: Taking taylor expansion of 1/2 in k
2.000 * [backup-simplify]: Simplify 1/2 into 1/2
2.000 * [taylor]: Taking taylor expansion of k in k
2.000 * [backup-simplify]: Simplify 0 into 0
2.000 * [backup-simplify]: Simplify 1 into 1
2.000 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
2.000 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
2.000 * [taylor]: Taking taylor expansion of 2 in k
2.000 * [backup-simplify]: Simplify 2 into 2
2.000 * [taylor]: Taking taylor expansion of (* n PI) in k
2.000 * [taylor]: Taking taylor expansion of n in k
2.000 * [backup-simplify]: Simplify n into n
2.000 * [taylor]: Taking taylor expansion of PI in k
2.000 * [backup-simplify]: Simplify PI into PI
2.000 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.001 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
2.001 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
2.001 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.001 * [backup-simplify]: Simplify (- 0) into 0
2.002 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.002 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
2.002 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
2.002 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.002 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.002 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.002 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.002 * [taylor]: Taking taylor expansion of 1/2 in n
2.002 * [backup-simplify]: Simplify 1/2 into 1/2
2.002 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.002 * [taylor]: Taking taylor expansion of 1/2 in n
2.002 * [backup-simplify]: Simplify 1/2 into 1/2
2.002 * [taylor]: Taking taylor expansion of k in n
2.002 * [backup-simplify]: Simplify k into k
2.002 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.002 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.002 * [taylor]: Taking taylor expansion of 2 in n
2.002 * [backup-simplify]: Simplify 2 into 2
2.002 * [taylor]: Taking taylor expansion of (* n PI) in n
2.002 * [taylor]: Taking taylor expansion of n in n
2.002 * [backup-simplify]: Simplify 0 into 0
2.002 * [backup-simplify]: Simplify 1 into 1
2.002 * [taylor]: Taking taylor expansion of PI in n
2.002 * [backup-simplify]: Simplify PI into PI
2.002 * [backup-simplify]: Simplify (* 0 PI) into 0
2.003 * [backup-simplify]: Simplify (* 2 0) into 0
2.004 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.005 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.005 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.005 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.005 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.006 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.006 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.007 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.008 * [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)))))
2.008 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.008 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.008 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.008 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.008 * [taylor]: Taking taylor expansion of 1/2 in n
2.008 * [backup-simplify]: Simplify 1/2 into 1/2
2.008 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.008 * [taylor]: Taking taylor expansion of 1/2 in n
2.008 * [backup-simplify]: Simplify 1/2 into 1/2
2.008 * [taylor]: Taking taylor expansion of k in n
2.008 * [backup-simplify]: Simplify k into k
2.008 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.008 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.008 * [taylor]: Taking taylor expansion of 2 in n
2.008 * [backup-simplify]: Simplify 2 into 2
2.008 * [taylor]: Taking taylor expansion of (* n PI) in n
2.008 * [taylor]: Taking taylor expansion of n in n
2.008 * [backup-simplify]: Simplify 0 into 0
2.008 * [backup-simplify]: Simplify 1 into 1
2.008 * [taylor]: Taking taylor expansion of PI in n
2.008 * [backup-simplify]: Simplify PI into PI
2.009 * [backup-simplify]: Simplify (* 0 PI) into 0
2.009 * [backup-simplify]: Simplify (* 2 0) into 0
2.010 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.014 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.015 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.015 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.015 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.015 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.016 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.017 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.018 * [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)))))
2.018 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
2.018 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
2.018 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.018 * [taylor]: Taking taylor expansion of 1/2 in k
2.018 * [backup-simplify]: Simplify 1/2 into 1/2
2.018 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.018 * [taylor]: Taking taylor expansion of 1/2 in k
2.018 * [backup-simplify]: Simplify 1/2 into 1/2
2.018 * [taylor]: Taking taylor expansion of k in k
2.018 * [backup-simplify]: Simplify 0 into 0
2.018 * [backup-simplify]: Simplify 1 into 1
2.018 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
2.018 * [taylor]: Taking taylor expansion of (log n) in k
2.018 * [taylor]: Taking taylor expansion of n in k
2.018 * [backup-simplify]: Simplify n into n
2.018 * [backup-simplify]: Simplify (log n) into (log n)
2.018 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.018 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.018 * [taylor]: Taking taylor expansion of 2 in k
2.018 * [backup-simplify]: Simplify 2 into 2
2.018 * [taylor]: Taking taylor expansion of PI in k
2.018 * [backup-simplify]: Simplify PI into PI
2.018 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.019 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.020 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.020 * [backup-simplify]: Simplify (- 0) into 0
2.020 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.021 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.022 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
2.022 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
2.023 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
2.024 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.025 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.026 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.026 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
2.026 * [backup-simplify]: Simplify (- 0) into 0
2.026 * [backup-simplify]: Simplify (+ 0 0) into 0
2.027 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.028 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
2.029 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.030 * [taylor]: Taking taylor expansion of 0 in k
2.030 * [backup-simplify]: Simplify 0 into 0
2.030 * [backup-simplify]: Simplify 0 into 0
2.030 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
2.031 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.033 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.034 * [backup-simplify]: Simplify (+ 0 0) into 0
2.035 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
2.035 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.036 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.038 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
2.041 * [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)))))))
2.044 * [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)))))))
2.046 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.048 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.051 * [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
2.052 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
2.052 * [backup-simplify]: Simplify (- 0) into 0
2.052 * [backup-simplify]: Simplify (+ 0 0) into 0
2.053 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.054 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.056 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.056 * [taylor]: Taking taylor expansion of 0 in k
2.056 * [backup-simplify]: Simplify 0 into 0
2.056 * [backup-simplify]: Simplify 0 into 0
2.056 * [backup-simplify]: Simplify 0 into 0
2.057 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
2.058 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.060 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.060 * [backup-simplify]: Simplify (+ 0 0) into 0
2.060 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
2.061 * [backup-simplify]: Simplify (- 0) into 0
2.061 * [backup-simplify]: Simplify (+ 0 0) into 0
2.062 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.065 * [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)))))
2.068 * [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)))))
2.074 * [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)))))
2.075 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
2.075 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
2.075 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
2.075 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
2.075 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
2.075 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.075 * [taylor]: Taking taylor expansion of 1/2 in k
2.075 * [backup-simplify]: Simplify 1/2 into 1/2
2.075 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.075 * [taylor]: Taking taylor expansion of 1/2 in k
2.075 * [backup-simplify]: Simplify 1/2 into 1/2
2.075 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.075 * [taylor]: Taking taylor expansion of k in k
2.075 * [backup-simplify]: Simplify 0 into 0
2.075 * [backup-simplify]: Simplify 1 into 1
2.075 * [backup-simplify]: Simplify (/ 1 1) into 1
2.075 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
2.075 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
2.075 * [taylor]: Taking taylor expansion of 2 in k
2.075 * [backup-simplify]: Simplify 2 into 2
2.075 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.075 * [taylor]: Taking taylor expansion of PI in k
2.075 * [backup-simplify]: Simplify PI into PI
2.075 * [taylor]: Taking taylor expansion of n in k
2.075 * [backup-simplify]: Simplify n into n
2.075 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.076 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
2.076 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
2.076 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.076 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.076 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.076 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
2.077 * [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))))
2.077 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.077 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.077 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.077 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.077 * [taylor]: Taking taylor expansion of 1/2 in n
2.077 * [backup-simplify]: Simplify 1/2 into 1/2
2.077 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.077 * [taylor]: Taking taylor expansion of 1/2 in n
2.077 * [backup-simplify]: Simplify 1/2 into 1/2
2.077 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.077 * [taylor]: Taking taylor expansion of k in n
2.077 * [backup-simplify]: Simplify k into k
2.077 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.077 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.077 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.077 * [taylor]: Taking taylor expansion of 2 in n
2.077 * [backup-simplify]: Simplify 2 into 2
2.077 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.077 * [taylor]: Taking taylor expansion of PI in n
2.077 * [backup-simplify]: Simplify PI into PI
2.077 * [taylor]: Taking taylor expansion of n in n
2.077 * [backup-simplify]: Simplify 0 into 0
2.077 * [backup-simplify]: Simplify 1 into 1
2.077 * [backup-simplify]: Simplify (/ PI 1) into PI
2.078 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.078 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.078 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.078 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.079 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.080 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.080 * [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)))
2.081 * [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))))
2.081 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.081 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.081 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.081 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.081 * [taylor]: Taking taylor expansion of 1/2 in n
2.081 * [backup-simplify]: Simplify 1/2 into 1/2
2.081 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.081 * [taylor]: Taking taylor expansion of 1/2 in n
2.081 * [backup-simplify]: Simplify 1/2 into 1/2
2.081 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.081 * [taylor]: Taking taylor expansion of k in n
2.081 * [backup-simplify]: Simplify k into k
2.081 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.081 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.081 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.081 * [taylor]: Taking taylor expansion of 2 in n
2.081 * [backup-simplify]: Simplify 2 into 2
2.082 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.082 * [taylor]: Taking taylor expansion of PI in n
2.082 * [backup-simplify]: Simplify PI into PI
2.082 * [taylor]: Taking taylor expansion of n in n
2.082 * [backup-simplify]: Simplify 0 into 0
2.082 * [backup-simplify]: Simplify 1 into 1
2.082 * [backup-simplify]: Simplify (/ PI 1) into PI
2.083 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.084 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.084 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.084 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.084 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.086 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.087 * [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)))
2.088 * [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))))
2.088 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
2.089 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
2.089 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.089 * [taylor]: Taking taylor expansion of 1/2 in k
2.089 * [backup-simplify]: Simplify 1/2 into 1/2
2.089 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.089 * [taylor]: Taking taylor expansion of 1/2 in k
2.089 * [backup-simplify]: Simplify 1/2 into 1/2
2.089 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.089 * [taylor]: Taking taylor expansion of k in k
2.089 * [backup-simplify]: Simplify 0 into 0
2.089 * [backup-simplify]: Simplify 1 into 1
2.089 * [backup-simplify]: Simplify (/ 1 1) into 1
2.089 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
2.089 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.089 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.089 * [taylor]: Taking taylor expansion of 2 in k
2.089 * [backup-simplify]: Simplify 2 into 2
2.089 * [taylor]: Taking taylor expansion of PI in k
2.089 * [backup-simplify]: Simplify PI into PI
2.090 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.091 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.091 * [taylor]: Taking taylor expansion of (log n) in k
2.091 * [taylor]: Taking taylor expansion of n in k
2.091 * [backup-simplify]: Simplify n into n
2.091 * [backup-simplify]: Simplify (log n) into (log n)
2.092 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.092 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.093 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.093 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.094 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
2.095 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
2.096 * [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))))
2.098 * [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))))
2.099 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.100 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.102 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.102 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.102 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.103 * [backup-simplify]: Simplify (- 0) into 0
2.103 * [backup-simplify]: Simplify (+ 0 0) into 0
2.105 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.106 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
2.108 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.108 * [taylor]: Taking taylor expansion of 0 in k
2.109 * [backup-simplify]: Simplify 0 into 0
2.109 * [backup-simplify]: Simplify 0 into 0
2.109 * [backup-simplify]: Simplify 0 into 0
2.110 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.112 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.115 * [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
2.115 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.115 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.116 * [backup-simplify]: Simplify (- 0) into 0
2.116 * [backup-simplify]: Simplify (+ 0 0) into 0
2.117 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.118 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
2.119 * [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
2.119 * [taylor]: Taking taylor expansion of 0 in k
2.119 * [backup-simplify]: Simplify 0 into 0
2.119 * [backup-simplify]: Simplify 0 into 0
2.119 * [backup-simplify]: Simplify 0 into 0
2.119 * [backup-simplify]: Simplify 0 into 0
2.120 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.121 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.124 * [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
2.124 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.127 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
2.127 * [backup-simplify]: Simplify (- 0) into 0
2.128 * [backup-simplify]: Simplify (+ 0 0) into 0
2.129 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.130 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
2.132 * [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
2.132 * [taylor]: Taking taylor expansion of 0 in k
2.132 * [backup-simplify]: Simplify 0 into 0
2.132 * [backup-simplify]: Simplify 0 into 0
2.132 * [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)))))
2.133 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
2.133 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
2.133 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
2.133 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
2.133 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
2.133 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.133 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.133 * [taylor]: Taking taylor expansion of 1/2 in k
2.133 * [backup-simplify]: Simplify 1/2 into 1/2
2.133 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.133 * [taylor]: Taking taylor expansion of k in k
2.133 * [backup-simplify]: Simplify 0 into 0
2.133 * [backup-simplify]: Simplify 1 into 1
2.133 * [backup-simplify]: Simplify (/ 1 1) into 1
2.133 * [taylor]: Taking taylor expansion of 1/2 in k
2.133 * [backup-simplify]: Simplify 1/2 into 1/2
2.133 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
2.133 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
2.133 * [taylor]: Taking taylor expansion of -2 in k
2.133 * [backup-simplify]: Simplify -2 into -2
2.133 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.134 * [taylor]: Taking taylor expansion of PI in k
2.134 * [backup-simplify]: Simplify PI into PI
2.134 * [taylor]: Taking taylor expansion of n in k
2.134 * [backup-simplify]: Simplify n into n
2.134 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.134 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
2.134 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
2.134 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.134 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.134 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
2.134 * [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)))
2.134 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.134 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.135 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.135 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.135 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.135 * [taylor]: Taking taylor expansion of 1/2 in n
2.135 * [backup-simplify]: Simplify 1/2 into 1/2
2.135 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.135 * [taylor]: Taking taylor expansion of k in n
2.135 * [backup-simplify]: Simplify k into k
2.135 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.135 * [taylor]: Taking taylor expansion of 1/2 in n
2.135 * [backup-simplify]: Simplify 1/2 into 1/2
2.135 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.135 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.135 * [taylor]: Taking taylor expansion of -2 in n
2.135 * [backup-simplify]: Simplify -2 into -2
2.135 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.135 * [taylor]: Taking taylor expansion of PI in n
2.135 * [backup-simplify]: Simplify PI into PI
2.135 * [taylor]: Taking taylor expansion of n in n
2.135 * [backup-simplify]: Simplify 0 into 0
2.135 * [backup-simplify]: Simplify 1 into 1
2.135 * [backup-simplify]: Simplify (/ PI 1) into PI
2.135 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.136 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.136 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.136 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.137 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.138 * [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)))
2.139 * [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))))
2.139 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.139 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.139 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.139 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.139 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.139 * [taylor]: Taking taylor expansion of 1/2 in n
2.139 * [backup-simplify]: Simplify 1/2 into 1/2
2.139 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.139 * [taylor]: Taking taylor expansion of k in n
2.139 * [backup-simplify]: Simplify k into k
2.139 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.139 * [taylor]: Taking taylor expansion of 1/2 in n
2.139 * [backup-simplify]: Simplify 1/2 into 1/2
2.139 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.139 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.139 * [taylor]: Taking taylor expansion of -2 in n
2.139 * [backup-simplify]: Simplify -2 into -2
2.139 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.139 * [taylor]: Taking taylor expansion of PI in n
2.139 * [backup-simplify]: Simplify PI into PI
2.139 * [taylor]: Taking taylor expansion of n in n
2.139 * [backup-simplify]: Simplify 0 into 0
2.139 * [backup-simplify]: Simplify 1 into 1
2.139 * [backup-simplify]: Simplify (/ PI 1) into PI
2.140 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.140 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.140 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.141 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.141 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.142 * [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)))
2.143 * [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))))
2.143 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
2.143 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
2.143 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.143 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.143 * [taylor]: Taking taylor expansion of 1/2 in k
2.143 * [backup-simplify]: Simplify 1/2 into 1/2
2.143 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.143 * [taylor]: Taking taylor expansion of k in k
2.143 * [backup-simplify]: Simplify 0 into 0
2.143 * [backup-simplify]: Simplify 1 into 1
2.143 * [backup-simplify]: Simplify (/ 1 1) into 1
2.143 * [taylor]: Taking taylor expansion of 1/2 in k
2.143 * [backup-simplify]: Simplify 1/2 into 1/2
2.144 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
2.144 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
2.144 * [taylor]: Taking taylor expansion of (* -2 PI) in k
2.144 * [taylor]: Taking taylor expansion of -2 in k
2.144 * [backup-simplify]: Simplify -2 into -2
2.144 * [taylor]: Taking taylor expansion of PI in k
2.144 * [backup-simplify]: Simplify PI into PI
2.144 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.145 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.145 * [taylor]: Taking taylor expansion of (log n) in k
2.145 * [taylor]: Taking taylor expansion of n in k
2.145 * [backup-simplify]: Simplify n into n
2.145 * [backup-simplify]: Simplify (log n) into (log n)
2.145 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.145 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.145 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.146 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
2.147 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
2.148 * [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))))
2.148 * [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))))
2.149 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.150 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.151 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
2.151 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.151 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.151 * [backup-simplify]: Simplify (+ 0 0) into 0
2.152 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.153 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
2.154 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.154 * [taylor]: Taking taylor expansion of 0 in k
2.154 * [backup-simplify]: Simplify 0 into 0
2.154 * [backup-simplify]: Simplify 0 into 0
2.154 * [backup-simplify]: Simplify 0 into 0
2.155 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.156 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.158 * [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
2.158 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.158 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.159 * [backup-simplify]: Simplify (+ 0 0) into 0
2.160 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.161 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
2.163 * [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
2.163 * [taylor]: Taking taylor expansion of 0 in k
2.163 * [backup-simplify]: Simplify 0 into 0
2.163 * [backup-simplify]: Simplify 0 into 0
2.163 * [backup-simplify]: Simplify 0 into 0
2.163 * [backup-simplify]: Simplify 0 into 0
2.164 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.165 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.168 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
2.169 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.170 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
2.170 * [backup-simplify]: Simplify (+ 0 0) into 0
2.171 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.172 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
2.174 * [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
2.174 * [taylor]: Taking taylor expansion of 0 in k
2.174 * [backup-simplify]: Simplify 0 into 0
2.174 * [backup-simplify]: Simplify 0 into 0
2.175 * [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)))))
2.175 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
2.176 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
2.176 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
2.176 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.176 * [taylor]: Taking taylor expansion of 2 in n
2.176 * [backup-simplify]: Simplify 2 into 2
2.176 * [taylor]: Taking taylor expansion of (* n PI) in n
2.176 * [taylor]: Taking taylor expansion of n in n
2.176 * [backup-simplify]: Simplify 0 into 0
2.176 * [backup-simplify]: Simplify 1 into 1
2.176 * [taylor]: Taking taylor expansion of PI in n
2.176 * [backup-simplify]: Simplify PI into PI
2.176 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.176 * [taylor]: Taking taylor expansion of 2 in n
2.176 * [backup-simplify]: Simplify 2 into 2
2.176 * [taylor]: Taking taylor expansion of (* n PI) in n
2.176 * [taylor]: Taking taylor expansion of n in n
2.176 * [backup-simplify]: Simplify 0 into 0
2.176 * [backup-simplify]: Simplify 1 into 1
2.176 * [taylor]: Taking taylor expansion of PI in n
2.176 * [backup-simplify]: Simplify PI into PI
2.177 * [backup-simplify]: Simplify (* 0 PI) into 0
2.177 * [backup-simplify]: Simplify (* 2 0) into 0
2.177 * [backup-simplify]: Simplify 0 into 0
2.178 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.179 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.179 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.180 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.181 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.181 * [backup-simplify]: Simplify 0 into 0
2.182 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.182 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.182 * [backup-simplify]: Simplify 0 into 0
2.183 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.184 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.184 * [backup-simplify]: Simplify 0 into 0
2.185 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.186 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
2.186 * [backup-simplify]: Simplify 0 into 0
2.187 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.188 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
2.188 * [backup-simplify]: Simplify 0 into 0
2.189 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
2.190 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
2.190 * [backup-simplify]: Simplify 0 into 0
2.191 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
2.191 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
2.191 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
2.191 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.191 * [taylor]: Taking taylor expansion of 2 in n
2.191 * [backup-simplify]: Simplify 2 into 2
2.191 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.191 * [taylor]: Taking taylor expansion of PI in n
2.191 * [backup-simplify]: Simplify PI into PI
2.191 * [taylor]: Taking taylor expansion of n in n
2.191 * [backup-simplify]: Simplify 0 into 0
2.191 * [backup-simplify]: Simplify 1 into 1
2.192 * [backup-simplify]: Simplify (/ PI 1) into PI
2.192 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.192 * [taylor]: Taking taylor expansion of 2 in n
2.192 * [backup-simplify]: Simplify 2 into 2
2.192 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.192 * [taylor]: Taking taylor expansion of PI in n
2.192 * [backup-simplify]: Simplify PI into PI
2.192 * [taylor]: Taking taylor expansion of n in n
2.192 * [backup-simplify]: Simplify 0 into 0
2.192 * [backup-simplify]: Simplify 1 into 1
2.192 * [backup-simplify]: Simplify (/ PI 1) into PI
2.192 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.193 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.193 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.194 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.194 * [backup-simplify]: Simplify 0 into 0
2.195 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.197 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.197 * [backup-simplify]: Simplify 0 into 0
2.198 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.199 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.199 * [backup-simplify]: Simplify 0 into 0
2.200 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.202 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.202 * [backup-simplify]: Simplify 0 into 0
2.203 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.205 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.205 * [backup-simplify]: Simplify 0 into 0
2.207 * [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
2.208 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.209 * [backup-simplify]: Simplify 0 into 0
2.209 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
2.210 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
2.210 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
2.210 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.210 * [taylor]: Taking taylor expansion of -2 in n
2.210 * [backup-simplify]: Simplify -2 into -2
2.210 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.210 * [taylor]: Taking taylor expansion of PI in n
2.210 * [backup-simplify]: Simplify PI into PI
2.210 * [taylor]: Taking taylor expansion of n in n
2.210 * [backup-simplify]: Simplify 0 into 0
2.210 * [backup-simplify]: Simplify 1 into 1
2.211 * [backup-simplify]: Simplify (/ PI 1) into PI
2.211 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.211 * [taylor]: Taking taylor expansion of -2 in n
2.211 * [backup-simplify]: Simplify -2 into -2
2.211 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.211 * [taylor]: Taking taylor expansion of PI in n
2.211 * [backup-simplify]: Simplify PI into PI
2.211 * [taylor]: Taking taylor expansion of n in n
2.211 * [backup-simplify]: Simplify 0 into 0
2.211 * [backup-simplify]: Simplify 1 into 1
2.212 * [backup-simplify]: Simplify (/ PI 1) into PI
2.212 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.213 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.214 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.215 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.215 * [backup-simplify]: Simplify 0 into 0
2.216 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.217 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.217 * [backup-simplify]: Simplify 0 into 0
2.219 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.220 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.220 * [backup-simplify]: Simplify 0 into 0
2.221 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.223 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.223 * [backup-simplify]: Simplify 0 into 0
2.224 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.226 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.226 * [backup-simplify]: Simplify 0 into 0
2.228 * [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
2.229 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.230 * [backup-simplify]: Simplify 0 into 0
2.230 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
2.230 * * * * [progress]: [ 3 / 3 ] generating series at (2)
2.231 * [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))))
2.231 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
2.231 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
2.231 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.231 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.231 * [taylor]: Taking taylor expansion of k in k
2.231 * [backup-simplify]: Simplify 0 into 0
2.231 * [backup-simplify]: Simplify 1 into 1
2.232 * [backup-simplify]: Simplify (/ 1 1) into 1
2.232 * [backup-simplify]: Simplify (sqrt 0) into 0
2.234 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.234 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
2.234 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
2.234 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
2.234 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.234 * [taylor]: Taking taylor expansion of 1/2 in k
2.234 * [backup-simplify]: Simplify 1/2 into 1/2
2.234 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.234 * [taylor]: Taking taylor expansion of 1/2 in k
2.234 * [backup-simplify]: Simplify 1/2 into 1/2
2.234 * [taylor]: Taking taylor expansion of k in k
2.234 * [backup-simplify]: Simplify 0 into 0
2.234 * [backup-simplify]: Simplify 1 into 1
2.234 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
2.234 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
2.234 * [taylor]: Taking taylor expansion of 2 in k
2.234 * [backup-simplify]: Simplify 2 into 2
2.234 * [taylor]: Taking taylor expansion of (* n PI) in k
2.234 * [taylor]: Taking taylor expansion of n in k
2.235 * [backup-simplify]: Simplify n into n
2.235 * [taylor]: Taking taylor expansion of PI in k
2.235 * [backup-simplify]: Simplify PI into PI
2.235 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.235 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
2.235 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
2.236 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.236 * [backup-simplify]: Simplify (- 0) into 0
2.237 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.237 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
2.237 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
2.237 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
2.237 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.237 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.237 * [taylor]: Taking taylor expansion of k in n
2.237 * [backup-simplify]: Simplify k into k
2.237 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.237 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.238 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.238 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.238 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.238 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.238 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.238 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.238 * [taylor]: Taking taylor expansion of 1/2 in n
2.238 * [backup-simplify]: Simplify 1/2 into 1/2
2.238 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.238 * [taylor]: Taking taylor expansion of 1/2 in n
2.238 * [backup-simplify]: Simplify 1/2 into 1/2
2.238 * [taylor]: Taking taylor expansion of k in n
2.238 * [backup-simplify]: Simplify k into k
2.238 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.238 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.238 * [taylor]: Taking taylor expansion of 2 in n
2.238 * [backup-simplify]: Simplify 2 into 2
2.238 * [taylor]: Taking taylor expansion of (* n PI) in n
2.238 * [taylor]: Taking taylor expansion of n in n
2.238 * [backup-simplify]: Simplify 0 into 0
2.238 * [backup-simplify]: Simplify 1 into 1
2.238 * [taylor]: Taking taylor expansion of PI in n
2.238 * [backup-simplify]: Simplify PI into PI
2.239 * [backup-simplify]: Simplify (* 0 PI) into 0
2.239 * [backup-simplify]: Simplify (* 2 0) into 0
2.244 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.246 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.247 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.248 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.248 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.248 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.249 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.250 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.252 * [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)))))
2.252 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
2.252 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.252 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.252 * [taylor]: Taking taylor expansion of k in n
2.252 * [backup-simplify]: Simplify k into k
2.252 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.252 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.252 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.252 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.252 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.252 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.252 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.252 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.252 * [taylor]: Taking taylor expansion of 1/2 in n
2.252 * [backup-simplify]: Simplify 1/2 into 1/2
2.252 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.252 * [taylor]: Taking taylor expansion of 1/2 in n
2.252 * [backup-simplify]: Simplify 1/2 into 1/2
2.252 * [taylor]: Taking taylor expansion of k in n
2.253 * [backup-simplify]: Simplify k into k
2.253 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.253 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.253 * [taylor]: Taking taylor expansion of 2 in n
2.253 * [backup-simplify]: Simplify 2 into 2
2.253 * [taylor]: Taking taylor expansion of (* n PI) in n
2.253 * [taylor]: Taking taylor expansion of n in n
2.253 * [backup-simplify]: Simplify 0 into 0
2.253 * [backup-simplify]: Simplify 1 into 1
2.253 * [taylor]: Taking taylor expansion of PI in n
2.253 * [backup-simplify]: Simplify PI into PI
2.253 * [backup-simplify]: Simplify (* 0 PI) into 0
2.254 * [backup-simplify]: Simplify (* 2 0) into 0
2.255 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.257 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.258 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.258 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.258 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.258 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.260 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.261 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.262 * [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)))))
2.264 * [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)))
2.264 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
2.264 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
2.264 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
2.264 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.264 * [taylor]: Taking taylor expansion of 1/2 in k
2.264 * [backup-simplify]: Simplify 1/2 into 1/2
2.264 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.264 * [taylor]: Taking taylor expansion of 1/2 in k
2.264 * [backup-simplify]: Simplify 1/2 into 1/2
2.264 * [taylor]: Taking taylor expansion of k in k
2.264 * [backup-simplify]: Simplify 0 into 0
2.264 * [backup-simplify]: Simplify 1 into 1
2.264 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
2.264 * [taylor]: Taking taylor expansion of (log n) in k
2.264 * [taylor]: Taking taylor expansion of n in k
2.264 * [backup-simplify]: Simplify n into n
2.264 * [backup-simplify]: Simplify (log n) into (log n)
2.264 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.264 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.264 * [taylor]: Taking taylor expansion of 2 in k
2.264 * [backup-simplify]: Simplify 2 into 2
2.264 * [taylor]: Taking taylor expansion of PI in k
2.264 * [backup-simplify]: Simplify PI into PI
2.265 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.266 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.266 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.267 * [backup-simplify]: Simplify (- 0) into 0
2.267 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.268 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.269 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
2.270 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
2.270 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.270 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.270 * [taylor]: Taking taylor expansion of k in k
2.270 * [backup-simplify]: Simplify 0 into 0
2.271 * [backup-simplify]: Simplify 1 into 1
2.271 * [backup-simplify]: Simplify (/ 1 1) into 1
2.271 * [backup-simplify]: Simplify (sqrt 0) into 0
2.273 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.274 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
2.274 * [backup-simplify]: Simplify 0 into 0
2.274 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.275 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.276 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.276 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
2.277 * [backup-simplify]: Simplify (- 0) into 0
2.277 * [backup-simplify]: Simplify (+ 0 0) into 0
2.278 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.278 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
2.280 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.280 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
2.280 * [taylor]: Taking taylor expansion of 0 in k
2.280 * [backup-simplify]: Simplify 0 into 0
2.281 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
2.281 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.283 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.283 * [backup-simplify]: Simplify (+ 0 0) into 0
2.283 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
2.283 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.284 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.285 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
2.287 * [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)))))))
2.289 * [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)))))))
2.290 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.291 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.292 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.293 * [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
2.294 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
2.294 * [backup-simplify]: Simplify (- 0) into 0
2.294 * [backup-simplify]: Simplify (+ 0 0) into 0
2.295 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.296 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.298 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.298 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.298 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
2.299 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
2.299 * [taylor]: Taking taylor expansion of 0 in k
2.299 * [backup-simplify]: Simplify 0 into 0
2.299 * [backup-simplify]: Simplify 0 into 0
2.300 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
2.302 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.303 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
2.303 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.305 * [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
2.306 * [backup-simplify]: Simplify (+ 0 0) into 0
2.306 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
2.306 * [backup-simplify]: Simplify (- 0) into 0
2.307 * [backup-simplify]: Simplify (+ 0 0) into 0
2.308 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.311 * [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)))))
2.317 * [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))))))))
2.320 * [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))))))))
2.321 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.322 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.329 * [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
2.330 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
2.330 * [backup-simplify]: Simplify (- 0) into 0
2.331 * [backup-simplify]: Simplify (+ 0 0) into 0
2.332 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.334 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.337 * [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
2.337 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.338 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
2.340 * [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
2.340 * [taylor]: Taking taylor expansion of 0 in k
2.340 * [backup-simplify]: Simplify 0 into 0
2.341 * [backup-simplify]: Simplify 0 into 0
2.341 * [backup-simplify]: Simplify 0 into 0
2.342 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.346 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.349 * [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
2.350 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.359 * [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
2.359 * [backup-simplify]: Simplify (+ 0 0) into 0
2.361 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
2.361 * [backup-simplify]: Simplify (- 0) into 0
2.362 * [backup-simplify]: Simplify (+ 0 0) into 0
2.364 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.371 * [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)))))))
2.391 * [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))))))))))))))
2.399 * [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))))))))))))))
2.411 * [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))))))))))))))))))))))
2.411 * [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)))))
2.411 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
2.411 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
2.411 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.411 * [taylor]: Taking taylor expansion of k in k
2.411 * [backup-simplify]: Simplify 0 into 0
2.411 * [backup-simplify]: Simplify 1 into 1
2.412 * [backup-simplify]: Simplify (sqrt 0) into 0
2.413 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.413 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
2.413 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
2.413 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
2.413 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.413 * [taylor]: Taking taylor expansion of 1/2 in k
2.413 * [backup-simplify]: Simplify 1/2 into 1/2
2.413 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.413 * [taylor]: Taking taylor expansion of 1/2 in k
2.413 * [backup-simplify]: Simplify 1/2 into 1/2
2.413 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.413 * [taylor]: Taking taylor expansion of k in k
2.413 * [backup-simplify]: Simplify 0 into 0
2.413 * [backup-simplify]: Simplify 1 into 1
2.413 * [backup-simplify]: Simplify (/ 1 1) into 1
2.413 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
2.413 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
2.413 * [taylor]: Taking taylor expansion of 2 in k
2.413 * [backup-simplify]: Simplify 2 into 2
2.413 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.413 * [taylor]: Taking taylor expansion of PI in k
2.413 * [backup-simplify]: Simplify PI into PI
2.413 * [taylor]: Taking taylor expansion of n in k
2.413 * [backup-simplify]: Simplify n into n
2.413 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.414 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
2.414 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
2.414 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.414 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.414 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.414 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
2.415 * [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))))
2.415 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
2.415 * [taylor]: Taking taylor expansion of (sqrt 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 (sqrt k) into (sqrt k)
2.415 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.415 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.415 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.415 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.415 * [taylor]: Taking taylor expansion of (- 1/2 (* 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 (* 1/2 (/ 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 (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
2.415 * [backup-simplify]: Simplify 1 into 1
2.415 * [backup-simplify]: Simplify (/ PI 1) into PI
2.416 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.416 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.417 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.417 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.417 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.418 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.418 * [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)))
2.419 * [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))))
2.419 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
2.419 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.419 * [taylor]: Taking taylor expansion of k in n
2.419 * [backup-simplify]: Simplify k into k
2.419 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.419 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.419 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.419 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.419 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.419 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.419 * [taylor]: Taking taylor expansion of 1/2 in n
2.419 * [backup-simplify]: Simplify 1/2 into 1/2
2.419 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.419 * [taylor]: Taking taylor expansion of 1/2 in n
2.419 * [backup-simplify]: Simplify 1/2 into 1/2
2.419 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.419 * [taylor]: Taking taylor expansion of k in n
2.419 * [backup-simplify]: Simplify k into k
2.420 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.420 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.420 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.420 * [taylor]: Taking taylor expansion of 2 in n
2.420 * [backup-simplify]: Simplify 2 into 2
2.420 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.420 * [taylor]: Taking taylor expansion of PI in n
2.420 * [backup-simplify]: Simplify PI into PI
2.420 * [taylor]: Taking taylor expansion of n in n
2.420 * [backup-simplify]: Simplify 0 into 0
2.420 * [backup-simplify]: Simplify 1 into 1
2.420 * [backup-simplify]: Simplify (/ PI 1) into PI
2.420 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.421 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.421 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.421 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.421 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.422 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.423 * [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)))
2.424 * [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))))
2.425 * [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))
2.425 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
2.425 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
2.425 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
2.425 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.425 * [taylor]: Taking taylor expansion of 1/2 in k
2.425 * [backup-simplify]: Simplify 1/2 into 1/2
2.425 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.425 * [taylor]: Taking taylor expansion of 1/2 in k
2.425 * [backup-simplify]: Simplify 1/2 into 1/2
2.425 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.425 * [taylor]: Taking taylor expansion of k in k
2.425 * [backup-simplify]: Simplify 0 into 0
2.425 * [backup-simplify]: Simplify 1 into 1
2.425 * [backup-simplify]: Simplify (/ 1 1) into 1
2.425 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
2.425 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.425 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.425 * [taylor]: Taking taylor expansion of 2 in k
2.425 * [backup-simplify]: Simplify 2 into 2
2.425 * [taylor]: Taking taylor expansion of PI in k
2.425 * [backup-simplify]: Simplify PI into PI
2.426 * [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) into -1/2
2.427 * [backup-simplify]: Simplify (+ 0 -1/2) 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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.430 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.430 * [taylor]: Taking taylor expansion of k in k
2.430 * [backup-simplify]: Simplify 0 into 0
2.430 * [backup-simplify]: Simplify 1 into 1
2.430 * [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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
2.433 * [backup-simplify]: Simplify 0 into 0
2.434 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.435 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.437 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.437 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.438 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.438 * [backup-simplify]: Simplify (- 0) into 0
2.439 * [backup-simplify]: Simplify (+ 0 0) into 0
2.440 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.442 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
2.444 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.445 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
2.445 * [taylor]: Taking taylor expansion of 0 in k
2.445 * [backup-simplify]: Simplify 0 into 0
2.445 * [backup-simplify]: Simplify 0 into 0
2.447 * [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))))))
2.449 * [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))))))
2.450 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.451 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.455 * [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
2.455 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.456 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.456 * [backup-simplify]: Simplify (- 0) into 0
2.457 * [backup-simplify]: Simplify (+ 0 0) into 0
2.459 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.460 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
2.463 * [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
2.463 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
2.465 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
2.465 * [taylor]: Taking taylor expansion of 0 in k
2.465 * [backup-simplify]: Simplify 0 into 0
2.465 * [backup-simplify]: Simplify 0 into 0
2.465 * [backup-simplify]: Simplify 0 into 0
2.468 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.470 * [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))))))
2.472 * [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))))))
2.473 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.474 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.483 * [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
2.483 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.485 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
2.485 * [backup-simplify]: Simplify (- 0) into 0
2.486 * [backup-simplify]: Simplify (+ 0 0) into 0
2.487 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.489 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
2.492 * [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
2.493 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
2.495 * [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
2.495 * [taylor]: Taking taylor expansion of 0 in k
2.495 * [backup-simplify]: Simplify 0 into 0
2.495 * [backup-simplify]: Simplify 0 into 0
2.495 * [backup-simplify]: Simplify 0 into 0
2.496 * [backup-simplify]: Simplify 0 into 0
2.500 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.502 * [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))))))
2.504 * [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))))))
2.508 * [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))))))))
2.509 * [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)))
2.509 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
2.509 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
2.509 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
2.509 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
2.509 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
2.509 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.509 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.509 * [taylor]: Taking taylor expansion of 1/2 in k
2.509 * [backup-simplify]: Simplify 1/2 into 1/2
2.509 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.509 * [taylor]: Taking taylor expansion of k in k
2.509 * [backup-simplify]: Simplify 0 into 0
2.509 * [backup-simplify]: Simplify 1 into 1
2.510 * [backup-simplify]: Simplify (/ 1 1) into 1
2.510 * [taylor]: Taking taylor expansion of 1/2 in k
2.510 * [backup-simplify]: Simplify 1/2 into 1/2
2.510 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
2.510 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
2.510 * [taylor]: Taking taylor expansion of -2 in k
2.510 * [backup-simplify]: Simplify -2 into -2
2.510 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.510 * [taylor]: Taking taylor expansion of PI in k
2.510 * [backup-simplify]: Simplify PI into PI
2.510 * [taylor]: Taking taylor expansion of n in k
2.510 * [backup-simplify]: Simplify n into n
2.510 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.510 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
2.510 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
2.511 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.511 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.511 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
2.511 * [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)))
2.511 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.511 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.512 * [taylor]: Taking taylor expansion of -1 in k
2.512 * [backup-simplify]: Simplify -1 into -1
2.512 * [taylor]: Taking taylor expansion of k in k
2.512 * [backup-simplify]: Simplify 0 into 0
2.512 * [backup-simplify]: Simplify 1 into 1
2.512 * [backup-simplify]: Simplify (/ -1 1) into -1
2.512 * [backup-simplify]: Simplify (sqrt 0) into 0
2.514 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.514 * [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))))
2.514 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
2.514 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.514 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.514 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.514 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.514 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.514 * [taylor]: Taking taylor expansion of 1/2 in n
2.514 * [backup-simplify]: Simplify 1/2 into 1/2
2.514 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.514 * [taylor]: Taking taylor expansion of k in n
2.514 * [backup-simplify]: Simplify k into k
2.514 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.514 * [taylor]: Taking taylor expansion of 1/2 in n
2.514 * [backup-simplify]: Simplify 1/2 into 1/2
2.514 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.514 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.514 * [taylor]: Taking taylor expansion of -2 in n
2.514 * [backup-simplify]: Simplify -2 into -2
2.514 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.514 * [taylor]: Taking taylor expansion of PI in n
2.515 * [backup-simplify]: Simplify PI into PI
2.515 * [taylor]: Taking taylor expansion of n in n
2.515 * [backup-simplify]: Simplify 0 into 0
2.515 * [backup-simplify]: Simplify 1 into 1
2.515 * [backup-simplify]: Simplify (/ PI 1) into PI
2.516 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.517 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.517 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.517 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.518 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.519 * [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)))
2.521 * [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))))
2.521 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.521 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.521 * [taylor]: Taking taylor expansion of -1 in n
2.521 * [backup-simplify]: Simplify -1 into -1
2.521 * [taylor]: Taking taylor expansion of k in n
2.521 * [backup-simplify]: Simplify k into k
2.521 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.521 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.521 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.522 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.523 * [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)))
2.523 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
2.523 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.523 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.523 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.523 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.523 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.523 * [taylor]: Taking taylor expansion of 1/2 in n
2.523 * [backup-simplify]: Simplify 1/2 into 1/2
2.523 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.523 * [taylor]: Taking taylor expansion of k in n
2.523 * [backup-simplify]: Simplify k into k
2.523 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.523 * [taylor]: Taking taylor expansion of 1/2 in n
2.523 * [backup-simplify]: Simplify 1/2 into 1/2
2.523 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.523 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.523 * [taylor]: Taking taylor expansion of -2 in n
2.523 * [backup-simplify]: Simplify -2 into -2
2.523 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.523 * [taylor]: Taking taylor expansion of PI in n
2.524 * [backup-simplify]: Simplify PI into PI
2.524 * [taylor]: Taking taylor expansion of n in n
2.524 * [backup-simplify]: Simplify 0 into 0
2.524 * [backup-simplify]: Simplify 1 into 1
2.524 * [backup-simplify]: Simplify (/ PI 1) into PI
2.525 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.526 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.526 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.526 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.527 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.529 * [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)))
2.530 * [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))))
2.530 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.530 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.530 * [taylor]: Taking taylor expansion of -1 in n
2.530 * [backup-simplify]: Simplify -1 into -1
2.530 * [taylor]: Taking taylor expansion of k in n
2.530 * [backup-simplify]: Simplify k into k
2.530 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.530 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.530 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.530 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.532 * [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)))
2.532 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
2.532 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
2.532 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
2.532 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.532 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.532 * [taylor]: Taking taylor expansion of 1/2 in k
2.532 * [backup-simplify]: Simplify 1/2 into 1/2
2.532 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.532 * [taylor]: Taking taylor expansion of k in k
2.532 * [backup-simplify]: Simplify 0 into 0
2.532 * [backup-simplify]: Simplify 1 into 1
2.532 * [backup-simplify]: Simplify (/ 1 1) into 1
2.533 * [taylor]: Taking taylor expansion of 1/2 in k
2.533 * [backup-simplify]: Simplify 1/2 into 1/2
2.533 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
2.533 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
2.533 * [taylor]: Taking taylor expansion of (* -2 PI) in k
2.533 * [taylor]: Taking taylor expansion of -2 in k
2.533 * [backup-simplify]: Simplify -2 into -2
2.533 * [taylor]: Taking taylor expansion of PI in k
2.533 * [backup-simplify]: Simplify PI into PI
2.533 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.534 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.534 * [taylor]: Taking taylor expansion of (log n) in k
2.534 * [taylor]: Taking taylor expansion of n in k
2.534 * [backup-simplify]: Simplify n into n
2.534 * [backup-simplify]: Simplify (log n) into (log n)
2.535 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.535 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.535 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.536 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
2.538 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
2.539 * [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))))
2.539 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.539 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.539 * [taylor]: Taking taylor expansion of -1 in k
2.539 * [backup-simplify]: Simplify -1 into -1
2.539 * [taylor]: Taking taylor expansion of k in k
2.539 * [backup-simplify]: Simplify 0 into 0
2.539 * [backup-simplify]: Simplify 1 into 1
2.539 * [backup-simplify]: Simplify (/ -1 1) into -1
2.540 * [backup-simplify]: Simplify (sqrt 0) into 0
2.541 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.543 * [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)))))
2.544 * [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)))))
2.545 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.545 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.547 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
2.547 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.547 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.547 * [backup-simplify]: Simplify (+ 0 0) into 0
2.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.549 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
2.550 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.551 * [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
2.551 * [taylor]: Taking taylor expansion of 0 in k
2.551 * [backup-simplify]: Simplify 0 into 0
2.551 * [backup-simplify]: Simplify 0 into 0
2.552 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
2.553 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.555 * [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))))))
2.556 * [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))))))
2.556 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.557 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.559 * [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
2.559 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.560 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.560 * [backup-simplify]: Simplify (+ 0 0) into 0
2.561 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.562 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
2.564 * [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
2.564 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.565 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
2.566 * [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
2.566 * [taylor]: Taking taylor expansion of 0 in k
2.566 * [backup-simplify]: Simplify 0 into 0
2.566 * [backup-simplify]: Simplify 0 into 0
2.566 * [backup-simplify]: Simplify 0 into 0
2.567 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.569 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.572 * [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))))))
2.573 * [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))))))
2.576 * [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)))))))))))
2.576 * * * [progress]: simplifying candidates
2.577 * * * * [progress]: [ 1 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.577 * * * * [progress]: [ 2 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.577 * * * * [progress]: [ 3 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.577 * * * * [progress]: [ 4 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.577 * * * * [progress]: [ 5 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.577 * * * * [progress]: [ 6 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.577 * * * * [progress]: [ 7 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.577 * * * * [progress]: [ 8 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))>
2.577 * * * * [progress]: [ 9 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
2.577 * * * * [progress]: [ 10 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
2.577 * * * * [progress]: [ 11 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.577 * * * * [progress]: [ 12 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))>
2.577 * * * * [progress]: [ 13 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))>
2.577 * * * * [progress]: [ 14 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.577 * * * * [progress]: [ 15 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt k)))>
2.577 * * * * [progress]: [ 16 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt k)))>
2.578 * * * * [progress]: [ 17 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt k)))>
2.578 * * * * [progress]: [ 18 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
2.578 * * * * [progress]: [ 19 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.578 * * * * [progress]: [ 20 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.578 * * * * [progress]: [ 21 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.578 * * * * [progress]: [ 22 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.578 * * * * [progress]: [ 23 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.578 * * * * [progress]: [ 24 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
2.578 * * * * [progress]: [ 25 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
2.578 * * * * [progress]: [ 26 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.578 * * * * [progress]: [ 27 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.578 * * * * [progress]: [ 28 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.578 * * * * [progress]: [ 29 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.578 * * * * [progress]: [ 30 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.578 * * * * [progress]: [ 31 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.578 * * * * [progress]: [ 32 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.578 * * * * [progress]: [ 33 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 34 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 35 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 36 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 37 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 38 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 39 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 40 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 41 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 42 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 43 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 44 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 45 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))>
2.579 * * * * [progress]: [ 46 / 127 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) 1))>
2.579 * * * * [progress]: [ 47 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.579 * * * * [progress]: [ 48 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.579 * * * * [progress]: [ 49 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.579 * * * * [progress]: [ 50 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.580 * * * * [progress]: [ 51 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
2.580 * * * * [progress]: [ 52 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.580 * * * * [progress]: [ 53 / 127 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.580 * * * * [progress]: [ 54 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
2.580 * * * * [progress]: [ 55 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.580 * * * * [progress]: [ 56 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.580 * * * * [progress]: [ 57 / 127 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.580 * * * * [progress]: [ 58 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (- (sqrt k))))>
2.580 * * * * [progress]: [ 59 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
2.580 * * * * [progress]: [ 60 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))))>
2.580 * * * * [progress]: [ 61 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.580 * * * * [progress]: [ 62 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1)) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.580 * * * * [progress]: [ 63 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.580 * * * * [progress]: [ 64 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.580 * * * * [progress]: [ 65 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
2.580 * * * * [progress]: [ 66 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))))>
2.580 * * * * [progress]: [ 67 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.581 * * * * [progress]: [ 68 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1)) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.581 * * * * [progress]: [ 69 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.581 * * * * [progress]: [ 70 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.581 * * * * [progress]: [ 71 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
2.581 * * * * [progress]: [ 72 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
2.581 * * * * [progress]: [ 73 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.581 * * * * [progress]: [ 74 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.581 * * * * [progress]: [ 75 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.581 * * * * [progress]: [ 76 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) 1) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.581 * * * * [progress]: [ 77 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
2.581 * * * * [progress]: [ 78 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
2.581 * * * * [progress]: [ 79 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.581 * * * * [progress]: [ 80 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt 1)) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.581 * * * * [progress]: [ 81 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.581 * * * * [progress]: [ 82 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.582 * * * * [progress]: [ 83 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
2.582 * * * * [progress]: [ 84 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
2.582 * * * * [progress]: [ 85 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.582 * * * * [progress]: [ 86 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.582 * * * * [progress]: [ 87 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.582 * * * * [progress]: [ 88 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.582 * * * * [progress]: [ 89 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
2.582 * * * * [progress]: [ 90 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
2.582 * * * * [progress]: [ 91 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.582 * * * * [progress]: [ 92 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
2.582 * * * * [progress]: [ 93 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.582 * * * * [progress]: [ 94 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
2.582 * * * * [progress]: [ 95 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))>
2.582 * * * * [progress]: [ 96 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))>
2.582 * * * * [progress]: [ 97 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
2.582 * * * * [progress]: [ 98 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
2.583 * * * * [progress]: [ 99 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
2.583 * * * * [progress]: [ 100 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
2.583 * * * * [progress]: [ 101 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
2.583 * * * * [progress]: [ 102 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
2.583 * * * * [progress]: [ 103 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
2.583 * * * * [progress]: [ 104 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
2.583 * * * * [progress]: [ 105 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
2.583 * * * * [progress]: [ 106 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.583 * * * * [progress]: [ 107 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k)))>
2.583 * * * * [progress]: [ 108 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.583 * * * * [progress]: [ 109 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
2.583 * * * * [progress]: [ 110 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
2.583 * * * * [progress]: [ 111 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
2.583 * * * * [progress]: [ 112 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
2.583 * * * * [progress]: [ 113 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
2.583 * * * * [progress]: [ 114 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
2.583 * * * * [progress]: [ 115 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
2.583 * * * * [progress]: [ 116 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
2.584 * * * * [progress]: [ 117 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))>
2.584 * * * * [progress]: [ 118 / 127 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.584 * * * * [progress]: [ 119 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
2.584 * * * * [progress]: [ 120 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
2.584 * * * * [progress]: [ 121 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
2.584 * * * * [progress]: [ 122 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.584 * * * * [progress]: [ 123 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.584 * * * * [progress]: [ 124 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.584 * * * * [progress]: [ 125 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
2.584 * * * * [progress]: [ 126 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
2.584 * * * * [progress]: [ 127 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
2.587 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (log (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (exp (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (* (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) 1)
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) 1)
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))
  (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) 1)
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt 1))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) 1)
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1)
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1)
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1)
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))
  (real->posit16 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
2.591 * * [simplify]: iteration 1: (267 enodes)
2.662 * * [simplify]: iteration 2: (644 enodes)
3.178 * * [simplify]: Extracting #0: cost 97 inf + 0
3.179 * * [simplify]: Extracting #1: cost 372 inf + 1
3.184 * * [simplify]: Extracting #2: cost 513 inf + 18891
3.205 * * [simplify]: Extracting #3: cost 411 inf + 87524
3.242 * * [simplify]: Extracting #4: cost 283 inf + 135704
3.293 * * [simplify]: Extracting #5: cost 156 inf + 192203
3.325 * * [simplify]: Extracting #6: cost 96 inf + 227990
3.374 * * [simplify]: Extracting #7: cost 25 inf + 269385
3.472 * * [simplify]: Extracting #8: cost 0 inf + 290477
3.574 * * [simplify]: Extracting #9: cost 0 inf + 287997
3.650 * * [simplify]: Extracting #10: cost 0 inf + 287757
3.727 * [simplify]: Simplified to:
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2))))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* PI 2) n) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* PI 2) n)
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (- (/ k 2)))
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* PI n)) (exp (* PI n)))
  (* n (* (* n n) (* PI (* (* PI PI) 8))))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* (cbrt n) (* PI 2))
  (* (sqrt n) (* PI 2))
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (exp (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ k (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))))
  (* (cbrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (* (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)) (* (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* (* PI 2) n)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* PI 2) n))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* PI 2) n))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* (* PI 2) n)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* PI 2) n))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* PI 2) n))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))
  (/ (/ (pow n (- 1/2 (/ k 2))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow n (- 1/2 (/ k 2)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow n (- 1/2 (/ k 2)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt k))
  (* (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (fabs (cbrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (fabs (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/2 (/ k 2)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/2 (/ k 2)))
  (/ (sqrt k) (pow (* (* PI 2) n) (- (/ k 2))))
  (/ (sqrt k) (pow (* (* PI 2) n) (- (/ k 2))))
  (/ (sqrt k) (pow (* PI 2) (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (* (sqrt k) (pow (* (* PI 2) n) (/ k 2)))
  (real->posit16 (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (+ (* -1/2 (* k (+ (* (sqrt (* (* PI 2) n)) (log n)) (* (sqrt (* (* PI 2) n)) (log (* PI 2)))))) (+ (* (* (* (log n) k) (* (log n) k)) (* (sqrt (* (* PI 2) n)) 1/8)) (+ (+ (* (* (log (* PI 2)) (* (* (sqrt (* (* PI 2) n)) (* k k)) (log (* PI 2)))) 1/8) (sqrt (* (* PI 2) n))) (* (* (sqrt (* (* PI 2) n)) (log (* PI 2))) (* (* (* (log n) k) k) 1/4)))))
  (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
  (- (+ (* (* (* (sqrt (* (* PI 2) n)) (* k k)) (log n)) (* (log (* PI 2)) +nan.0)) (- (* (- +nan.0) (* (* (sqrt (* (* PI 2) n)) (* k k)) (log (* PI 2)))) (+ (+ (- (* (* k (sqrt (* (* PI 2) n))) +nan.0) (* (sqrt (* (* PI 2) n)) +nan.0)) (+ (+ (* (* (log (* PI 2)) (* (* (sqrt (* (* PI 2) n)) (* k k)) (log (* PI 2)))) +nan.0) (* (* (* (sqrt (* (* PI 2) n)) (* k k)) (log n)) (- +nan.0))) (+ (- (* (* k k) (* (sqrt (* (* PI 2) n)) +nan.0)) (* (* (* (log (* PI 2)) +nan.0) (sqrt (* (* PI 2) n))) k)) (* (* (log n) k) (* (sqrt (* (* PI 2) n)) +nan.0))))) (* (* (* (* (log n) k) (* (log n) k)) (sqrt (* (* PI 2) n))) (- +nan.0))))))
  (- (+ (- (* (/ +nan.0 (* k k)) (/ (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) k)) (/ (* (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) +nan.0) k)) (/ (/ (* (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) +nan.0) k) k)))
  (- (- (/ +nan.0 (/ k (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))))) (* +nan.0 (- (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* k k)) (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))))))
3.749 * * * [progress]: adding candidates to table
4.844 * * [progress]: iteration 2 / 4
4.844 * * * [progress]: picking best candidate
4.883 * * * * [pick]: Picked  #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
4.883 * * * [progress]: localizing error
4.909 * * * [progress]: generating rewritten candidates
4.909 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2)
4.932 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1)
4.947 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2)
4.957 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
5.005 * * * [progress]: generating series expansions
5.005 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2)
5.007 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
5.007 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
5.007 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
5.007 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
5.007 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
5.007 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
5.007 * [taylor]: Taking taylor expansion of 1/2 in k
5.007 * [backup-simplify]: Simplify 1/2 into 1/2
5.007 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
5.007 * [taylor]: Taking taylor expansion of 1/2 in k
5.007 * [backup-simplify]: Simplify 1/2 into 1/2
5.007 * [taylor]: Taking taylor expansion of k in k
5.007 * [backup-simplify]: Simplify 0 into 0
5.007 * [backup-simplify]: Simplify 1 into 1
5.007 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.007 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.007 * [taylor]: Taking taylor expansion of 2 in k
5.007 * [backup-simplify]: Simplify 2 into 2
5.007 * [taylor]: Taking taylor expansion of (* n PI) in k
5.007 * [taylor]: Taking taylor expansion of n in k
5.007 * [backup-simplify]: Simplify n into n
5.007 * [taylor]: Taking taylor expansion of PI in k
5.007 * [backup-simplify]: Simplify PI into PI
5.007 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.007 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.007 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.008 * [backup-simplify]: Simplify (* 1/2 0) into 0
5.008 * [backup-simplify]: Simplify (- 0) into 0
5.009 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.009 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.009 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.009 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
5.009 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
5.009 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
5.009 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
5.009 * [taylor]: Taking taylor expansion of 1/2 in n
5.009 * [backup-simplify]: Simplify 1/2 into 1/2
5.009 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
5.009 * [taylor]: Taking taylor expansion of 1/2 in n
5.009 * [backup-simplify]: Simplify 1/2 into 1/2
5.009 * [taylor]: Taking taylor expansion of k in n
5.009 * [backup-simplify]: Simplify k into k
5.010 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.010 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.010 * [taylor]: Taking taylor expansion of 2 in n
5.010 * [backup-simplify]: Simplify 2 into 2
5.010 * [taylor]: Taking taylor expansion of (* n PI) in n
5.010 * [taylor]: Taking taylor expansion of n in n
5.010 * [backup-simplify]: Simplify 0 into 0
5.010 * [backup-simplify]: Simplify 1 into 1
5.010 * [taylor]: Taking taylor expansion of PI in n
5.010 * [backup-simplify]: Simplify PI into PI
5.011 * [backup-simplify]: Simplify (* 0 PI) into 0
5.012 * [backup-simplify]: Simplify (* 2 0) into 0
5.014 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.015 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.016 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.017 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
5.017 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
5.017 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
5.018 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.019 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
5.020 * [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)))))
5.021 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
5.021 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
5.021 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
5.021 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
5.021 * [taylor]: Taking taylor expansion of 1/2 in n
5.021 * [backup-simplify]: Simplify 1/2 into 1/2
5.021 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
5.021 * [taylor]: Taking taylor expansion of 1/2 in n
5.021 * [backup-simplify]: Simplify 1/2 into 1/2
5.021 * [taylor]: Taking taylor expansion of k in n
5.021 * [backup-simplify]: Simplify k into k
5.021 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.021 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.021 * [taylor]: Taking taylor expansion of 2 in n
5.021 * [backup-simplify]: Simplify 2 into 2
5.021 * [taylor]: Taking taylor expansion of (* n PI) in n
5.021 * [taylor]: Taking taylor expansion of n in n
5.021 * [backup-simplify]: Simplify 0 into 0
5.021 * [backup-simplify]: Simplify 1 into 1
5.021 * [taylor]: Taking taylor expansion of PI in n
5.021 * [backup-simplify]: Simplify PI into PI
5.022 * [backup-simplify]: Simplify (* 0 PI) into 0
5.022 * [backup-simplify]: Simplify (* 2 0) into 0
5.024 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.025 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.026 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.026 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
5.027 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
5.027 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
5.028 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.029 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
5.030 * [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)))))
5.031 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
5.031 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
5.031 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
5.031 * [taylor]: Taking taylor expansion of 1/2 in k
5.031 * [backup-simplify]: Simplify 1/2 into 1/2
5.031 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
5.031 * [taylor]: Taking taylor expansion of 1/2 in k
5.031 * [backup-simplify]: Simplify 1/2 into 1/2
5.031 * [taylor]: Taking taylor expansion of k in k
5.031 * [backup-simplify]: Simplify 0 into 0
5.031 * [backup-simplify]: Simplify 1 into 1
5.031 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
5.031 * [taylor]: Taking taylor expansion of (log n) in k
5.031 * [taylor]: Taking taylor expansion of n in k
5.031 * [backup-simplify]: Simplify n into n
5.031 * [backup-simplify]: Simplify (log n) into (log n)
5.031 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.031 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.031 * [taylor]: Taking taylor expansion of 2 in k
5.031 * [backup-simplify]: Simplify 2 into 2
5.031 * [taylor]: Taking taylor expansion of PI in k
5.031 * [backup-simplify]: Simplify PI into PI
5.032 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.033 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.033 * [backup-simplify]: Simplify (* 1/2 0) into 0
5.034 * [backup-simplify]: Simplify (- 0) into 0
5.034 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.035 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.036 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
5.038 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.039 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.040 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.041 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.043 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.043 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
5.044 * [backup-simplify]: Simplify (- 0) into 0
5.044 * [backup-simplify]: Simplify (+ 0 0) into 0
5.046 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.047 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
5.049 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.049 * [taylor]: Taking taylor expansion of 0 in k
5.049 * [backup-simplify]: Simplify 0 into 0
5.049 * [backup-simplify]: Simplify 0 into 0
5.050 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
5.051 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.058 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.059 * [backup-simplify]: Simplify (+ 0 0) into 0
5.060 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
5.060 * [backup-simplify]: Simplify (- 1/2) into -1/2
5.060 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
5.062 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
5.065 * [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)))))))
5.069 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
5.070 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.071 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.075 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.076 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
5.077 * [backup-simplify]: Simplify (- 0) into 0
5.077 * [backup-simplify]: Simplify (+ 0 0) into 0
5.078 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.080 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.083 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.083 * [taylor]: Taking taylor expansion of 0 in k
5.083 * [backup-simplify]: Simplify 0 into 0
5.083 * [backup-simplify]: Simplify 0 into 0
5.083 * [backup-simplify]: Simplify 0 into 0
5.084 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
5.086 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.089 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.089 * [backup-simplify]: Simplify (+ 0 0) into 0
5.090 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
5.091 * [backup-simplify]: Simplify (- 0) into 0
5.091 * [backup-simplify]: Simplify (+ 0 0) into 0
5.093 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.097 * [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)))))
5.103 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
5.113 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
5.114 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
5.114 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
5.114 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
5.114 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.114 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.114 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
5.114 * [taylor]: Taking taylor expansion of 1/2 in k
5.114 * [backup-simplify]: Simplify 1/2 into 1/2
5.114 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.114 * [taylor]: Taking taylor expansion of 1/2 in k
5.114 * [backup-simplify]: Simplify 1/2 into 1/2
5.114 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.115 * [taylor]: Taking taylor expansion of k in k
5.115 * [backup-simplify]: Simplify 0 into 0
5.115 * [backup-simplify]: Simplify 1 into 1
5.115 * [backup-simplify]: Simplify (/ 1 1) into 1
5.115 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.115 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.115 * [taylor]: Taking taylor expansion of 2 in k
5.115 * [backup-simplify]: Simplify 2 into 2
5.115 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.115 * [taylor]: Taking taylor expansion of PI in k
5.115 * [backup-simplify]: Simplify PI into PI
5.115 * [taylor]: Taking taylor expansion of n in k
5.115 * [backup-simplify]: Simplify n into n
5.115 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.115 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.116 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.116 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.117 * [backup-simplify]: Simplify (- 1/2) into -1/2
5.117 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
5.117 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.118 * [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))))
5.118 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
5.118 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.118 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.118 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
5.118 * [taylor]: Taking taylor expansion of 1/2 in n
5.118 * [backup-simplify]: Simplify 1/2 into 1/2
5.118 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.118 * [taylor]: Taking taylor expansion of 1/2 in n
5.118 * [backup-simplify]: Simplify 1/2 into 1/2
5.118 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.118 * [taylor]: Taking taylor expansion of k in n
5.118 * [backup-simplify]: Simplify k into k
5.118 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.118 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.118 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.118 * [taylor]: Taking taylor expansion of 2 in n
5.118 * [backup-simplify]: Simplify 2 into 2
5.118 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.118 * [taylor]: Taking taylor expansion of PI in n
5.118 * [backup-simplify]: Simplify PI into PI
5.118 * [taylor]: Taking taylor expansion of n in n
5.118 * [backup-simplify]: Simplify 0 into 0
5.118 * [backup-simplify]: Simplify 1 into 1
5.119 * [backup-simplify]: Simplify (/ PI 1) into PI
5.119 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.121 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.121 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.121 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
5.121 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
5.122 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.124 * [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)))
5.125 * [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))))
5.125 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
5.125 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.125 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.125 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
5.125 * [taylor]: Taking taylor expansion of 1/2 in n
5.125 * [backup-simplify]: Simplify 1/2 into 1/2
5.125 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.125 * [taylor]: Taking taylor expansion of 1/2 in n
5.125 * [backup-simplify]: Simplify 1/2 into 1/2
5.125 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.125 * [taylor]: Taking taylor expansion of k in n
5.125 * [backup-simplify]: Simplify k into k
5.126 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.126 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.126 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.126 * [taylor]: Taking taylor expansion of 2 in n
5.126 * [backup-simplify]: Simplify 2 into 2
5.126 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.126 * [taylor]: Taking taylor expansion of PI in n
5.126 * [backup-simplify]: Simplify PI into PI
5.126 * [taylor]: Taking taylor expansion of n in n
5.126 * [backup-simplify]: Simplify 0 into 0
5.126 * [backup-simplify]: Simplify 1 into 1
5.127 * [backup-simplify]: Simplify (/ PI 1) into PI
5.127 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.128 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.128 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.129 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
5.129 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
5.130 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.132 * [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)))
5.133 * [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))))
5.133 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
5.134 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
5.134 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
5.134 * [taylor]: Taking taylor expansion of 1/2 in k
5.134 * [backup-simplify]: Simplify 1/2 into 1/2
5.134 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.134 * [taylor]: Taking taylor expansion of 1/2 in k
5.134 * [backup-simplify]: Simplify 1/2 into 1/2
5.134 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.134 * [taylor]: Taking taylor expansion of k in k
5.134 * [backup-simplify]: Simplify 0 into 0
5.134 * [backup-simplify]: Simplify 1 into 1
5.134 * [backup-simplify]: Simplify (/ 1 1) into 1
5.134 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
5.134 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.134 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.134 * [taylor]: Taking taylor expansion of 2 in k
5.134 * [backup-simplify]: Simplify 2 into 2
5.134 * [taylor]: Taking taylor expansion of PI in k
5.134 * [backup-simplify]: Simplify PI into PI
5.135 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.136 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.136 * [taylor]: Taking taylor expansion of (log n) in k
5.136 * [taylor]: Taking taylor expansion of n in k
5.136 * [backup-simplify]: Simplify n into n
5.136 * [backup-simplify]: Simplify (log n) into (log n)
5.137 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.137 * [backup-simplify]: Simplify (- 1/2) into -1/2
5.138 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
5.138 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.139 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
5.140 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
5.142 * [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))))
5.144 * [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))))
5.145 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.146 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.148 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.148 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.149 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
5.149 * [backup-simplify]: Simplify (- 0) into 0
5.150 * [backup-simplify]: Simplify (+ 0 0) into 0
5.151 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.153 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.155 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
5.155 * [taylor]: Taking taylor expansion of 0 in k
5.155 * [backup-simplify]: Simplify 0 into 0
5.155 * [backup-simplify]: Simplify 0 into 0
5.155 * [backup-simplify]: Simplify 0 into 0
5.156 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.157 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.161 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.161 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.162 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
5.163 * [backup-simplify]: Simplify (- 0) into 0
5.163 * [backup-simplify]: Simplify (+ 0 0) into 0
5.164 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.166 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
5.169 * [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
5.169 * [taylor]: Taking taylor expansion of 0 in k
5.169 * [backup-simplify]: Simplify 0 into 0
5.169 * [backup-simplify]: Simplify 0 into 0
5.169 * [backup-simplify]: Simplify 0 into 0
5.169 * [backup-simplify]: Simplify 0 into 0
5.170 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.172 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.178 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
5.178 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.179 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
5.180 * [backup-simplify]: Simplify (- 0) into 0
5.180 * [backup-simplify]: Simplify (+ 0 0) into 0
5.182 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.184 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
5.186 * [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
5.186 * [taylor]: Taking taylor expansion of 0 in k
5.186 * [backup-simplify]: Simplify 0 into 0
5.187 * [backup-simplify]: Simplify 0 into 0
5.188 * [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)))))
5.188 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
5.189 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
5.189 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
5.189 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
5.189 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
5.189 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
5.189 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.189 * [taylor]: Taking taylor expansion of 1/2 in k
5.189 * [backup-simplify]: Simplify 1/2 into 1/2
5.189 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.189 * [taylor]: Taking taylor expansion of k in k
5.189 * [backup-simplify]: Simplify 0 into 0
5.189 * [backup-simplify]: Simplify 1 into 1
5.189 * [backup-simplify]: Simplify (/ 1 1) into 1
5.189 * [taylor]: Taking taylor expansion of 1/2 in k
5.189 * [backup-simplify]: Simplify 1/2 into 1/2
5.189 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.189 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.189 * [taylor]: Taking taylor expansion of -2 in k
5.189 * [backup-simplify]: Simplify -2 into -2
5.189 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.190 * [taylor]: Taking taylor expansion of PI in k
5.190 * [backup-simplify]: Simplify PI into PI
5.190 * [taylor]: Taking taylor expansion of n in k
5.190 * [backup-simplify]: Simplify n into n
5.190 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.190 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.190 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.190 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.191 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.191 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.191 * [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)))
5.191 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
5.191 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
5.191 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
5.191 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
5.191 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.191 * [taylor]: Taking taylor expansion of 1/2 in n
5.191 * [backup-simplify]: Simplify 1/2 into 1/2
5.191 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.191 * [taylor]: Taking taylor expansion of k in n
5.191 * [backup-simplify]: Simplify k into k
5.192 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.192 * [taylor]: Taking taylor expansion of 1/2 in n
5.192 * [backup-simplify]: Simplify 1/2 into 1/2
5.192 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.192 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.192 * [taylor]: Taking taylor expansion of -2 in n
5.192 * [backup-simplify]: Simplify -2 into -2
5.192 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.192 * [taylor]: Taking taylor expansion of PI in n
5.192 * [backup-simplify]: Simplify PI into PI
5.192 * [taylor]: Taking taylor expansion of n in n
5.192 * [backup-simplify]: Simplify 0 into 0
5.192 * [backup-simplify]: Simplify 1 into 1
5.192 * [backup-simplify]: Simplify (/ PI 1) into PI
5.193 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.194 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.194 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.194 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
5.196 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.197 * [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)))
5.198 * [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))))
5.198 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
5.198 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
5.198 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
5.198 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
5.198 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.198 * [taylor]: Taking taylor expansion of 1/2 in n
5.198 * [backup-simplify]: Simplify 1/2 into 1/2
5.198 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.198 * [taylor]: Taking taylor expansion of k in n
5.198 * [backup-simplify]: Simplify k into k
5.199 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.199 * [taylor]: Taking taylor expansion of 1/2 in n
5.199 * [backup-simplify]: Simplify 1/2 into 1/2
5.199 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.199 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.199 * [taylor]: Taking taylor expansion of -2 in n
5.199 * [backup-simplify]: Simplify -2 into -2
5.199 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.199 * [taylor]: Taking taylor expansion of PI in n
5.199 * [backup-simplify]: Simplify PI into PI
5.199 * [taylor]: Taking taylor expansion of n in n
5.199 * [backup-simplify]: Simplify 0 into 0
5.199 * [backup-simplify]: Simplify 1 into 1
5.199 * [backup-simplify]: Simplify (/ PI 1) into PI
5.200 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.201 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.201 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.201 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
5.203 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.204 * [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)))
5.205 * [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))))
5.205 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
5.205 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
5.205 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
5.205 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.205 * [taylor]: Taking taylor expansion of 1/2 in k
5.205 * [backup-simplify]: Simplify 1/2 into 1/2
5.205 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.205 * [taylor]: Taking taylor expansion of k in k
5.205 * [backup-simplify]: Simplify 0 into 0
5.205 * [backup-simplify]: Simplify 1 into 1
5.206 * [backup-simplify]: Simplify (/ 1 1) into 1
5.206 * [taylor]: Taking taylor expansion of 1/2 in k
5.206 * [backup-simplify]: Simplify 1/2 into 1/2
5.206 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
5.206 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
5.206 * [taylor]: Taking taylor expansion of (* -2 PI) in k
5.206 * [taylor]: Taking taylor expansion of -2 in k
5.206 * [backup-simplify]: Simplify -2 into -2
5.206 * [taylor]: Taking taylor expansion of PI in k
5.206 * [backup-simplify]: Simplify PI into PI
5.207 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.208 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.208 * [taylor]: Taking taylor expansion of (log n) in k
5.208 * [taylor]: Taking taylor expansion of n in k
5.208 * [backup-simplify]: Simplify n into n
5.208 * [backup-simplify]: Simplify (log n) into (log n)
5.211 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.212 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.212 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.213 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
5.214 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
5.215 * [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))))
5.217 * [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))))
5.218 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.219 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.221 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
5.221 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.222 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
5.222 * [backup-simplify]: Simplify (+ 0 0) into 0
5.224 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.225 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
5.227 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
5.227 * [taylor]: Taking taylor expansion of 0 in k
5.227 * [backup-simplify]: Simplify 0 into 0
5.227 * [backup-simplify]: Simplify 0 into 0
5.227 * [backup-simplify]: Simplify 0 into 0
5.228 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.230 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.233 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
5.233 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.234 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
5.234 * [backup-simplify]: Simplify (+ 0 0) into 0
5.235 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.236 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
5.238 * [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
5.238 * [taylor]: Taking taylor expansion of 0 in k
5.238 * [backup-simplify]: Simplify 0 into 0
5.238 * [backup-simplify]: Simplify 0 into 0
5.238 * [backup-simplify]: Simplify 0 into 0
5.238 * [backup-simplify]: Simplify 0 into 0
5.239 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.240 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.243 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
5.244 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.245 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
5.245 * [backup-simplify]: Simplify (+ 0 0) into 0
5.246 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.247 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
5.249 * [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
5.249 * [taylor]: Taking taylor expansion of 0 in k
5.249 * [backup-simplify]: Simplify 0 into 0
5.249 * [backup-simplify]: Simplify 0 into 0
5.250 * [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)))))
5.250 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1)
5.251 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
5.251 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
5.251 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.251 * [taylor]: Taking taylor expansion of 2 in n
5.251 * [backup-simplify]: Simplify 2 into 2
5.251 * [taylor]: Taking taylor expansion of (* n PI) in n
5.251 * [taylor]: Taking taylor expansion of n in n
5.251 * [backup-simplify]: Simplify 0 into 0
5.251 * [backup-simplify]: Simplify 1 into 1
5.251 * [taylor]: Taking taylor expansion of PI in n
5.251 * [backup-simplify]: Simplify PI into PI
5.251 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.251 * [taylor]: Taking taylor expansion of 2 in n
5.251 * [backup-simplify]: Simplify 2 into 2
5.251 * [taylor]: Taking taylor expansion of (* n PI) in n
5.251 * [taylor]: Taking taylor expansion of n in n
5.251 * [backup-simplify]: Simplify 0 into 0
5.251 * [backup-simplify]: Simplify 1 into 1
5.251 * [taylor]: Taking taylor expansion of PI in n
5.251 * [backup-simplify]: Simplify PI into PI
5.252 * [backup-simplify]: Simplify (* 0 PI) into 0
5.252 * [backup-simplify]: Simplify (* 2 0) into 0
5.252 * [backup-simplify]: Simplify 0 into 0
5.253 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.254 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.254 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.255 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.256 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.256 * [backup-simplify]: Simplify 0 into 0
5.257 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.257 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.257 * [backup-simplify]: Simplify 0 into 0
5.259 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.261 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
5.261 * [backup-simplify]: Simplify 0 into 0
5.263 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.265 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
5.265 * [backup-simplify]: Simplify 0 into 0
5.267 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.269 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
5.269 * [backup-simplify]: Simplify 0 into 0
5.271 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
5.273 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
5.273 * [backup-simplify]: Simplify 0 into 0
5.274 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
5.274 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
5.274 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
5.274 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.274 * [taylor]: Taking taylor expansion of 2 in n
5.274 * [backup-simplify]: Simplify 2 into 2
5.274 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.274 * [taylor]: Taking taylor expansion of PI in n
5.275 * [backup-simplify]: Simplify PI into PI
5.275 * [taylor]: Taking taylor expansion of n in n
5.275 * [backup-simplify]: Simplify 0 into 0
5.275 * [backup-simplify]: Simplify 1 into 1
5.275 * [backup-simplify]: Simplify (/ PI 1) into PI
5.275 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.275 * [taylor]: Taking taylor expansion of 2 in n
5.275 * [backup-simplify]: Simplify 2 into 2
5.275 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.275 * [taylor]: Taking taylor expansion of PI in n
5.275 * [backup-simplify]: Simplify PI into PI
5.275 * [taylor]: Taking taylor expansion of n in n
5.275 * [backup-simplify]: Simplify 0 into 0
5.275 * [backup-simplify]: Simplify 1 into 1
5.276 * [backup-simplify]: Simplify (/ PI 1) into PI
5.276 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.277 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.278 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.279 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.279 * [backup-simplify]: Simplify 0 into 0
5.280 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.281 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.281 * [backup-simplify]: Simplify 0 into 0
5.282 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.284 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.284 * [backup-simplify]: Simplify 0 into 0
5.285 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.286 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.287 * [backup-simplify]: Simplify 0 into 0
5.288 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.289 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.289 * [backup-simplify]: Simplify 0 into 0
5.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.292 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.292 * [backup-simplify]: Simplify 0 into 0
5.293 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
5.294 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
5.294 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
5.294 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.294 * [taylor]: Taking taylor expansion of -2 in n
5.294 * [backup-simplify]: Simplify -2 into -2
5.294 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.294 * [taylor]: Taking taylor expansion of PI in n
5.294 * [backup-simplify]: Simplify PI into PI
5.294 * [taylor]: Taking taylor expansion of n in n
5.294 * [backup-simplify]: Simplify 0 into 0
5.294 * [backup-simplify]: Simplify 1 into 1
5.295 * [backup-simplify]: Simplify (/ PI 1) into PI
5.295 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.295 * [taylor]: Taking taylor expansion of -2 in n
5.295 * [backup-simplify]: Simplify -2 into -2
5.295 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.295 * [taylor]: Taking taylor expansion of PI in n
5.295 * [backup-simplify]: Simplify PI into PI
5.295 * [taylor]: Taking taylor expansion of n in n
5.295 * [backup-simplify]: Simplify 0 into 0
5.295 * [backup-simplify]: Simplify 1 into 1
5.296 * [backup-simplify]: Simplify (/ PI 1) into PI
5.296 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.297 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.298 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.299 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.299 * [backup-simplify]: Simplify 0 into 0
5.300 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.301 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.301 * [backup-simplify]: Simplify 0 into 0
5.302 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.302 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.303 * [backup-simplify]: Simplify 0 into 0
5.303 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.304 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.304 * [backup-simplify]: Simplify 0 into 0
5.305 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.306 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.306 * [backup-simplify]: Simplify 0 into 0
5.306 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.307 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.307 * [backup-simplify]: Simplify 0 into 0
5.308 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
5.308 * * * * [progress]: [ 3 / 4 ] generating series at (2 2)
5.308 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k))
5.308 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0
5.308 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n
5.308 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
5.308 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
5.308 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
5.308 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
5.308 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
5.308 * [taylor]: Taking taylor expansion of 1/2 in n
5.309 * [backup-simplify]: Simplify 1/2 into 1/2
5.309 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
5.309 * [taylor]: Taking taylor expansion of 1/2 in n
5.309 * [backup-simplify]: Simplify 1/2 into 1/2
5.309 * [taylor]: Taking taylor expansion of k in n
5.309 * [backup-simplify]: Simplify k into k
5.309 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.309 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.309 * [taylor]: Taking taylor expansion of 2 in n
5.309 * [backup-simplify]: Simplify 2 into 2
5.309 * [taylor]: Taking taylor expansion of (* n PI) in n
5.309 * [taylor]: Taking taylor expansion of n in n
5.309 * [backup-simplify]: Simplify 0 into 0
5.309 * [backup-simplify]: Simplify 1 into 1
5.309 * [taylor]: Taking taylor expansion of PI in n
5.309 * [backup-simplify]: Simplify PI into PI
5.309 * [backup-simplify]: Simplify (* 0 PI) into 0
5.309 * [backup-simplify]: Simplify (* 2 0) into 0
5.310 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.312 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.312 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.312 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
5.312 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
5.312 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
5.313 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.314 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
5.315 * [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)))))
5.316 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
5.316 * [taylor]: Taking taylor expansion of (sqrt k) in n
5.316 * [taylor]: Taking taylor expansion of k in n
5.316 * [backup-simplify]: Simplify k into k
5.316 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
5.316 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
5.316 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k
5.316 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
5.316 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
5.316 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
5.316 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
5.316 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
5.316 * [taylor]: Taking taylor expansion of 1/2 in k
5.316 * [backup-simplify]: Simplify 1/2 into 1/2
5.316 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
5.316 * [taylor]: Taking taylor expansion of 1/2 in k
5.316 * [backup-simplify]: Simplify 1/2 into 1/2
5.316 * [taylor]: Taking taylor expansion of k in k
5.316 * [backup-simplify]: Simplify 0 into 0
5.316 * [backup-simplify]: Simplify 1 into 1
5.316 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.316 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.316 * [taylor]: Taking taylor expansion of 2 in k
5.316 * [backup-simplify]: Simplify 2 into 2
5.316 * [taylor]: Taking taylor expansion of (* n PI) in k
5.316 * [taylor]: Taking taylor expansion of n in k
5.316 * [backup-simplify]: Simplify n into n
5.316 * [taylor]: Taking taylor expansion of PI in k
5.316 * [backup-simplify]: Simplify PI into PI
5.316 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.316 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.316 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.317 * [backup-simplify]: Simplify (* 1/2 0) into 0
5.317 * [backup-simplify]: Simplify (- 0) into 0
5.317 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.317 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.317 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.317 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2))))
5.317 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.317 * [taylor]: Taking taylor expansion of k in k
5.317 * [backup-simplify]: Simplify 0 into 0
5.317 * [backup-simplify]: Simplify 1 into 1
5.318 * [backup-simplify]: Simplify (sqrt 0) into 0
5.319 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.319 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k
5.319 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
5.319 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
5.319 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
5.319 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
5.319 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
5.319 * [taylor]: Taking taylor expansion of 1/2 in k
5.319 * [backup-simplify]: Simplify 1/2 into 1/2
5.319 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
5.319 * [taylor]: Taking taylor expansion of 1/2 in k
5.319 * [backup-simplify]: Simplify 1/2 into 1/2
5.319 * [taylor]: Taking taylor expansion of k in k
5.319 * [backup-simplify]: Simplify 0 into 0
5.319 * [backup-simplify]: Simplify 1 into 1
5.319 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.319 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.319 * [taylor]: Taking taylor expansion of 2 in k
5.319 * [backup-simplify]: Simplify 2 into 2
5.319 * [taylor]: Taking taylor expansion of (* n PI) in k
5.319 * [taylor]: Taking taylor expansion of n in k
5.319 * [backup-simplify]: Simplify n into n
5.319 * [taylor]: Taking taylor expansion of PI in k
5.319 * [backup-simplify]: Simplify PI into PI
5.319 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.319 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.319 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.319 * [backup-simplify]: Simplify (* 1/2 0) into 0
5.320 * [backup-simplify]: Simplify (- 0) into 0
5.320 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.320 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.320 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.320 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2))))
5.320 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.320 * [taylor]: Taking taylor expansion of k in k
5.320 * [backup-simplify]: Simplify 0 into 0
5.320 * [backup-simplify]: Simplify 1 into 1
5.321 * [backup-simplify]: Simplify (sqrt 0) into 0
5.321 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.322 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0
5.322 * [taylor]: Taking taylor expansion of 0 in n
5.322 * [backup-simplify]: Simplify 0 into 0
5.322 * [backup-simplify]: Simplify 0 into 0
5.322 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
5.323 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
5.324 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
5.324 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
5.325 * [backup-simplify]: Simplify (- 1/2) into -1/2
5.325 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
5.326 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
5.326 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))
5.327 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))
5.329 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))
5.329 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n
5.329 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n
5.329 * [taylor]: Taking taylor expansion of +nan.0 in n
5.329 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.329 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n
5.329 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
5.329 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n
5.329 * [taylor]: Taking taylor expansion of (* n PI) in n
5.329 * [taylor]: Taking taylor expansion of n in n
5.329 * [backup-simplify]: Simplify 0 into 0
5.329 * [backup-simplify]: Simplify 1 into 1
5.329 * [taylor]: Taking taylor expansion of PI in n
5.329 * [backup-simplify]: Simplify PI into PI
5.330 * [backup-simplify]: Simplify (* 0 PI) into 0
5.331 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.332 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI)
5.332 * [backup-simplify]: Simplify (sqrt 0) into 0
5.335 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
5.335 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n
5.335 * [taylor]: Taking taylor expansion of 1/2 in n
5.335 * [backup-simplify]: Simplify 1/2 into 1/2
5.335 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2)
5.336 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
5.342 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.343 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0
5.348 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.351 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.353 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.353 * [backup-simplify]: Simplify 0 into 0
5.355 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.355 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
5.356 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
5.357 * [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
5.357 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
5.358 * [backup-simplify]: Simplify (- 0) into 0
5.358 * [backup-simplify]: Simplify (+ 0 0) into 0
5.358 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
5.359 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))
5.361 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))))
5.365 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))))
5.365 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n
5.365 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n
5.365 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n
5.365 * [taylor]: Taking taylor expansion of +nan.0 in n
5.365 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.365 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n
5.365 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n
5.365 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.365 * [taylor]: Taking taylor expansion of 2 in n
5.365 * [backup-simplify]: Simplify 2 into 2
5.365 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.365 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.366 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n
5.366 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.366 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.366 * [taylor]: Taking taylor expansion of 2 in n
5.366 * [backup-simplify]: Simplify 2 into 2
5.366 * [taylor]: Taking taylor expansion of (* n PI) in n
5.366 * [taylor]: Taking taylor expansion of n in n
5.366 * [backup-simplify]: Simplify 0 into 0
5.366 * [backup-simplify]: Simplify 1 into 1
5.366 * [taylor]: Taking taylor expansion of PI in n
5.366 * [backup-simplify]: Simplify PI into PI
5.366 * [backup-simplify]: Simplify (* 0 PI) into 0
5.366 * [backup-simplify]: Simplify (* 2 0) into 0
5.367 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.368 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.369 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.369 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n
5.369 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n
5.369 * [taylor]: Taking taylor expansion of 1/2 in n
5.369 * [backup-simplify]: Simplify 1/2 into 1/2
5.369 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2)
5.370 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
5.370 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
5.370 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n
5.370 * [taylor]: Taking taylor expansion of (* n PI) in n
5.370 * [taylor]: Taking taylor expansion of n in n
5.370 * [backup-simplify]: Simplify 0 into 0
5.370 * [backup-simplify]: Simplify 1 into 1
5.370 * [taylor]: Taking taylor expansion of PI in n
5.370 * [backup-simplify]: Simplify PI into PI
5.370 * [backup-simplify]: Simplify (* 0 PI) into 0
5.371 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.371 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI)
5.372 * [backup-simplify]: Simplify (sqrt 0) into 0
5.373 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
5.373 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n
5.373 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n
5.373 * [taylor]: Taking taylor expansion of +nan.0 in n
5.373 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.373 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n
5.373 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
5.373 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n
5.373 * [taylor]: Taking taylor expansion of (* n PI) in n
5.373 * [taylor]: Taking taylor expansion of n in n
5.373 * [backup-simplify]: Simplify 0 into 0
5.373 * [backup-simplify]: Simplify 1 into 1
5.373 * [taylor]: Taking taylor expansion of PI in n
5.373 * [backup-simplify]: Simplify PI into PI
5.374 * [backup-simplify]: Simplify (* 0 PI) into 0
5.375 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.375 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI)
5.375 * [backup-simplify]: Simplify (sqrt 0) into 0
5.377 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
5.377 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n
5.377 * [taylor]: Taking taylor expansion of 1/2 in n
5.377 * [backup-simplify]: Simplify 1/2 into 1/2
5.377 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2)
5.378 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
5.379 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.380 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2)
5.381 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))
5.384 * [backup-simplify]: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))
5.385 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.386 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0
5.387 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.388 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.390 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.392 * [backup-simplify]: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0
5.395 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0
5.399 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))
5.402 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0
5.415 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))
5.419 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.420 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0
5.425 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.429 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.447 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
5.472 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
5.487 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
5.487 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0
5.488 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.489 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0
5.492 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2))
5.496 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
5.502 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
5.508 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
5.512 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
5.534 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI)))))))))))
5.535 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k)))
5.535 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0
5.535 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n
5.535 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
5.535 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
5.535 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.535 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.535 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
5.535 * [taylor]: Taking taylor expansion of 1/2 in n
5.535 * [backup-simplify]: Simplify 1/2 into 1/2
5.535 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.535 * [taylor]: Taking taylor expansion of 1/2 in n
5.535 * [backup-simplify]: Simplify 1/2 into 1/2
5.535 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.535 * [taylor]: Taking taylor expansion of k in n
5.535 * [backup-simplify]: Simplify k into k
5.535 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.535 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.535 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.535 * [taylor]: Taking taylor expansion of 2 in n
5.535 * [backup-simplify]: Simplify 2 into 2
5.535 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.535 * [taylor]: Taking taylor expansion of PI in n
5.535 * [backup-simplify]: Simplify PI into PI
5.535 * [taylor]: Taking taylor expansion of n in n
5.535 * [backup-simplify]: Simplify 0 into 0
5.535 * [backup-simplify]: Simplify 1 into 1
5.536 * [backup-simplify]: Simplify (/ PI 1) into PI
5.536 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.537 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.537 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.537 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
5.537 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
5.538 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.539 * [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)))
5.540 * [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))))
5.540 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
5.540 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
5.540 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.540 * [taylor]: Taking taylor expansion of k in n
5.540 * [backup-simplify]: Simplify k into k
5.540 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.540 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
5.541 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.541 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
5.541 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k
5.541 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
5.541 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
5.541 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.541 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.541 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
5.541 * [taylor]: Taking taylor expansion of 1/2 in k
5.541 * [backup-simplify]: Simplify 1/2 into 1/2
5.541 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.541 * [taylor]: Taking taylor expansion of 1/2 in k
5.541 * [backup-simplify]: Simplify 1/2 into 1/2
5.541 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.541 * [taylor]: Taking taylor expansion of k in k
5.541 * [backup-simplify]: Simplify 0 into 0
5.541 * [backup-simplify]: Simplify 1 into 1
5.541 * [backup-simplify]: Simplify (/ 1 1) into 1
5.541 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.541 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.541 * [taylor]: Taking taylor expansion of 2 in k
5.541 * [backup-simplify]: Simplify 2 into 2
5.541 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.541 * [taylor]: Taking taylor expansion of PI in k
5.541 * [backup-simplify]: Simplify PI into PI
5.541 * [taylor]: Taking taylor expansion of n in k
5.541 * [backup-simplify]: Simplify n into n
5.541 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.541 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.541 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.542 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.542 * [backup-simplify]: Simplify (- 1/2) into -1/2
5.542 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
5.542 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.542 * [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))))
5.543 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
5.543 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.543 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.543 * [taylor]: Taking taylor expansion of k in k
5.543 * [backup-simplify]: Simplify 0 into 0
5.543 * [backup-simplify]: Simplify 1 into 1
5.543 * [backup-simplify]: Simplify (/ 1 1) into 1
5.543 * [backup-simplify]: Simplify (sqrt 0) into 0
5.544 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.544 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k
5.544 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
5.544 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
5.544 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.544 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.544 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
5.544 * [taylor]: Taking taylor expansion of 1/2 in k
5.544 * [backup-simplify]: Simplify 1/2 into 1/2
5.544 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.544 * [taylor]: Taking taylor expansion of 1/2 in k
5.544 * [backup-simplify]: Simplify 1/2 into 1/2
5.544 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.544 * [taylor]: Taking taylor expansion of k in k
5.544 * [backup-simplify]: Simplify 0 into 0
5.544 * [backup-simplify]: Simplify 1 into 1
5.545 * [backup-simplify]: Simplify (/ 1 1) into 1
5.545 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.545 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.545 * [taylor]: Taking taylor expansion of 2 in k
5.545 * [backup-simplify]: Simplify 2 into 2
5.545 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.545 * [taylor]: Taking taylor expansion of PI in k
5.545 * [backup-simplify]: Simplify PI into PI
5.545 * [taylor]: Taking taylor expansion of n in k
5.545 * [backup-simplify]: Simplify n into n
5.545 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.545 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.545 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.545 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.545 * [backup-simplify]: Simplify (- 1/2) into -1/2
5.546 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
5.546 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.546 * [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))))
5.546 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
5.546 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.546 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.546 * [taylor]: Taking taylor expansion of k in k
5.546 * [backup-simplify]: Simplify 0 into 0
5.546 * [backup-simplify]: Simplify 1 into 1
5.546 * [backup-simplify]: Simplify (/ 1 1) into 1
5.547 * [backup-simplify]: Simplify (sqrt 0) into 0
5.547 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.548 * [backup-simplify]: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0
5.548 * [taylor]: Taking taylor expansion of 0 in n
5.548 * [backup-simplify]: Simplify 0 into 0
5.548 * [backup-simplify]: Simplify 0 into 0
5.548 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
5.548 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))
5.548 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n
5.548 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n
5.548 * [taylor]: Taking taylor expansion of +nan.0 in n
5.548 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.548 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
5.548 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
5.548 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.548 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.548 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
5.548 * [taylor]: Taking taylor expansion of 1/2 in n
5.549 * [backup-simplify]: Simplify 1/2 into 1/2
5.549 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.549 * [taylor]: Taking taylor expansion of 1/2 in n
5.549 * [backup-simplify]: Simplify 1/2 into 1/2
5.549 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.549 * [taylor]: Taking taylor expansion of k in n
5.549 * [backup-simplify]: Simplify k into k
5.549 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.549 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.549 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.549 * [taylor]: Taking taylor expansion of 2 in n
5.549 * [backup-simplify]: Simplify 2 into 2
5.549 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.549 * [taylor]: Taking taylor expansion of PI in n
5.549 * [backup-simplify]: Simplify PI into PI
5.549 * [taylor]: Taking taylor expansion of n in n
5.549 * [backup-simplify]: Simplify 0 into 0
5.549 * [backup-simplify]: Simplify 1 into 1
5.549 * [backup-simplify]: Simplify (/ PI 1) into PI
5.549 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.550 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.550 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.550 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
5.550 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
5.551 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.552 * [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)))
5.553 * [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))))
5.554 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
5.555 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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)))))
5.555 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
5.556 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
5.556 * [backup-simplify]: Simplify 0 into 0
5.557 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.559 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.559 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
5.560 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))
5.560 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n
5.560 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n
5.560 * [taylor]: Taking taylor expansion of +nan.0 in n
5.560 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.560 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
5.560 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
5.560 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.560 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.560 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
5.560 * [taylor]: Taking taylor expansion of 1/2 in n
5.560 * [backup-simplify]: Simplify 1/2 into 1/2
5.560 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.560 * [taylor]: Taking taylor expansion of 1/2 in n
5.560 * [backup-simplify]: Simplify 1/2 into 1/2
5.560 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.560 * [taylor]: Taking taylor expansion of k in n
5.560 * [backup-simplify]: Simplify k into k
5.560 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.560 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.560 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.560 * [taylor]: Taking taylor expansion of 2 in n
5.560 * [backup-simplify]: Simplify 2 into 2
5.560 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.560 * [taylor]: Taking taylor expansion of PI in n
5.560 * [backup-simplify]: Simplify PI into PI
5.560 * [taylor]: Taking taylor expansion of n in n
5.560 * [backup-simplify]: Simplify 0 into 0
5.560 * [backup-simplify]: Simplify 1 into 1
5.560 * [backup-simplify]: Simplify (/ PI 1) into PI
5.561 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.561 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.562 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.562 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
5.562 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
5.563 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.564 * [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)))
5.566 * [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))))
5.567 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
5.568 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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)))))
5.570 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
5.571 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
5.572 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.573 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.575 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.575 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.576 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
5.576 * [backup-simplify]: Simplify (- 0) into 0
5.577 * [backup-simplify]: Simplify (+ 0 0) into 0
5.582 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.584 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.586 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
5.588 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0
5.590 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
5.591 * [backup-simplify]: Simplify (- 0) into 0
5.591 * [backup-simplify]: Simplify 0 into 0
5.591 * [backup-simplify]: Simplify 0 into 0
5.592 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.596 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.597 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
5.599 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))
5.599 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n
5.599 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n
5.599 * [taylor]: Taking taylor expansion of +nan.0 in n
5.599 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.599 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
5.599 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
5.599 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.599 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.599 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
5.599 * [taylor]: Taking taylor expansion of 1/2 in n
5.599 * [backup-simplify]: Simplify 1/2 into 1/2
5.599 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.599 * [taylor]: Taking taylor expansion of 1/2 in n
5.599 * [backup-simplify]: Simplify 1/2 into 1/2
5.599 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.599 * [taylor]: Taking taylor expansion of k in n
5.599 * [backup-simplify]: Simplify k into k
5.599 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.599 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.599 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.599 * [taylor]: Taking taylor expansion of 2 in n
5.599 * [backup-simplify]: Simplify 2 into 2
5.599 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.599 * [taylor]: Taking taylor expansion of PI in n
5.599 * [backup-simplify]: Simplify PI into PI
5.599 * [taylor]: Taking taylor expansion of n in n
5.599 * [backup-simplify]: Simplify 0 into 0
5.599 * [backup-simplify]: Simplify 1 into 1
5.600 * [backup-simplify]: Simplify (/ PI 1) into PI
5.601 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.602 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.602 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.602 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
5.602 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
5.604 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.606 * [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)))
5.607 * [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))))
5.609 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
5.610 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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)))))
5.611 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
5.613 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
5.617 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))))))))
5.618 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)))
5.618 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0
5.618 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n
5.618 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
5.618 * [taylor]: Taking taylor expansion of (/ -1 k) in n
5.618 * [taylor]: Taking taylor expansion of -1 in n
5.618 * [backup-simplify]: Simplify -1 into -1
5.618 * [taylor]: Taking taylor expansion of k in n
5.618 * [backup-simplify]: Simplify k into k
5.618 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
5.618 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
5.618 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
5.618 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
5.618 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
5.618 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
5.618 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
5.618 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
5.618 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.618 * [taylor]: Taking taylor expansion of 1/2 in n
5.619 * [backup-simplify]: Simplify 1/2 into 1/2
5.619 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.619 * [taylor]: Taking taylor expansion of k in n
5.619 * [backup-simplify]: Simplify k into k
5.619 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.619 * [taylor]: Taking taylor expansion of 1/2 in n
5.619 * [backup-simplify]: Simplify 1/2 into 1/2
5.619 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.619 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.619 * [taylor]: Taking taylor expansion of -2 in n
5.619 * [backup-simplify]: Simplify -2 into -2
5.619 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.619 * [taylor]: Taking taylor expansion of PI in n
5.619 * [backup-simplify]: Simplify PI into PI
5.619 * [taylor]: Taking taylor expansion of n in n
5.619 * [backup-simplify]: Simplify 0 into 0
5.619 * [backup-simplify]: Simplify 1 into 1
5.620 * [backup-simplify]: Simplify (/ PI 1) into PI
5.620 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.621 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.621 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.622 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
5.623 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.624 * [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)))
5.625 * [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))))
5.626 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
5.626 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k
5.626 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.626 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.626 * [taylor]: Taking taylor expansion of -1 in k
5.626 * [backup-simplify]: Simplify -1 into -1
5.626 * [taylor]: Taking taylor expansion of k in k
5.626 * [backup-simplify]: Simplify 0 into 0
5.626 * [backup-simplify]: Simplify 1 into 1
5.627 * [backup-simplify]: Simplify (/ -1 1) into -1
5.627 * [backup-simplify]: Simplify (sqrt 0) into 0
5.628 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.628 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
5.628 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
5.628 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
5.628 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
5.628 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.628 * [taylor]: Taking taylor expansion of 1/2 in k
5.628 * [backup-simplify]: Simplify 1/2 into 1/2
5.628 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.628 * [taylor]: Taking taylor expansion of k in k
5.628 * [backup-simplify]: Simplify 0 into 0
5.628 * [backup-simplify]: Simplify 1 into 1
5.628 * [backup-simplify]: Simplify (/ 1 1) into 1
5.628 * [taylor]: Taking taylor expansion of 1/2 in k
5.628 * [backup-simplify]: Simplify 1/2 into 1/2
5.628 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.628 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.628 * [taylor]: Taking taylor expansion of -2 in k
5.628 * [backup-simplify]: Simplify -2 into -2
5.628 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.628 * [taylor]: Taking taylor expansion of PI in k
5.628 * [backup-simplify]: Simplify PI into PI
5.628 * [taylor]: Taking taylor expansion of n in k
5.629 * [backup-simplify]: Simplify n into n
5.629 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.629 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.629 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.629 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.629 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.629 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.629 * [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)))
5.630 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
5.630 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k
5.630 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.630 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.630 * [taylor]: Taking taylor expansion of -1 in k
5.630 * [backup-simplify]: Simplify -1 into -1
5.630 * [taylor]: Taking taylor expansion of k in k
5.630 * [backup-simplify]: Simplify 0 into 0
5.630 * [backup-simplify]: Simplify 1 into 1
5.630 * [backup-simplify]: Simplify (/ -1 1) into -1
5.630 * [backup-simplify]: Simplify (sqrt 0) into 0
5.631 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.631 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
5.631 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
5.631 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
5.631 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
5.631 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.631 * [taylor]: Taking taylor expansion of 1/2 in k
5.631 * [backup-simplify]: Simplify 1/2 into 1/2
5.631 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.631 * [taylor]: Taking taylor expansion of k in k
5.631 * [backup-simplify]: Simplify 0 into 0
5.631 * [backup-simplify]: Simplify 1 into 1
5.632 * [backup-simplify]: Simplify (/ 1 1) into 1
5.632 * [taylor]: Taking taylor expansion of 1/2 in k
5.632 * [backup-simplify]: Simplify 1/2 into 1/2
5.632 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.632 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.632 * [taylor]: Taking taylor expansion of -2 in k
5.632 * [backup-simplify]: Simplify -2 into -2
5.632 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.632 * [taylor]: Taking taylor expansion of PI in k
5.632 * [backup-simplify]: Simplify PI into PI
5.632 * [taylor]: Taking taylor expansion of n in k
5.632 * [backup-simplify]: Simplify n into n
5.632 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.632 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.632 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.632 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.632 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.632 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.633 * [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)))
5.633 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
5.633 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
5.633 * [taylor]: Taking taylor expansion of +nan.0 in n
5.633 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.633 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n
5.633 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
5.633 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.633 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.633 * [taylor]: Taking taylor expansion of -2 in n
5.633 * [backup-simplify]: Simplify -2 into -2
5.633 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.633 * [taylor]: Taking taylor expansion of PI in n
5.633 * [backup-simplify]: Simplify PI into PI
5.633 * [taylor]: Taking taylor expansion of n in n
5.633 * [backup-simplify]: Simplify 0 into 0
5.633 * [backup-simplify]: Simplify 1 into 1
5.633 * [backup-simplify]: Simplify (/ PI 1) into PI
5.634 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.634 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.634 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
5.634 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.634 * [taylor]: Taking taylor expansion of 1/2 in n
5.634 * [backup-simplify]: Simplify 1/2 into 1/2
5.634 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.634 * [taylor]: Taking taylor expansion of k in n
5.634 * [backup-simplify]: Simplify k into k
5.635 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.635 * [taylor]: Taking taylor expansion of 1/2 in n
5.635 * [backup-simplify]: Simplify 1/2 into 1/2
5.635 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.636 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.636 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
5.636 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
5.637 * [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))))
5.638 * [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)))))
5.639 * [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)))))
5.639 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
5.641 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.642 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))
5.642 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n
5.642 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
5.642 * [taylor]: Taking taylor expansion of +nan.0 in n
5.642 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.642 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
5.642 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n
5.642 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
5.642 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.642 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.642 * [taylor]: Taking taylor expansion of -2 in n
5.642 * [backup-simplify]: Simplify -2 into -2
5.642 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.642 * [taylor]: Taking taylor expansion of PI in n
5.642 * [backup-simplify]: Simplify PI into PI
5.642 * [taylor]: Taking taylor expansion of n in n
5.642 * [backup-simplify]: Simplify 0 into 0
5.642 * [backup-simplify]: Simplify 1 into 1
5.642 * [backup-simplify]: Simplify (/ PI 1) into PI
5.643 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.643 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.643 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
5.643 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.643 * [taylor]: Taking taylor expansion of 1/2 in n
5.643 * [backup-simplify]: Simplify 1/2 into 1/2
5.643 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.643 * [taylor]: Taking taylor expansion of k in n
5.643 * [backup-simplify]: Simplify k into k
5.643 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.643 * [taylor]: Taking taylor expansion of 1/2 in n
5.643 * [backup-simplify]: Simplify 1/2 into 1/2
5.644 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.645 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.645 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
5.645 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
5.646 * [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))))
5.647 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
5.648 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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)))))
5.649 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
5.649 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
5.650 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.651 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.651 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
5.651 * [backup-simplify]: Simplify (+ 0 0) into 0
5.652 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.652 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.653 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
5.655 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
5.657 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
5.661 * [backup-simplify]: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0
5.661 * [backup-simplify]: Simplify 0 into 0
5.662 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.667 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.668 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))
5.668 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n
5.668 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
5.668 * [taylor]: Taking taylor expansion of +nan.0 in n
5.668 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.668 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
5.668 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n
5.668 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
5.668 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.668 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.668 * [taylor]: Taking taylor expansion of -2 in n
5.668 * [backup-simplify]: Simplify -2 into -2
5.668 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.668 * [taylor]: Taking taylor expansion of PI in n
5.668 * [backup-simplify]: Simplify PI into PI
5.668 * [taylor]: Taking taylor expansion of n in n
5.668 * [backup-simplify]: Simplify 0 into 0
5.668 * [backup-simplify]: Simplify 1 into 1
5.669 * [backup-simplify]: Simplify (/ PI 1) into PI
5.670 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.671 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.671 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
5.671 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.671 * [taylor]: Taking taylor expansion of 1/2 in n
5.671 * [backup-simplify]: Simplify 1/2 into 1/2
5.671 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.671 * [taylor]: Taking taylor expansion of k in n
5.671 * [backup-simplify]: Simplify k into k
5.671 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.671 * [taylor]: Taking taylor expansion of 1/2 in n
5.671 * [backup-simplify]: Simplify 1/2 into 1/2
5.673 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.673 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.673 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
5.675 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
5.676 * [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))))
5.677 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
5.679 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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)))))
5.680 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
5.681 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
5.686 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
5.686 * * * * [progress]: [ 4 / 4 ] generating series at (2)
5.687 * [backup-simplify]: Simplify (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))))
5.687 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0
5.687 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
5.687 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
5.687 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.687 * [taylor]: Taking taylor expansion of k in n
5.687 * [backup-simplify]: Simplify k into k
5.687 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.687 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
5.687 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.688 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
5.688 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
5.688 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
5.688 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
5.688 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
5.688 * [taylor]: Taking taylor expansion of 1/2 in n
5.688 * [backup-simplify]: Simplify 1/2 into 1/2
5.688 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
5.688 * [taylor]: Taking taylor expansion of 1/2 in n
5.688 * [backup-simplify]: Simplify 1/2 into 1/2
5.688 * [taylor]: Taking taylor expansion of k in n
5.688 * [backup-simplify]: Simplify k into k
5.688 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.688 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.688 * [taylor]: Taking taylor expansion of 2 in n
5.688 * [backup-simplify]: Simplify 2 into 2
5.688 * [taylor]: Taking taylor expansion of (* n PI) in n
5.688 * [taylor]: Taking taylor expansion of n in n
5.688 * [backup-simplify]: Simplify 0 into 0
5.688 * [backup-simplify]: Simplify 1 into 1
5.688 * [taylor]: Taking taylor expansion of PI in n
5.688 * [backup-simplify]: Simplify PI into PI
5.689 * [backup-simplify]: Simplify (* 0 PI) into 0
5.689 * [backup-simplify]: Simplify (* 2 0) into 0
5.691 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.693 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.694 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.695 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
5.695 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
5.695 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
5.696 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.698 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
5.699 * [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)))))
5.699 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
5.699 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.699 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.699 * [taylor]: Taking taylor expansion of k in k
5.699 * [backup-simplify]: Simplify 0 into 0
5.699 * [backup-simplify]: Simplify 1 into 1
5.700 * [backup-simplify]: Simplify (/ 1 1) into 1
5.700 * [backup-simplify]: Simplify (sqrt 0) into 0
5.702 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.702 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
5.702 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
5.702 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
5.702 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
5.702 * [taylor]: Taking taylor expansion of 1/2 in k
5.702 * [backup-simplify]: Simplify 1/2 into 1/2
5.702 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
5.702 * [taylor]: Taking taylor expansion of 1/2 in k
5.702 * [backup-simplify]: Simplify 1/2 into 1/2
5.702 * [taylor]: Taking taylor expansion of k in k
5.702 * [backup-simplify]: Simplify 0 into 0
5.702 * [backup-simplify]: Simplify 1 into 1
5.702 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.702 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.703 * [taylor]: Taking taylor expansion of 2 in k
5.703 * [backup-simplify]: Simplify 2 into 2
5.703 * [taylor]: Taking taylor expansion of (* n PI) in k
5.703 * [taylor]: Taking taylor expansion of n in k
5.703 * [backup-simplify]: Simplify n into n
5.703 * [taylor]: Taking taylor expansion of PI in k
5.703 * [backup-simplify]: Simplify PI into PI
5.703 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.703 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.703 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.703 * [backup-simplify]: Simplify (* 1/2 0) into 0
5.704 * [backup-simplify]: Simplify (- 0) into 0
5.704 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.705 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.705 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.705 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
5.705 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.705 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.705 * [taylor]: Taking taylor expansion of k in k
5.705 * [backup-simplify]: Simplify 0 into 0
5.705 * [backup-simplify]: Simplify 1 into 1
5.705 * [backup-simplify]: Simplify (/ 1 1) into 1
5.706 * [backup-simplify]: Simplify (sqrt 0) into 0
5.707 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.707 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
5.707 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
5.707 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
5.707 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
5.707 * [taylor]: Taking taylor expansion of 1/2 in k
5.707 * [backup-simplify]: Simplify 1/2 into 1/2
5.707 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
5.707 * [taylor]: Taking taylor expansion of 1/2 in k
5.708 * [backup-simplify]: Simplify 1/2 into 1/2
5.708 * [taylor]: Taking taylor expansion of k in k
5.708 * [backup-simplify]: Simplify 0 into 0
5.708 * [backup-simplify]: Simplify 1 into 1
5.708 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.708 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.708 * [taylor]: Taking taylor expansion of 2 in k
5.708 * [backup-simplify]: Simplify 2 into 2
5.708 * [taylor]: Taking taylor expansion of (* n PI) in k
5.708 * [taylor]: Taking taylor expansion of n in k
5.708 * [backup-simplify]: Simplify n into n
5.708 * [taylor]: Taking taylor expansion of PI in k
5.708 * [backup-simplify]: Simplify PI into PI
5.708 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.708 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.708 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.709 * [backup-simplify]: Simplify (* 1/2 0) into 0
5.709 * [backup-simplify]: Simplify (- 0) into 0
5.709 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.710 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.710 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.710 * [backup-simplify]: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0
5.710 * [taylor]: Taking taylor expansion of 0 in n
5.710 * [backup-simplify]: Simplify 0 into 0
5.710 * [backup-simplify]: Simplify 0 into 0
5.711 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
5.711 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
5.712 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
5.713 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
5.714 * [backup-simplify]: Simplify (- 1/2) into -1/2
5.714 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
5.715 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
5.715 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))
5.715 * [backup-simplify]: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
5.715 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
5.715 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
5.715 * [taylor]: Taking taylor expansion of +nan.0 in n
5.716 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.716 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
5.716 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.716 * [taylor]: Taking taylor expansion of 2 in n
5.716 * [backup-simplify]: Simplify 2 into 2
5.716 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.717 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.717 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.717 * [taylor]: Taking taylor expansion of (* n PI) in n
5.717 * [taylor]: Taking taylor expansion of n in n
5.717 * [backup-simplify]: Simplify 0 into 0
5.717 * [backup-simplify]: Simplify 1 into 1
5.717 * [taylor]: Taking taylor expansion of PI in n
5.717 * [backup-simplify]: Simplify PI into PI
5.721 * [backup-simplify]: Simplify (* 0 PI) into 0
5.723 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.724 * [backup-simplify]: Simplify (sqrt 0) into 0
5.725 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.726 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
5.726 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.727 * [backup-simplify]: Simplify (- 0) into 0
5.727 * [backup-simplify]: Simplify 0 into 0
5.727 * [backup-simplify]: Simplify 0 into 0
5.728 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
5.729 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
5.730 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
5.731 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
5.731 * [backup-simplify]: Simplify (- 0) into 0
5.731 * [backup-simplify]: Simplify (+ 0 0) into 0
5.732 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
5.732 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))
5.733 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.735 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.735 * [backup-simplify]: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))
5.735 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n
5.735 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n
5.735 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
5.735 * [taylor]: Taking taylor expansion of +nan.0 in n
5.735 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.735 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
5.735 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
5.735 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.735 * [taylor]: Taking taylor expansion of 2 in n
5.735 * [backup-simplify]: Simplify 2 into 2
5.736 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.736 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.736 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.736 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.736 * [taylor]: Taking taylor expansion of 2 in n
5.736 * [backup-simplify]: Simplify 2 into 2
5.736 * [taylor]: Taking taylor expansion of (* n PI) in n
5.736 * [taylor]: Taking taylor expansion of n in n
5.736 * [backup-simplify]: Simplify 0 into 0
5.736 * [backup-simplify]: Simplify 1 into 1
5.736 * [taylor]: Taking taylor expansion of PI in n
5.736 * [backup-simplify]: Simplify PI into PI
5.737 * [backup-simplify]: Simplify (* 0 PI) into 0
5.737 * [backup-simplify]: Simplify (* 2 0) into 0
5.738 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.739 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.740 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.740 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.740 * [taylor]: Taking taylor expansion of (* n PI) in n
5.740 * [taylor]: Taking taylor expansion of n in n
5.740 * [backup-simplify]: Simplify 0 into 0
5.740 * [backup-simplify]: Simplify 1 into 1
5.740 * [taylor]: Taking taylor expansion of PI in n
5.740 * [backup-simplify]: Simplify PI into PI
5.740 * [backup-simplify]: Simplify (* 0 PI) into 0
5.741 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.741 * [backup-simplify]: Simplify (sqrt 0) into 0
5.742 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.742 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
5.742 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
5.742 * [taylor]: Taking taylor expansion of +nan.0 in n
5.742 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.742 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
5.742 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.742 * [taylor]: Taking taylor expansion of 2 in n
5.742 * [backup-simplify]: Simplify 2 into 2
5.743 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.743 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.743 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.743 * [taylor]: Taking taylor expansion of (* n PI) in n
5.743 * [taylor]: Taking taylor expansion of n in n
5.743 * [backup-simplify]: Simplify 0 into 0
5.743 * [backup-simplify]: Simplify 1 into 1
5.743 * [taylor]: Taking taylor expansion of PI in n
5.743 * [backup-simplify]: Simplify PI into PI
5.743 * [backup-simplify]: Simplify (* 0 PI) into 0
5.744 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.745 * [backup-simplify]: Simplify (sqrt 0) into 0
5.745 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.746 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.747 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
5.748 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
5.749 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.749 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
5.749 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.749 * [backup-simplify]: Simplify (- 0) into 0
5.750 * [backup-simplify]: Simplify (+ 0 0) into 0
5.750 * [backup-simplify]: Simplify (- 0) into 0
5.750 * [backup-simplify]: Simplify 0 into 0
5.752 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
5.756 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
5.759 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
5.761 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
5.762 * [backup-simplify]: Simplify 0 into 0
5.763 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.764 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
5.767 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0
5.768 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
5.769 * [backup-simplify]: Simplify (- 0) into 0
5.769 * [backup-simplify]: Simplify (+ 0 0) into 0
5.771 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
5.772 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))
5.773 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.776 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.777 * [backup-simplify]: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))))
5.777 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n
5.777 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n
5.777 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
5.777 * [taylor]: Taking taylor expansion of +nan.0 in n
5.777 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.777 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
5.777 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
5.777 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.777 * [taylor]: Taking taylor expansion of 2 in n
5.777 * [backup-simplify]: Simplify 2 into 2
5.777 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.778 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.778 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.778 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.778 * [taylor]: Taking taylor expansion of 2 in n
5.778 * [backup-simplify]: Simplify 2 into 2
5.778 * [taylor]: Taking taylor expansion of (* n PI) in n
5.778 * [taylor]: Taking taylor expansion of n in n
5.778 * [backup-simplify]: Simplify 0 into 0
5.778 * [backup-simplify]: Simplify 1 into 1
5.778 * [taylor]: Taking taylor expansion of PI in n
5.778 * [backup-simplify]: Simplify PI into PI
5.778 * [backup-simplify]: Simplify (* 0 PI) into 0
5.779 * [backup-simplify]: Simplify (* 2 0) into 0
5.780 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.781 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.781 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.782 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.782 * [taylor]: Taking taylor expansion of (* n PI) in n
5.782 * [taylor]: Taking taylor expansion of n in n
5.782 * [backup-simplify]: Simplify 0 into 0
5.782 * [backup-simplify]: Simplify 1 into 1
5.782 * [taylor]: Taking taylor expansion of PI in n
5.782 * [backup-simplify]: Simplify PI into PI
5.782 * [backup-simplify]: Simplify (* 0 PI) into 0
5.783 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.783 * [backup-simplify]: Simplify (sqrt 0) into 0
5.784 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.784 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n
5.784 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n
5.784 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
5.784 * [taylor]: Taking taylor expansion of +nan.0 in n
5.784 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.784 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
5.784 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
5.784 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.784 * [taylor]: Taking taylor expansion of 2 in n
5.784 * [backup-simplify]: Simplify 2 into 2
5.785 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.785 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.785 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
5.785 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.785 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.785 * [taylor]: Taking taylor expansion of 2 in n
5.785 * [backup-simplify]: Simplify 2 into 2
5.785 * [taylor]: Taking taylor expansion of (* n PI) in n
5.785 * [taylor]: Taking taylor expansion of n in n
5.785 * [backup-simplify]: Simplify 0 into 0
5.785 * [backup-simplify]: Simplify 1 into 1
5.785 * [taylor]: Taking taylor expansion of PI in n
5.785 * [backup-simplify]: Simplify PI into PI
5.785 * [backup-simplify]: Simplify (* 0 PI) into 0
5.786 * [backup-simplify]: Simplify (* 2 0) into 0
5.787 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.788 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.789 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.790 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.790 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.790 * [taylor]: Taking taylor expansion of (* n PI) in n
5.790 * [taylor]: Taking taylor expansion of n in n
5.790 * [backup-simplify]: Simplify 0 into 0
5.790 * [backup-simplify]: Simplify 1 into 1
5.790 * [taylor]: Taking taylor expansion of PI in n
5.790 * [backup-simplify]: Simplify PI into PI
5.791 * [backup-simplify]: Simplify (* 0 PI) into 0
5.792 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.792 * [backup-simplify]: Simplify (sqrt 0) into 0
5.793 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.793 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
5.793 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
5.793 * [taylor]: Taking taylor expansion of +nan.0 in n
5.793 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.793 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
5.793 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.793 * [taylor]: Taking taylor expansion of 2 in n
5.793 * [backup-simplify]: Simplify 2 into 2
5.793 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.794 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.794 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.794 * [taylor]: Taking taylor expansion of (* n PI) in n
5.794 * [taylor]: Taking taylor expansion of n in n
5.794 * [backup-simplify]: Simplify 0 into 0
5.794 * [backup-simplify]: Simplify 1 into 1
5.794 * [taylor]: Taking taylor expansion of PI in n
5.794 * [backup-simplify]: Simplify PI into PI
5.794 * [backup-simplify]: Simplify (* 0 PI) into 0
5.795 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.795 * [backup-simplify]: Simplify (sqrt 0) into 0
5.796 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.797 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.798 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
5.799 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
5.799 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.800 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.801 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.803 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
5.805 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
5.806 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
5.807 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.807 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
5.808 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.808 * [backup-simplify]: Simplify (- 0) into 0
5.809 * [backup-simplify]: Simplify (+ 0 0) into 0
5.809 * [backup-simplify]: Simplify (- 0) into 0
5.809 * [backup-simplify]: Simplify (+ 0 0) into 0
5.810 * [backup-simplify]: Simplify (- 0) into 0
5.810 * [backup-simplify]: Simplify 0 into 0
5.811 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.813 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.814 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.816 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.818 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
5.820 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
5.827 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
5.830 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
5.840 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
5.844 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
5.852 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))
5.857 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))))
5.861 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))))
5.862 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.865 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
5.866 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
5.869 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
5.875 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
5.878 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
5.880 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
5.889 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
5.889 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
5.890 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0
5.890 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
5.890 * [taylor]: Taking taylor expansion of (sqrt k) in n
5.890 * [taylor]: Taking taylor expansion of k in n
5.890 * [backup-simplify]: Simplify k into k
5.890 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
5.890 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
5.890 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
5.890 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.890 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.890 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
5.890 * [taylor]: Taking taylor expansion of 1/2 in n
5.890 * [backup-simplify]: Simplify 1/2 into 1/2
5.890 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.890 * [taylor]: Taking taylor expansion of 1/2 in n
5.890 * [backup-simplify]: Simplify 1/2 into 1/2
5.890 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.890 * [taylor]: Taking taylor expansion of k in n
5.890 * [backup-simplify]: Simplify k into k
5.890 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.890 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.890 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.890 * [taylor]: Taking taylor expansion of 2 in n
5.890 * [backup-simplify]: Simplify 2 into 2
5.890 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.890 * [taylor]: Taking taylor expansion of PI in n
5.890 * [backup-simplify]: Simplify PI into PI
5.890 * [taylor]: Taking taylor expansion of n in n
5.890 * [backup-simplify]: Simplify 0 into 0
5.890 * [backup-simplify]: Simplify 1 into 1
5.890 * [backup-simplify]: Simplify (/ PI 1) into PI
5.891 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.891 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.891 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.891 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
5.892 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
5.892 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.893 * [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)))
5.894 * [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))))
5.894 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
5.894 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.894 * [taylor]: Taking taylor expansion of k in k
5.894 * [backup-simplify]: Simplify 0 into 0
5.894 * [backup-simplify]: Simplify 1 into 1
5.894 * [backup-simplify]: Simplify (sqrt 0) into 0
5.895 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.895 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
5.895 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.895 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.895 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
5.895 * [taylor]: Taking taylor expansion of 1/2 in k
5.895 * [backup-simplify]: Simplify 1/2 into 1/2
5.895 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.895 * [taylor]: Taking taylor expansion of 1/2 in k
5.895 * [backup-simplify]: Simplify 1/2 into 1/2
5.895 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.895 * [taylor]: Taking taylor expansion of k in k
5.895 * [backup-simplify]: Simplify 0 into 0
5.895 * [backup-simplify]: Simplify 1 into 1
5.896 * [backup-simplify]: Simplify (/ 1 1) into 1
5.896 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.896 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.896 * [taylor]: Taking taylor expansion of 2 in k
5.896 * [backup-simplify]: Simplify 2 into 2
5.896 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.896 * [taylor]: Taking taylor expansion of PI in k
5.896 * [backup-simplify]: Simplify PI into PI
5.896 * [taylor]: Taking taylor expansion of n in k
5.896 * [backup-simplify]: Simplify n into n
5.896 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.896 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.896 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.896 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.897 * [backup-simplify]: Simplify (- 1/2) into -1/2
5.897 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
5.897 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.897 * [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))))
5.897 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
5.897 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.897 * [taylor]: Taking taylor expansion of k in k
5.897 * [backup-simplify]: Simplify 0 into 0
5.897 * [backup-simplify]: Simplify 1 into 1
5.897 * [backup-simplify]: Simplify (sqrt 0) into 0
5.898 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.898 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
5.898 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.898 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.898 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
5.898 * [taylor]: Taking taylor expansion of 1/2 in k
5.898 * [backup-simplify]: Simplify 1/2 into 1/2
5.898 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.898 * [taylor]: Taking taylor expansion of 1/2 in k
5.898 * [backup-simplify]: Simplify 1/2 into 1/2
5.898 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.898 * [taylor]: Taking taylor expansion of k in k
5.898 * [backup-simplify]: Simplify 0 into 0
5.898 * [backup-simplify]: Simplify 1 into 1
5.899 * [backup-simplify]: Simplify (/ 1 1) into 1
5.899 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.899 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.899 * [taylor]: Taking taylor expansion of 2 in k
5.899 * [backup-simplify]: Simplify 2 into 2
5.899 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.899 * [taylor]: Taking taylor expansion of PI in k
5.899 * [backup-simplify]: Simplify PI into PI
5.899 * [taylor]: Taking taylor expansion of n in k
5.899 * [backup-simplify]: Simplify n into n
5.899 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.899 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.899 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.899 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.899 * [backup-simplify]: Simplify (- 1/2) into -1/2
5.900 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
5.900 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.900 * [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))))
5.900 * [backup-simplify]: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0
5.900 * [taylor]: Taking taylor expansion of 0 in n
5.900 * [backup-simplify]: Simplify 0 into 0
5.900 * [backup-simplify]: Simplify 0 into 0
5.901 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))
5.901 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n
5.901 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
5.901 * [taylor]: Taking taylor expansion of +nan.0 in n
5.901 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.901 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
5.901 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.901 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.901 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
5.901 * [taylor]: Taking taylor expansion of 1/2 in n
5.901 * [backup-simplify]: Simplify 1/2 into 1/2
5.901 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.901 * [taylor]: Taking taylor expansion of 1/2 in n
5.901 * [backup-simplify]: Simplify 1/2 into 1/2
5.901 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.901 * [taylor]: Taking taylor expansion of k in n
5.901 * [backup-simplify]: Simplify k into k
5.901 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.901 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.901 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.901 * [taylor]: Taking taylor expansion of 2 in n
5.901 * [backup-simplify]: Simplify 2 into 2
5.901 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.901 * [taylor]: Taking taylor expansion of PI in n
5.901 * [backup-simplify]: Simplify PI into PI
5.901 * [taylor]: Taking taylor expansion of n in n
5.901 * [backup-simplify]: Simplify 0 into 0
5.901 * [backup-simplify]: Simplify 1 into 1
5.901 * [backup-simplify]: Simplify (/ PI 1) into PI
5.902 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.903 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.903 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.903 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
5.903 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
5.905 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.906 * [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)))
5.907 * [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))))
5.908 * [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)))))
5.910 * [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))))))
5.911 * [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))))))
5.911 * [backup-simplify]: Simplify 0 into 0
5.914 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.915 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))
5.915 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n
5.915 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
5.915 * [taylor]: Taking taylor expansion of +nan.0 in n
5.915 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.915 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
5.915 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.915 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.915 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
5.915 * [taylor]: Taking taylor expansion of 1/2 in n
5.915 * [backup-simplify]: Simplify 1/2 into 1/2
5.915 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.915 * [taylor]: Taking taylor expansion of 1/2 in n
5.915 * [backup-simplify]: Simplify 1/2 into 1/2
5.915 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.915 * [taylor]: Taking taylor expansion of k in n
5.915 * [backup-simplify]: Simplify k into k
5.916 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.916 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.916 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.916 * [taylor]: Taking taylor expansion of 2 in n
5.916 * [backup-simplify]: Simplify 2 into 2
5.916 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.916 * [taylor]: Taking taylor expansion of PI in n
5.916 * [backup-simplify]: Simplify PI into PI
5.916 * [taylor]: Taking taylor expansion of n in n
5.916 * [backup-simplify]: Simplify 0 into 0
5.916 * [backup-simplify]: Simplify 1 into 1
5.916 * [backup-simplify]: Simplify (/ PI 1) into PI
5.917 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.918 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.918 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.918 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
5.918 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
5.920 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.921 * [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)))
5.922 * [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))))
5.923 * [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)))))
5.925 * [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))))))
5.926 * [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))))))
5.927 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.928 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.930 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.930 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.930 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
5.931 * [backup-simplify]: Simplify (- 0) into 0
5.931 * [backup-simplify]: Simplify (+ 0 0) into 0
5.933 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.934 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.937 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
5.938 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
5.939 * [backup-simplify]: Simplify (- 0) into 0
5.939 * [backup-simplify]: Simplify 0 into 0
5.939 * [backup-simplify]: Simplify 0 into 0
5.946 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.948 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))
5.948 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n
5.948 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
5.948 * [taylor]: Taking taylor expansion of +nan.0 in n
5.948 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.948 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
5.948 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.948 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.948 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
5.948 * [taylor]: Taking taylor expansion of 1/2 in n
5.948 * [backup-simplify]: Simplify 1/2 into 1/2
5.948 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.948 * [taylor]: Taking taylor expansion of 1/2 in n
5.948 * [backup-simplify]: Simplify 1/2 into 1/2
5.948 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.948 * [taylor]: Taking taylor expansion of k in n
5.948 * [backup-simplify]: Simplify k into k
5.948 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.948 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.948 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.948 * [taylor]: Taking taylor expansion of 2 in n
5.948 * [backup-simplify]: Simplify 2 into 2
5.948 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.948 * [taylor]: Taking taylor expansion of PI in n
5.948 * [backup-simplify]: Simplify PI into PI
5.948 * [taylor]: Taking taylor expansion of n in n
5.948 * [backup-simplify]: Simplify 0 into 0
5.949 * [backup-simplify]: Simplify 1 into 1
5.949 * [backup-simplify]: Simplify (/ PI 1) into PI
5.950 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.951 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.951 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.951 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
5.951 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
5.952 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.954 * [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)))
5.955 * [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))))
5.956 * [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)))))
5.958 * [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))))))
5.959 * [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))))))
5.964 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) 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))))))))
5.965 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
5.965 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0
5.965 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
5.965 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
5.965 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
5.965 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
5.965 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
5.965 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.965 * [taylor]: Taking taylor expansion of 1/2 in n
5.965 * [backup-simplify]: Simplify 1/2 into 1/2
5.965 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.965 * [taylor]: Taking taylor expansion of k in n
5.965 * [backup-simplify]: Simplify k into k
5.965 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.965 * [taylor]: Taking taylor expansion of 1/2 in n
5.965 * [backup-simplify]: Simplify 1/2 into 1/2
5.965 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.965 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.965 * [taylor]: Taking taylor expansion of -2 in n
5.965 * [backup-simplify]: Simplify -2 into -2
5.965 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.965 * [taylor]: Taking taylor expansion of PI in n
5.965 * [backup-simplify]: Simplify PI into PI
5.965 * [taylor]: Taking taylor expansion of n in n
5.965 * [backup-simplify]: Simplify 0 into 0
5.965 * [backup-simplify]: Simplify 1 into 1
5.966 * [backup-simplify]: Simplify (/ PI 1) into PI
5.966 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.968 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.968 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.968 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
5.970 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.971 * [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)))
5.973 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
5.973 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
5.973 * [taylor]: Taking taylor expansion of (/ -1 k) in n
5.973 * [taylor]: Taking taylor expansion of -1 in n
5.973 * [backup-simplify]: Simplify -1 into -1
5.973 * [taylor]: Taking taylor expansion of k in n
5.973 * [backup-simplify]: Simplify k into k
5.973 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
5.973 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
5.973 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
5.973 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
5.974 * [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)))
5.975 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
5.975 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
5.975 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
5.975 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
5.975 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
5.975 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.975 * [taylor]: Taking taylor expansion of 1/2 in k
5.975 * [backup-simplify]: Simplify 1/2 into 1/2
5.975 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.975 * [taylor]: Taking taylor expansion of k in k
5.975 * [backup-simplify]: Simplify 0 into 0
5.975 * [backup-simplify]: Simplify 1 into 1
5.975 * [backup-simplify]: Simplify (/ 1 1) into 1
5.975 * [taylor]: Taking taylor expansion of 1/2 in k
5.975 * [backup-simplify]: Simplify 1/2 into 1/2
5.975 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.975 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.975 * [taylor]: Taking taylor expansion of -2 in k
5.975 * [backup-simplify]: Simplify -2 into -2
5.975 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.975 * [taylor]: Taking taylor expansion of PI in k
5.975 * [backup-simplify]: Simplify PI into PI
5.975 * [taylor]: Taking taylor expansion of n in k
5.976 * [backup-simplify]: Simplify n into n
5.976 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.976 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.976 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.976 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.977 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.977 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.977 * [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)))
5.977 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.977 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.977 * [taylor]: Taking taylor expansion of -1 in k
5.977 * [backup-simplify]: Simplify -1 into -1
5.977 * [taylor]: Taking taylor expansion of k in k
5.977 * [backup-simplify]: Simplify 0 into 0
5.977 * [backup-simplify]: Simplify 1 into 1
5.978 * [backup-simplify]: Simplify (/ -1 1) into -1
5.978 * [backup-simplify]: Simplify (sqrt 0) into 0
5.979 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.980 * [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))))
5.980 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
5.980 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
5.980 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
5.980 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
5.980 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
5.980 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.980 * [taylor]: Taking taylor expansion of 1/2 in k
5.980 * [backup-simplify]: Simplify 1/2 into 1/2
5.980 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.980 * [taylor]: Taking taylor expansion of k in k
5.980 * [backup-simplify]: Simplify 0 into 0
5.980 * [backup-simplify]: Simplify 1 into 1
5.980 * [backup-simplify]: Simplify (/ 1 1) into 1
5.980 * [taylor]: Taking taylor expansion of 1/2 in k
5.980 * [backup-simplify]: Simplify 1/2 into 1/2
5.980 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.980 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.981 * [taylor]: Taking taylor expansion of -2 in k
5.981 * [backup-simplify]: Simplify -2 into -2
5.981 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.981 * [taylor]: Taking taylor expansion of PI in k
5.981 * [backup-simplify]: Simplify PI into PI
5.981 * [taylor]: Taking taylor expansion of n in k
5.981 * [backup-simplify]: Simplify n into n
5.981 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.981 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.981 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.981 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.982 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.982 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.983 * [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)))
5.983 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.983 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.983 * [taylor]: Taking taylor expansion of -1 in k
5.983 * [backup-simplify]: Simplify -1 into -1
5.983 * [taylor]: Taking taylor expansion of k in k
5.983 * [backup-simplify]: Simplify 0 into 0
5.983 * [backup-simplify]: Simplify 1 into 1
5.983 * [backup-simplify]: Simplify (/ -1 1) into -1
5.984 * [backup-simplify]: Simplify (sqrt 0) into 0
5.985 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.985 * [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))))
5.985 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
5.985 * [taylor]: Taking taylor expansion of +nan.0 in n
5.985 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.985 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n
5.986 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
5.986 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.986 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.986 * [taylor]: Taking taylor expansion of -2 in n
5.986 * [backup-simplify]: Simplify -2 into -2
5.986 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.986 * [taylor]: Taking taylor expansion of PI in n
5.986 * [backup-simplify]: Simplify PI into PI
5.986 * [taylor]: Taking taylor expansion of n in n
5.986 * [backup-simplify]: Simplify 0 into 0
5.986 * [backup-simplify]: Simplify 1 into 1
5.986 * [backup-simplify]: Simplify (/ PI 1) into PI
5.987 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.988 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.988 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
5.988 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.988 * [taylor]: Taking taylor expansion of 1/2 in n
5.988 * [backup-simplify]: Simplify 1/2 into 1/2
5.988 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.988 * [taylor]: Taking taylor expansion of k in n
5.988 * [backup-simplify]: Simplify k into k
5.988 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.988 * [taylor]: Taking taylor expansion of 1/2 in n
5.988 * [backup-simplify]: Simplify 1/2 into 1/2
5.990 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.990 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.990 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
5.991 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
5.993 * [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))))
5.994 * [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)))))
5.995 * [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)))))
5.996 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
6.000 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.001 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))
6.001 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
6.001 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
6.001 * [taylor]: Taking taylor expansion of +nan.0 in n
6.001 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.001 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n
6.001 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
6.001 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.001 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.001 * [taylor]: Taking taylor expansion of -2 in n
6.001 * [backup-simplify]: Simplify -2 into -2
6.001 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.001 * [taylor]: Taking taylor expansion of PI in n
6.001 * [backup-simplify]: Simplify PI into PI
6.002 * [taylor]: Taking taylor expansion of n in n
6.002 * [backup-simplify]: Simplify 0 into 0
6.002 * [backup-simplify]: Simplify 1 into 1
6.002 * [backup-simplify]: Simplify (/ PI 1) into PI
6.003 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.004 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.004 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
6.004 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
6.004 * [taylor]: Taking taylor expansion of 1/2 in n
6.004 * [backup-simplify]: Simplify 1/2 into 1/2
6.004 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.004 * [taylor]: Taking taylor expansion of k in n
6.004 * [backup-simplify]: Simplify k into k
6.004 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.004 * [taylor]: Taking taylor expansion of 1/2 in n
6.004 * [backup-simplify]: Simplify 1/2 into 1/2
6.006 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.006 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
6.006 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
6.007 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
6.009 * [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))))
6.010 * [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)))))
6.011 * [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))))))
6.013 * [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))))))
6.014 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.015 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.015 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
6.015 * [backup-simplify]: Simplify (+ 0 0) into 0
6.016 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.017 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
6.019 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
6.021 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
6.023 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
6.025 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0
6.025 * [backup-simplify]: Simplify 0 into 0
6.026 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.031 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.033 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))
6.033 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
6.033 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
6.033 * [taylor]: Taking taylor expansion of +nan.0 in n
6.033 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.033 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n
6.033 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
6.033 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.033 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.033 * [taylor]: Taking taylor expansion of -2 in n
6.033 * [backup-simplify]: Simplify -2 into -2
6.033 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.033 * [taylor]: Taking taylor expansion of PI in n
6.033 * [backup-simplify]: Simplify PI into PI
6.033 * [taylor]: Taking taylor expansion of n in n
6.033 * [backup-simplify]: Simplify 0 into 0
6.033 * [backup-simplify]: Simplify 1 into 1
6.034 * [backup-simplify]: Simplify (/ PI 1) into PI
6.034 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.036 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.036 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
6.036 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
6.036 * [taylor]: Taking taylor expansion of 1/2 in n
6.036 * [backup-simplify]: Simplify 1/2 into 1/2
6.036 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.036 * [taylor]: Taking taylor expansion of k in n
6.036 * [backup-simplify]: Simplify k into k
6.036 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.036 * [taylor]: Taking taylor expansion of 1/2 in n
6.036 * [backup-simplify]: Simplify 1/2 into 1/2
6.038 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.038 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
6.038 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
6.039 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
6.040 * [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))))
6.042 * [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)))))
6.044 * [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))))))
6.045 * [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))))))
6.050 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +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)))))))))))
6.050 * * * [progress]: simplifying candidates
6.050 * * * * [progress]: [ 1 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))))))>
6.050 * * * * [progress]: [ 2 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))))))>
6.050 * * * * [progress]: [ 3 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))))))>
6.050 * * * * [progress]: [ 4 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))))))>
6.050 * * * * [progress]: [ 5 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))))))>
6.050 * * * * [progress]: [ 6 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))))))>
6.050 * * * * [progress]: [ 7 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))))))>
6.050 * * * * [progress]: [ 8 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2))))))>
6.050 * * * * [progress]: [ 9 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))))>
6.051 * * * * [progress]: [ 10 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))))))>
6.051 * * * * [progress]: [ 11 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))))))>
6.051 * * * * [progress]: [ 12 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))))))>
6.051 * * * * [progress]: [ 13 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))))))>
6.051 * * * * [progress]: [ 14 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))))))>
6.051 * * * * [progress]: [ 15 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.051 * * * * [progress]: [ 16 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.051 * * * * [progress]: [ 17 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.051 * * * * [progress]: [ 18 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1))))>
6.051 * * * * [progress]: [ 19 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.051 * * * * [progress]: [ 20 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.051 * * * * [progress]: [ 21 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (* (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))))))))>
6.051 * * * * [progress]: [ 22 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (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))))))))>
6.051 * * * * [progress]: [ 23 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.052 * * * * [progress]: [ 24 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
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6.052 * * * * [progress]: [ 26 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
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6.052 * * * * [progress]: [ 34 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2))))))>
6.052 * * * * [progress]: [ 35 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2))))))>
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6.053 * * * * [progress]: [ 39 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))))))>
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6.053 * * * * [progress]: [ 47 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))))))>
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6.054 * * * * [progress]: [ 53 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (log (exp (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.054 * * * * [progress]: [ 54 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.054 * * * * [progress]: [ 55 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.054 * * * * [progress]: [ 56 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.054 * * * * [progress]: [ 57 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.054 * * * * [progress]: [ 58 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (- (sqrt k)) (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.054 * * * * [progress]: [ 59 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2)) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.054 * * * * [progress]: [ 60 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2)) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.054 * * * * [progress]: [ 61 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2)))) (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.054 * * * * [progress]: [ 62 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
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6.054 * * * * [progress]: [ 64 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.055 * * * * [progress]: [ 65 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.055 * * * * [progress]: [ 66 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2)) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.055 * * * * [progress]: [ 67 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2)) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.055 * * * * [progress]: [ 68 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2)))) (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.055 * * * * [progress]: [ 69 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
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6.055 * * * * [progress]: [ 71 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.056 * * * * [progress]: [ 72 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
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6.056 * * * * [progress]: [ 78 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
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6.057 * * * * [progress]: [ 91 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.057 * * * * [progress]: [ 92 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
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6.058 * * * * [progress]: [ 97 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (* (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))))))))>
6.058 * * * * [progress]: [ 98 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.058 * * * * [progress]: [ 99 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
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6.058 * * * * [progress]: [ 107 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (* (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)))))))>
6.058 * * * * [progress]: [ 108 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.058 * * * * [progress]: [ 109 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) 1) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
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6.059 * * * * [progress]: [ 111 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k))))))>
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6.060 * * * * [progress]: [ 133 / 355 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (log (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.060 * * * * [progress]: [ 134 / 355 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))))))>
6.060 * * * * [progress]: [ 135 / 355 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))))))>
6.060 * * * * [progress]: [ 136 / 355 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))))))>
6.060 * * * * [progress]: [ 137 / 355 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))))))>
6.060 * * * * [progress]: [ 138 / 355 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.061 * * * * [progress]: [ 139 / 355 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (log (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.061 * * * * [progress]: [ 140 / 355 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.061 * * * * [progress]: [ 141 / 355 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.061 * * * * [progress]: [ 142 / 355 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* 1 1) 1) (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.061 * * * * [progress]: [ 143 / 355 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* 1 1) 1) (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.061 * * * * [progress]: [ 144 / 355 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (cbrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (cbrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.061 * * * * [progress]: [ 145 / 355 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.061 * * * * [progress]: [ 146 / 355 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (sqrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.061 * * * * [progress]: [ 147 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (- 1) (- (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.061 * * * * [progress]: [ 148 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.061 * * * * [progress]: [ 149 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.061 * * * * [progress]: [ 150 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.061 * * * * [progress]: [ 151 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.062 * * * * [progress]: [ 152 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.062 * * * * [progress]: [ 153 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.062 * * * * [progress]: [ 154 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.062 * * * * [progress]: [ 155 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.062 * * * * [progress]: [ 156 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.062 * * * * [progress]: [ 157 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.062 * * * * [progress]: [ 158 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.062 * * * * [progress]: [ 159 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2))))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.062 * * * * [progress]: [ 160 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.062 * * * * [progress]: [ 161 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.062 * * * * [progress]: [ 162 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.062 * * * * [progress]: [ 163 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.062 * * * * [progress]: [ 164 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.063 * * * * [progress]: [ 165 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.063 * * * * [progress]: [ 166 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.063 * * * * [progress]: [ 167 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.063 * * * * [progress]: [ 168 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.063 * * * * [progress]: [ 169 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) 1)) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.063 * * * * [progress]: [ 170 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.063 * * * * [progress]: [ 171 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.063 * * * * [progress]: [ 172 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.063 * * * * [progress]: [ 173 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (pow n (- 1/2 (/ k 2))))) (/ (cbrt 1) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.063 * * * * [progress]: [ 174 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.063 * * * * [progress]: [ 175 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.063 * * * * [progress]: [ 176 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) 1)) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.064 * * * * [progress]: [ 177 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.064 * * * * [progress]: [ 178 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.064 * * * * [progress]: [ 179 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.064 * * * * [progress]: [ 180 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.064 * * * * [progress]: [ 181 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.064 * * * * [progress]: [ 182 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.064 * * * * [progress]: [ 183 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) 1)) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.064 * * * * [progress]: [ 184 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.064 * * * * [progress]: [ 185 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.064 * * * * [progress]: [ 186 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.064 * * * * [progress]: [ 187 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (pow n (- 1/2 (/ k 2))))) (/ (cbrt 1) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.064 * * * * [progress]: [ 188 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.064 * * * * [progress]: [ 189 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.065 * * * * [progress]: [ 190 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 1)) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.065 * * * * [progress]: [ 191 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.065 * * * * [progress]: [ 192 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.065 * * * * [progress]: [ 193 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt k)) (/ (cbrt 1) (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.065 * * * * [progress]: [ 194 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (pow (* n (* 2 PI)) (/ k 2)))))>
6.065 * * * * [progress]: [ 195 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.065 * * * * [progress]: [ 196 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.065 * * * * [progress]: [ 197 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.065 * * * * [progress]: [ 198 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.065 * * * * [progress]: [ 199 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.065 * * * * [progress]: [ 200 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.065 * * * * [progress]: [ 201 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.065 * * * * [progress]: [ 202 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.065 * * * * [progress]: [ 203 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.066 * * * * [progress]: [ 204 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.066 * * * * [progress]: [ 205 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.066 * * * * [progress]: [ 206 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2))))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.066 * * * * [progress]: [ 207 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.066 * * * * [progress]: [ 208 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.066 * * * * [progress]: [ 209 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.066 * * * * [progress]: [ 210 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.066 * * * * [progress]: [ 211 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.066 * * * * [progress]: [ 212 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.066 * * * * [progress]: [ 213 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.066 * * * * [progress]: [ 214 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.066 * * * * [progress]: [ 215 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.066 * * * * [progress]: [ 216 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) 1)) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.067 * * * * [progress]: [ 217 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.067 * * * * [progress]: [ 218 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.067 * * * * [progress]: [ 219 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.067 * * * * [progress]: [ 220 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (pow n (- 1/2 (/ k 2))))) (/ (sqrt 1) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.067 * * * * [progress]: [ 221 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.067 * * * * [progress]: [ 222 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.067 * * * * [progress]: [ 223 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) 1)) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.067 * * * * [progress]: [ 224 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.067 * * * * [progress]: [ 225 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.067 * * * * [progress]: [ 226 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.067 * * * * [progress]: [ 227 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.067 * * * * [progress]: [ 228 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.067 * * * * [progress]: [ 229 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.068 * * * * [progress]: [ 230 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) 1)) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.068 * * * * [progress]: [ 231 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.068 * * * * [progress]: [ 232 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.068 * * * * [progress]: [ 233 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.068 * * * * [progress]: [ 234 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (pow n (- 1/2 (/ k 2))))) (/ (sqrt 1) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.068 * * * * [progress]: [ 235 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.068 * * * * [progress]: [ 236 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.068 * * * * [progress]: [ 237 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 1)) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.068 * * * * [progress]: [ 238 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.068 * * * * [progress]: [ 239 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.068 * * * * [progress]: [ 240 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt k)) (/ (sqrt 1) (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.068 * * * * [progress]: [ 241 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (pow (* n (* 2 PI)) (/ k 2)))))>
6.068 * * * * [progress]: [ 242 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.068 * * * * [progress]: [ 243 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.069 * * * * [progress]: [ 244 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.069 * * * * [progress]: [ 245 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.069 * * * * [progress]: [ 246 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.069 * * * * [progress]: [ 247 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.069 * * * * [progress]: [ 248 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.069 * * * * [progress]: [ 249 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.069 * * * * [progress]: [ 250 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.069 * * * * [progress]: [ 251 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.069 * * * * [progress]: [ 252 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.069 * * * * [progress]: [ 253 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.069 * * * * [progress]: [ 254 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.069 * * * * [progress]: [ 255 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.069 * * * * [progress]: [ 256 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.070 * * * * [progress]: [ 257 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.070 * * * * [progress]: [ 258 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.070 * * * * [progress]: [ 259 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.070 * * * * [progress]: [ 260 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.070 * * * * [progress]: [ 261 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.070 * * * * [progress]: [ 262 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.070 * * * * [progress]: [ 263 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) 1)) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.070 * * * * [progress]: [ 264 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.070 * * * * [progress]: [ 265 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.070 * * * * [progress]: [ 266 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.070 * * * * [progress]: [ 267 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.070 * * * * [progress]: [ 268 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.070 * * * * [progress]: [ 269 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.071 * * * * [progress]: [ 270 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) 1)) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.071 * * * * [progress]: [ 271 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.071 * * * * [progress]: [ 272 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.071 * * * * [progress]: [ 273 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.071 * * * * [progress]: [ 274 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.071 * * * * [progress]: [ 275 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.071 * * * * [progress]: [ 276 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.071 * * * * [progress]: [ 277 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) 1)) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.071 * * * * [progress]: [ 278 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.071 * * * * [progress]: [ 279 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.071 * * * * [progress]: [ 280 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
6.071 * * * * [progress]: [ 281 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
6.071 * * * * [progress]: [ 282 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.072 * * * * [progress]: [ 283 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.072 * * * * [progress]: [ 284 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 1)) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.072 * * * * [progress]: [ 285 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
6.072 * * * * [progress]: [ 286 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.072 * * * * [progress]: [ 287 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ 1 (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.072 * * * * [progress]: [ 288 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))) (/ 1 (pow (* n (* 2 PI)) (/ k 2)))))>
6.072 * * * * [progress]: [ 289 / 355 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.072 * * * * [progress]: [ 290 / 355 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.072 * * * * [progress]: [ 291 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1)))>
6.072 * * * * [progress]: [ 292 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.072 * * * * [progress]: [ 293 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.072 * * * * [progress]: [ 294 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
6.072 * * * * [progress]: [ 295 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
6.072 * * * * [progress]: [ 296 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
6.072 * * * * [progress]: [ 297 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.073 * * * * [progress]: [ 298 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.073 * * * * [progress]: [ 299 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
6.073 * * * * [progress]: [ 300 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
6.073 * * * * [progress]: [ 301 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
6.073 * * * * [progress]: [ 302 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
6.073 * * * * [progress]: [ 303 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2))))) (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
6.073 * * * * [progress]: [ 304 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.073 * * * * [progress]: [ 305 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.073 * * * * [progress]: [ 306 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
6.073 * * * * [progress]: [ 307 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
6.073 * * * * [progress]: [ 308 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
6.073 * * * * [progress]: [ 309 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
6.073 * * * * [progress]: [ 310 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
6.074 * * * * [progress]: [ 311 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.074 * * * * [progress]: [ 312 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.074 * * * * [progress]: [ 313 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
6.074 * * * * [progress]: [ 314 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
6.074 * * * * [progress]: [ 315 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
6.074 * * * * [progress]: [ 316 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
6.074 * * * * [progress]: [ 317 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (pow n (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
6.074 * * * * [progress]: [ 318 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (* (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)))))))>
6.074 * * * * [progress]: [ 319 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.074 * * * * [progress]: [ 320 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
6.074 * * * * [progress]: [ 321 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
6.074 * * * * [progress]: [ 322 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
6.074 * * * * [progress]: [ 323 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
6.074 * * * * [progress]: [ 324 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
6.074 * * * * [progress]: [ 325 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.075 * * * * [progress]: [ 326 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.075 * * * * [progress]: [ 327 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
6.075 * * * * [progress]: [ 328 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
6.075 * * * * [progress]: [ 329 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
6.075 * * * * [progress]: [ 330 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
6.075 * * * * [progress]: [ 331 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow n (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
6.075 * * * * [progress]: [ 332 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (* (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)))))))>
6.075 * * * * [progress]: [ 333 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
6.075 * * * * [progress]: [ 334 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
6.075 * * * * [progress]: [ 335 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
6.075 * * * * [progress]: [ 336 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
6.075 * * * * [progress]: [ 337 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (sqrt k)) (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
6.075 * * * * [progress]: [ 338 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))) (pow (* n (* 2 PI)) (/ k 2))))>
6.075 * * * * [progress]: [ 339 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt 1) (cbrt 1)) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt 1))))>
6.075 * * * * [progress]: [ 340 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt 1) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1))))>
6.076 * * * * [progress]: [ 341 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1)))>
6.076 * * * * [progress]: [ 342 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))>
6.076 * * * * [progress]: [ 343 / 355 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
6.076 * * * * [progress]: [ 344 / 355 ] 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))))))))>
6.076 * * * * [progress]: [ 345 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))))>
6.076 * * * * [progress]: [ 346 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))>
6.076 * * * * [progress]: [ 347 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))>
6.076 * * * * [progress]: [ 348 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))>
6.076 * * * * [progress]: [ 349 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))>
6.076 * * * * [progress]: [ 350 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI)))))))))))))>
6.076 * * * * [progress]: [ 351 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))))))))))>
6.076 * * * * [progress]: [ 352 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))))>
6.076 * * * * [progress]: [ 353 / 355 ] 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))))))))))))))>
6.076 * * * * [progress]: [ 354 / 355 ] 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)))))))))>
6.077 * * * * [progress]: [ 355 / 355 ] 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))))))))))))>
6.085 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (log (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (exp (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (- (sqrt k))
  (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))
  (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))
  (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))
  (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)
  (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (* (cbrt k) (cbrt k))) 1)
  (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) 1)
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt 1) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (sqrt 1) (* (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)))))
  (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt 1) 1)
  (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) 1)
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ 1 (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ 1 (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ 1 (pow n (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ 1 (* (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)))))
  (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 1)
  (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt k) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt k) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) 1)
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
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  (/ 1 (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1))
  (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt 1) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt 1) 1))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ 1 (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))
  (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ 1 1))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 1)
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (sqrt k))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (pow (* n (* 2 PI)) (/ k 2)))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1)
  (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt 1) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt 1) 1))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ 1 (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ 1 1))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 1)
  (/ 1 (sqrt k))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) 1/2)))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt 1))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1)
  (/ 1 (sqrt k))
  (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ 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 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI)))))))))))
  (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))))))))
  (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 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)))))))))))))
  (- (+ (* +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)))))))))))
6.101 * * [simplify]: iteration 1: (532 enodes)
7.361 * * [simplify]: iteration 2: (1424 enodes)
11.788 * * [simplify]: Extracting #0: cost 164 inf + 0
11.798 * * [simplify]: Extracting #1: cost 765 inf + 2
11.807 * * [simplify]: Extracting #2: cost 1061 inf + 4150
11.825 * * [simplify]: Extracting #3: cost 1062 inf + 39468
11.869 * * [simplify]: Extracting #4: cost 768 inf + 149237
11.948 * * [simplify]: Extracting #5: cost 395 inf + 296582
12.049 * * [simplify]: Extracting #6: cost 88 inf + 441130
12.163 * * [simplify]: Extracting #7: cost 16 inf + 476243
12.311 * * [simplify]: Extracting #8: cost 0 inf + 485961
12.409 * * [simplify]: Extracting #9: cost 0 inf + 485441
12.506 * [simplify]: Simplified to:
  (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))
  (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))
  (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))
  (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2))))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* PI 2) n) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* PI 2) n)
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ (- k) 2))
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ (- k) 2))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))
  (exp (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* PI n)) (exp (* PI n)))
  (* n (* n (* (* (* (* PI PI) 8) PI) 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)
  (* 2 (* PI (cbrt n)))
  (* (sqrt n) (* PI 2))
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (- (log (sqrt k)) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))))
  (exp (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (* (sqrt k) k) (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (* (cbrt (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (cbrt (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (* (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (sqrt (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (sqrt (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (- (sqrt k))
  (- (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (/ (cbrt (sqrt k)) (sqrt (* (* PI 2) n))) (cbrt (sqrt k)))
  (/ (cbrt (sqrt k)) (pow (* (* PI 2) n) (/ (- k) 2)))
  (* (/ (cbrt (sqrt k)) (sqrt (* (* PI 2) n))) (cbrt (sqrt k)))
  (/ (cbrt (sqrt k)) (pow (* (* PI 2) n) (/ (- k) 2)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))
  (/ (cbrt (sqrt k)) (pow (* PI 2) (- 1/2 (/ k 2))))
  (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (* (cbrt (sqrt k)) (cbrt (sqrt k)))
  (/ (cbrt (sqrt k)) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (cbrt (sqrt k)) (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (cbrt (sqrt k))))
  (/ (cbrt (sqrt k)) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (/ (fabs (cbrt k)) (sqrt (* (* PI 2) n)))
  (/ (sqrt (cbrt k)) (pow (* (* PI 2) n) (/ (- k) 2)))
  (/ (fabs (cbrt k)) (sqrt (* (* PI 2) n)))
  (/ (sqrt (cbrt k)) (pow (* (* PI 2) n) (/ (- k) 2)))
  (/ (fabs (cbrt k)) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt (cbrt k)) (pow (* PI 2) (- 1/2 (/ k 2))))
  (/ (/ (fabs (cbrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (fabs (cbrt k)) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (sqrt (cbrt k)) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (fabs (cbrt k))
  (/ (sqrt (cbrt k)) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (fabs (cbrt k)) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (/ (sqrt (cbrt k)) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (/ (sqrt (sqrt k)) (sqrt (* (* PI 2) n)))
  (/ (sqrt (sqrt k)) (pow (* (* PI 2) n) (/ (- k) 2)))
  (/ (sqrt (sqrt k)) (sqrt (* (* PI 2) n)))
  (/ (sqrt (sqrt k)) (pow (* (* PI 2) n) (/ (- k) 2)))
  (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* PI 2) (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (sqrt (sqrt k))
  (/ (sqrt (sqrt k)) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (/ (sqrt (sqrt k)) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (/ 1 (sqrt (* (* PI 2) n)))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- k) 2)))
  (/ 1 (sqrt (* (* PI 2) n)))
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  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ 1 (cbrt (sqrt k))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (* (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (/ 1 (cbrt (sqrt k))))
  (/ 1 (/ (fabs (cbrt k)) (sqrt (* (* PI 2) n))))
  (* (/ 1 (sqrt (cbrt k))) (pow (* (* PI 2) n) (/ (- k) 2)))
  (/ 1 (/ (fabs (cbrt k)) (sqrt (* (* PI 2) n))))
  (* (/ 1 (sqrt (cbrt k))) (pow (* (* PI 2) n) (/ (- k) 2)))
  (* (/ 1 (fabs (cbrt k))) (pow n (- 1/2 (/ k 2))))
  (* (pow (* PI 2) (- 1/2 (/ k 2))) (/ 1 (sqrt (cbrt k))))
  (* (/ 1 (fabs (cbrt k))) (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ (* 1 (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (sqrt (cbrt k)))
  (* (/ 1 (fabs (cbrt k))) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (cbrt k)) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ 1 (fabs (cbrt k)))
  (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (/ 1 (sqrt (cbrt k))))
  (* (/ 1 (fabs (cbrt k))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (* (/ 1 (sqrt (cbrt k))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (* (* PI 2) n))))
  (* (pow (* (* PI 2) n) (/ (- k) 2)) (/ 1 (sqrt (sqrt k))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (* (* PI 2) n))))
  (* (pow (* (* PI 2) n) (/ (- k) 2)) (/ 1 (sqrt (sqrt k))))
  (* (/ 1 (sqrt (sqrt k))) (pow n (- 1/2 (/ k 2))))
  (* (pow (* PI 2) (- 1/2 (/ k 2))) (/ 1 (sqrt (sqrt k))))
  (* (* (/ 1 (sqrt (sqrt k))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ 1 (sqrt (sqrt k)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (sqrt (* (* PI 2) n))
  (/ (* 1 (pow (* (* PI 2) n) (/ (- k) 2))) (sqrt k))
  (sqrt (* (* PI 2) n))
  (/ (* 1 (pow (* (* PI 2) n) (/ (- k) 2))) (sqrt k))
  (pow n (- 1/2 (/ k 2)))
  (* (pow (* PI 2) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (* (/ 1 (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (* 1 (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (sqrt k))
  1
  (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (* (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (/ 1 (sqrt k)))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (* (* PI 2) n))))
  (* (pow (* (* PI 2) n) (/ (- k) 2)) (/ 1 (sqrt (sqrt k))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (* (* PI 2) n))))
  (* (pow (* (* PI 2) n) (/ (- k) 2)) (/ 1 (sqrt (sqrt k))))
  (* (/ 1 (sqrt (sqrt k))) (pow n (- 1/2 (/ k 2))))
  (* (pow (* PI 2) (- 1/2 (/ k 2))) (/ 1 (sqrt (sqrt k))))
  (* (* (/ 1 (sqrt (sqrt k))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ 1 (sqrt (sqrt k)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (sqrt (* (* PI 2) n))
  (/ (* 1 (pow (* (* PI 2) n) (/ (- k) 2))) (sqrt k))
  (sqrt (* (* PI 2) n))
  (/ (* 1 (pow (* (* PI 2) n) (/ (- k) 2))) (sqrt k))
  (pow n (- 1/2 (/ k 2)))
  (* (pow (* PI 2) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (* (/ 1 (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (* 1 (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (sqrt k))
  1
  (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (* (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (/ 1 (sqrt k)))
  1
  (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
  (/ 1 (sqrt k))
  (pow (* (* PI 2) n) (- 1/2 (/ k 2)))
  (* (/ 1 (sqrt k)) (sqrt (* (* PI 2) n)))
  (/ 1 (pow (* (* PI 2) n) (/ k 2)))
  (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ 1 (* (cbrt (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))))
  (/ 1 (sqrt (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (* (* PI 2) n)))
  (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (* (* PI 2) n)))
  (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (pow n (- 1/2 (/ k 2))))
  (/ 1 (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (/ 1 (/ (fabs (cbrt k)) (sqrt (* (* PI 2) n))))
  (/ 1 (/ (fabs (cbrt k)) (sqrt (* (* PI 2) n))))
  (* (/ 1 (fabs (cbrt k))) (pow n (- 1/2 (/ k 2))))
  (* (/ 1 (fabs (cbrt k))) (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (* (/ 1 (fabs (cbrt k))) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ 1 (fabs (cbrt k)))
  (* (/ 1 (fabs (cbrt k))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (* (* PI 2) n))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (* (* PI 2) n))))
  (* (/ 1 (sqrt (sqrt k))) (pow n (- 1/2 (/ k 2))))
  (* (* (/ 1 (sqrt (sqrt k))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ 1 (sqrt (sqrt k)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (pow n (- 1/2 (/ k 2)))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  1
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (* (* PI 2) n))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (* (* PI 2) n))))
  (* (/ 1 (sqrt (sqrt k))) (pow n (- 1/2 (/ k 2))))
  (* (* (/ 1 (sqrt (sqrt k))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))))
  (/ 1 (sqrt (sqrt k)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (pow n (- 1/2 (/ k 2)))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  1
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  1
  (/ 1 (sqrt k))
  (* (/ 1 (sqrt k)) (sqrt (* (* PI 2) n)))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ 1 (sqrt k))
  (real->posit16 (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))
  (- (+ (+ (* (* (log (* PI 2)) 1/4) (* (sqrt (* (* PI 2) n)) (* (log n) (* k k)))) (+ (* (* 1/8 (sqrt (* (* PI 2) n))) (* (log n) (* (log n) (* k k)))) (sqrt (* (* PI 2) n)))) (* (* (sqrt (* (* PI 2) n)) (* k k)) (* (* (log (* PI 2)) (log (* PI 2))) 1/8))) (* (* k (+ (* (sqrt (* (* PI 2) n)) (log n)) (* (log (* PI 2)) (sqrt (* (* PI 2) n))))) 1/2))
  (exp (* (- 1/2 (* k 1/2)) (log (* (* PI 2) n))))
  (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
  (+ (* (* (/ (sqrt 2) PI) (* (* (log (* PI 2)) 1/2) (* k k))) (- +nan.0)) (- (* +nan.0 (* (/ (sqrt 1/2) PI) (* k k))) (- (/ (* n +nan.0) (/ PI (/ (* k (sqrt 1/2)) PI))) (* +nan.0 (- (/ (log n) (/ (/ PI (* k (* k 1/2))) (sqrt 2))) (/ (* k (sqrt 1/2)) PI))))))
  (+ (/ (- +nan.0) (* (exp (* (- 1/2 (* k 1/2)) (log (* (* PI 2) n)))) k)) (- (/ +nan.0 (* k (* k (exp (* (- 1/2 (* k 1/2)) (log (* (* PI 2) n))))))) (/ +nan.0 (exp (* (- 1/2 (* k 1/2)) (log (* (* PI 2) n)))))))
  (- (- (/ (/ +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))) (* k k)) (- (/ (/ +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))) k) (/ +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))))))
  (- (* (- +nan.0) (* (sqrt 2) (* k (* PI n)))) (+ (* (* (sqrt 2) +nan.0) (- (* PI n))) (- (* (* (sqrt 2) (* k (* PI n))) (* +nan.0 (log (* PI 2)))) (* (* (sqrt 2) +nan.0) (- (* (* PI n) (* (log n) k)) (* (* n PI) (* n PI)))))))
  (- (- (* (/ +nan.0 (* k k)) (/ (exp (* (- 1/2 (* k 1/2)) (log (* (* PI 2) n)))) k)) (* +nan.0 (- (/ (exp (* (- 1/2 (* k 1/2)) (log (* (* PI 2) n)))) k) (/ (/ (exp (* (- 1/2 (* k 1/2)) (log (* (* PI 2) n)))) k) k)))))
  (- (- (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))) (/ k +nan.0)) (* +nan.0 (- (/ (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))) k) k) (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))))))
12.575 * * * [progress]: adding candidates to table
15.258 * * [progress]: iteration 3 / 4
15.258 * * * [progress]: picking best candidate
15.303 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
15.304 * * * [progress]: localizing error
15.353 * * * [progress]: generating rewritten candidates
15.353 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
15.384 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
15.412 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1)
15.427 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
15.473 * * * [progress]: generating series expansions
15.474 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
15.474 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
15.474 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
15.474 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
15.474 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
15.474 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
15.474 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
15.474 * [taylor]: Taking taylor expansion of 1/2 in k
15.475 * [backup-simplify]: Simplify 1/2 into 1/2
15.475 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.475 * [taylor]: Taking taylor expansion of 1 in k
15.475 * [backup-simplify]: Simplify 1 into 1
15.475 * [taylor]: Taking taylor expansion of k in k
15.475 * [backup-simplify]: Simplify 0 into 0
15.475 * [backup-simplify]: Simplify 1 into 1
15.475 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
15.475 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
15.475 * [taylor]: Taking taylor expansion of 2 in k
15.475 * [backup-simplify]: Simplify 2 into 2
15.475 * [taylor]: Taking taylor expansion of (* n PI) in k
15.475 * [taylor]: Taking taylor expansion of n in k
15.475 * [backup-simplify]: Simplify n into n
15.475 * [taylor]: Taking taylor expansion of PI in k
15.475 * [backup-simplify]: Simplify PI into PI
15.475 * [backup-simplify]: Simplify (* n PI) into (* n PI)
15.475 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
15.475 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
15.475 * [backup-simplify]: Simplify (- 0) into 0
15.475 * [backup-simplify]: Simplify (+ 1 0) into 1
15.476 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.476 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
15.476 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
15.476 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
15.476 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
15.476 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
15.476 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
15.476 * [taylor]: Taking taylor expansion of 1/2 in n
15.476 * [backup-simplify]: Simplify 1/2 into 1/2
15.476 * [taylor]: Taking taylor expansion of (- 1 k) in n
15.476 * [taylor]: Taking taylor expansion of 1 in n
15.476 * [backup-simplify]: Simplify 1 into 1
15.476 * [taylor]: Taking taylor expansion of k in n
15.476 * [backup-simplify]: Simplify k into k
15.476 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
15.476 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
15.476 * [taylor]: Taking taylor expansion of 2 in n
15.476 * [backup-simplify]: Simplify 2 into 2
15.476 * [taylor]: Taking taylor expansion of (* n PI) in n
15.476 * [taylor]: Taking taylor expansion of n in n
15.476 * [backup-simplify]: Simplify 0 into 0
15.476 * [backup-simplify]: Simplify 1 into 1
15.476 * [taylor]: Taking taylor expansion of PI in n
15.476 * [backup-simplify]: Simplify PI into PI
15.477 * [backup-simplify]: Simplify (* 0 PI) into 0
15.477 * [backup-simplify]: Simplify (* 2 0) into 0
15.478 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.479 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
15.480 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
15.480 * [backup-simplify]: Simplify (- k) into (- k)
15.480 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
15.480 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
15.481 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
15.481 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
15.482 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
15.482 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
15.482 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
15.482 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
15.482 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
15.482 * [taylor]: Taking taylor expansion of 1/2 in n
15.482 * [backup-simplify]: Simplify 1/2 into 1/2
15.482 * [taylor]: Taking taylor expansion of (- 1 k) in n
15.482 * [taylor]: Taking taylor expansion of 1 in n
15.482 * [backup-simplify]: Simplify 1 into 1
15.482 * [taylor]: Taking taylor expansion of k in n
15.482 * [backup-simplify]: Simplify k into k
15.482 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
15.482 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
15.482 * [taylor]: Taking taylor expansion of 2 in n
15.482 * [backup-simplify]: Simplify 2 into 2
15.482 * [taylor]: Taking taylor expansion of (* n PI) in n
15.482 * [taylor]: Taking taylor expansion of n in n
15.482 * [backup-simplify]: Simplify 0 into 0
15.482 * [backup-simplify]: Simplify 1 into 1
15.482 * [taylor]: Taking taylor expansion of PI in n
15.482 * [backup-simplify]: Simplify PI into PI
15.483 * [backup-simplify]: Simplify (* 0 PI) into 0
15.483 * [backup-simplify]: Simplify (* 2 0) into 0
15.484 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.485 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
15.486 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
15.486 * [backup-simplify]: Simplify (- k) into (- k)
15.486 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
15.486 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
15.487 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
15.487 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
15.488 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
15.488 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
15.488 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
15.488 * [taylor]: Taking taylor expansion of 1/2 in k
15.488 * [backup-simplify]: Simplify 1/2 into 1/2
15.488 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
15.488 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.488 * [taylor]: Taking taylor expansion of 1 in k
15.488 * [backup-simplify]: Simplify 1 into 1
15.488 * [taylor]: Taking taylor expansion of k in k
15.488 * [backup-simplify]: Simplify 0 into 0
15.488 * [backup-simplify]: Simplify 1 into 1
15.488 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
15.488 * [taylor]: Taking taylor expansion of (log n) in k
15.488 * [taylor]: Taking taylor expansion of n in k
15.489 * [backup-simplify]: Simplify n into n
15.489 * [backup-simplify]: Simplify (log n) into (log n)
15.489 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
15.489 * [taylor]: Taking taylor expansion of (* 2 PI) in k
15.489 * [taylor]: Taking taylor expansion of 2 in k
15.489 * [backup-simplify]: Simplify 2 into 2
15.489 * [taylor]: Taking taylor expansion of PI in k
15.489 * [backup-simplify]: Simplify PI into PI
15.489 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
15.490 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
15.490 * [backup-simplify]: Simplify (- 0) into 0
15.490 * [backup-simplify]: Simplify (+ 1 0) into 1
15.491 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
15.492 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
15.492 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
15.493 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
15.494 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
15.494 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
15.495 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
15.496 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
15.496 * [backup-simplify]: Simplify (- 0) into 0
15.497 * [backup-simplify]: Simplify (+ 0 0) into 0
15.497 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
15.498 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
15.499 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
15.500 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
15.500 * [taylor]: Taking taylor expansion of 0 in k
15.500 * [backup-simplify]: Simplify 0 into 0
15.500 * [backup-simplify]: Simplify 0 into 0
15.500 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
15.501 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
15.502 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
15.502 * [backup-simplify]: Simplify (+ 0 0) into 0
15.502 * [backup-simplify]: Simplify (- 1) into -1
15.503 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.508 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
15.509 * [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)))))
15.512 * [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)))))))
15.513 * [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)))))))
15.514 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
15.515 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
15.517 * [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
15.517 * [backup-simplify]: Simplify (- 0) into 0
15.518 * [backup-simplify]: Simplify (+ 0 0) into 0
15.518 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
15.519 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
15.520 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
15.522 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
15.522 * [taylor]: Taking taylor expansion of 0 in k
15.522 * [backup-simplify]: Simplify 0 into 0
15.522 * [backup-simplify]: Simplify 0 into 0
15.522 * [backup-simplify]: Simplify 0 into 0
15.523 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
15.524 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
15.526 * [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
15.526 * [backup-simplify]: Simplify (+ 0 0) into 0
15.526 * [backup-simplify]: Simplify (- 0) into 0
15.527 * [backup-simplify]: Simplify (+ 0 0) into 0
15.529 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
15.532 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
15.536 * [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)))))
15.540 * [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)))))
15.546 * [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)))))
15.546 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
15.546 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
15.546 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
15.546 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
15.546 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
15.546 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
15.546 * [taylor]: Taking taylor expansion of 1/2 in k
15.546 * [backup-simplify]: Simplify 1/2 into 1/2
15.546 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
15.546 * [taylor]: Taking taylor expansion of 1 in k
15.546 * [backup-simplify]: Simplify 1 into 1
15.546 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.547 * [taylor]: Taking taylor expansion of k in k
15.547 * [backup-simplify]: Simplify 0 into 0
15.547 * [backup-simplify]: Simplify 1 into 1
15.547 * [backup-simplify]: Simplify (/ 1 1) into 1
15.547 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
15.547 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
15.547 * [taylor]: Taking taylor expansion of 2 in k
15.547 * [backup-simplify]: Simplify 2 into 2
15.547 * [taylor]: Taking taylor expansion of (/ PI n) in k
15.547 * [taylor]: Taking taylor expansion of PI in k
15.547 * [backup-simplify]: Simplify PI into PI
15.547 * [taylor]: Taking taylor expansion of n in k
15.547 * [backup-simplify]: Simplify n into n
15.547 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
15.547 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
15.547 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
15.547 * [backup-simplify]: Simplify (- 1) into -1
15.548 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.548 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
15.548 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
15.548 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
15.548 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
15.548 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
15.548 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
15.548 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
15.548 * [taylor]: Taking taylor expansion of 1/2 in n
15.548 * [backup-simplify]: Simplify 1/2 into 1/2
15.548 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
15.548 * [taylor]: Taking taylor expansion of 1 in n
15.548 * [backup-simplify]: Simplify 1 into 1
15.548 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.548 * [taylor]: Taking taylor expansion of k in n
15.548 * [backup-simplify]: Simplify k into k
15.548 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.548 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
15.548 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
15.548 * [taylor]: Taking taylor expansion of 2 in n
15.548 * [backup-simplify]: Simplify 2 into 2
15.548 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.548 * [taylor]: Taking taylor expansion of PI in n
15.548 * [backup-simplify]: Simplify PI into PI
15.548 * [taylor]: Taking taylor expansion of n in n
15.548 * [backup-simplify]: Simplify 0 into 0
15.548 * [backup-simplify]: Simplify 1 into 1
15.549 * [backup-simplify]: Simplify (/ PI 1) into PI
15.549 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
15.550 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
15.550 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
15.550 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
15.550 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
15.551 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
15.552 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
15.552 * [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)))))
15.552 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
15.552 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
15.552 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
15.552 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
15.552 * [taylor]: Taking taylor expansion of 1/2 in n
15.552 * [backup-simplify]: Simplify 1/2 into 1/2
15.552 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
15.553 * [taylor]: Taking taylor expansion of 1 in n
15.553 * [backup-simplify]: Simplify 1 into 1
15.553 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.553 * [taylor]: Taking taylor expansion of k in n
15.553 * [backup-simplify]: Simplify k into k
15.553 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.553 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
15.553 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
15.553 * [taylor]: Taking taylor expansion of 2 in n
15.553 * [backup-simplify]: Simplify 2 into 2
15.553 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.553 * [taylor]: Taking taylor expansion of PI in n
15.553 * [backup-simplify]: Simplify PI into PI
15.553 * [taylor]: Taking taylor expansion of n in n
15.553 * [backup-simplify]: Simplify 0 into 0
15.553 * [backup-simplify]: Simplify 1 into 1
15.553 * [backup-simplify]: Simplify (/ PI 1) into PI
15.554 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
15.554 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
15.554 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
15.554 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
15.554 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
15.555 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
15.556 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
15.557 * [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)))))
15.557 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
15.557 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
15.557 * [taylor]: Taking taylor expansion of 1/2 in k
15.557 * [backup-simplify]: Simplify 1/2 into 1/2
15.557 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
15.557 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
15.557 * [taylor]: Taking taylor expansion of 1 in k
15.557 * [backup-simplify]: Simplify 1 into 1
15.557 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.557 * [taylor]: Taking taylor expansion of k in k
15.557 * [backup-simplify]: Simplify 0 into 0
15.557 * [backup-simplify]: Simplify 1 into 1
15.557 * [backup-simplify]: Simplify (/ 1 1) into 1
15.557 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
15.557 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
15.557 * [taylor]: Taking taylor expansion of (* 2 PI) in k
15.557 * [taylor]: Taking taylor expansion of 2 in k
15.558 * [backup-simplify]: Simplify 2 into 2
15.558 * [taylor]: Taking taylor expansion of PI in k
15.558 * [backup-simplify]: Simplify PI into PI
15.558 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
15.559 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
15.559 * [taylor]: Taking taylor expansion of (log n) in k
15.559 * [taylor]: Taking taylor expansion of n in k
15.559 * [backup-simplify]: Simplify n into n
15.559 * [backup-simplify]: Simplify (log n) into (log n)
15.559 * [backup-simplify]: Simplify (- 1) into -1
15.559 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.559 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
15.560 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
15.561 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
15.561 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
15.562 * [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)))))
15.563 * [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)))))
15.564 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
15.565 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
15.566 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
15.566 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
15.566 * [backup-simplify]: Simplify (- 0) into 0
15.566 * [backup-simplify]: Simplify (+ 0 0) into 0
15.567 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
15.568 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
15.568 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
15.570 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
15.570 * [taylor]: Taking taylor expansion of 0 in k
15.570 * [backup-simplify]: Simplify 0 into 0
15.570 * [backup-simplify]: Simplify 0 into 0
15.570 * [backup-simplify]: Simplify 0 into 0
15.570 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.571 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
15.573 * [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
15.573 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
15.574 * [backup-simplify]: Simplify (- 0) into 0
15.574 * [backup-simplify]: Simplify (+ 0 0) into 0
15.575 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
15.576 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
15.578 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
15.580 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
15.580 * [taylor]: Taking taylor expansion of 0 in k
15.580 * [backup-simplify]: Simplify 0 into 0
15.580 * [backup-simplify]: Simplify 0 into 0
15.580 * [backup-simplify]: Simplify 0 into 0
15.580 * [backup-simplify]: Simplify 0 into 0
15.581 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.582 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
15.586 * [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
15.586 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
15.586 * [backup-simplify]: Simplify (- 0) into 0
15.586 * [backup-simplify]: Simplify (+ 0 0) into 0
15.587 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
15.588 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
15.590 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
15.591 * [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
15.591 * [taylor]: Taking taylor expansion of 0 in k
15.591 * [backup-simplify]: Simplify 0 into 0
15.591 * [backup-simplify]: Simplify 0 into 0
15.592 * [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))))))
15.593 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
15.593 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
15.593 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
15.593 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
15.593 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
15.593 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
15.593 * [taylor]: Taking taylor expansion of 1/2 in k
15.593 * [backup-simplify]: Simplify 1/2 into 1/2
15.593 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
15.593 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.593 * [taylor]: Taking taylor expansion of k in k
15.593 * [backup-simplify]: Simplify 0 into 0
15.593 * [backup-simplify]: Simplify 1 into 1
15.593 * [backup-simplify]: Simplify (/ 1 1) into 1
15.593 * [taylor]: Taking taylor expansion of 1 in k
15.593 * [backup-simplify]: Simplify 1 into 1
15.593 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
15.593 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
15.593 * [taylor]: Taking taylor expansion of -2 in k
15.593 * [backup-simplify]: Simplify -2 into -2
15.593 * [taylor]: Taking taylor expansion of (/ PI n) in k
15.593 * [taylor]: Taking taylor expansion of PI in k
15.593 * [backup-simplify]: Simplify PI into PI
15.593 * [taylor]: Taking taylor expansion of n in k
15.593 * [backup-simplify]: Simplify n into n
15.594 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
15.594 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
15.594 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
15.594 * [backup-simplify]: Simplify (+ 1 0) into 1
15.594 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.594 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
15.594 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
15.594 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
15.594 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
15.595 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
15.595 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
15.595 * [taylor]: Taking taylor expansion of 1/2 in n
15.595 * [backup-simplify]: Simplify 1/2 into 1/2
15.595 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
15.595 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.595 * [taylor]: Taking taylor expansion of k in n
15.595 * [backup-simplify]: Simplify k into k
15.595 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.595 * [taylor]: Taking taylor expansion of 1 in n
15.595 * [backup-simplify]: Simplify 1 into 1
15.595 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
15.595 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
15.595 * [taylor]: Taking taylor expansion of -2 in n
15.595 * [backup-simplify]: Simplify -2 into -2
15.595 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.595 * [taylor]: Taking taylor expansion of PI in n
15.595 * [backup-simplify]: Simplify PI into PI
15.595 * [taylor]: Taking taylor expansion of n in n
15.595 * [backup-simplify]: Simplify 0 into 0
15.595 * [backup-simplify]: Simplify 1 into 1
15.595 * [backup-simplify]: Simplify (/ PI 1) into PI
15.596 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
15.596 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
15.596 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
15.597 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
15.598 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
15.598 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
15.599 * [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)))))
15.599 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
15.599 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
15.599 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
15.599 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
15.599 * [taylor]: Taking taylor expansion of 1/2 in n
15.599 * [backup-simplify]: Simplify 1/2 into 1/2
15.599 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
15.599 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.600 * [taylor]: Taking taylor expansion of k in n
15.600 * [backup-simplify]: Simplify k into k
15.600 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.600 * [taylor]: Taking taylor expansion of 1 in n
15.600 * [backup-simplify]: Simplify 1 into 1
15.600 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
15.600 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
15.600 * [taylor]: Taking taylor expansion of -2 in n
15.600 * [backup-simplify]: Simplify -2 into -2
15.600 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.600 * [taylor]: Taking taylor expansion of PI in n
15.600 * [backup-simplify]: Simplify PI into PI
15.600 * [taylor]: Taking taylor expansion of n in n
15.600 * [backup-simplify]: Simplify 0 into 0
15.600 * [backup-simplify]: Simplify 1 into 1
15.600 * [backup-simplify]: Simplify (/ PI 1) into PI
15.601 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
15.601 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
15.601 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
15.602 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
15.603 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
15.604 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
15.605 * [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)))))
15.605 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
15.605 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
15.605 * [taylor]: Taking taylor expansion of 1/2 in k
15.605 * [backup-simplify]: Simplify 1/2 into 1/2
15.605 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
15.605 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
15.605 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.605 * [taylor]: Taking taylor expansion of k in k
15.605 * [backup-simplify]: Simplify 0 into 0
15.605 * [backup-simplify]: Simplify 1 into 1
15.605 * [backup-simplify]: Simplify (/ 1 1) into 1
15.605 * [taylor]: Taking taylor expansion of 1 in k
15.606 * [backup-simplify]: Simplify 1 into 1
15.606 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
15.606 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
15.606 * [taylor]: Taking taylor expansion of (* -2 PI) in k
15.606 * [taylor]: Taking taylor expansion of -2 in k
15.606 * [backup-simplify]: Simplify -2 into -2
15.606 * [taylor]: Taking taylor expansion of PI in k
15.606 * [backup-simplify]: Simplify PI into PI
15.611 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
15.612 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
15.612 * [taylor]: Taking taylor expansion of (log n) in k
15.612 * [taylor]: Taking taylor expansion of n in k
15.612 * [backup-simplify]: Simplify n into n
15.612 * [backup-simplify]: Simplify (log n) into (log n)
15.612 * [backup-simplify]: Simplify (+ 1 0) into 1
15.612 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
15.613 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
15.614 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
15.615 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
15.615 * [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)))))
15.616 * [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)))))
15.617 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
15.617 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
15.618 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
15.619 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
15.619 * [backup-simplify]: Simplify (+ 0 0) into 0
15.619 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
15.620 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
15.621 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
15.622 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
15.622 * [taylor]: Taking taylor expansion of 0 in k
15.622 * [backup-simplify]: Simplify 0 into 0
15.622 * [backup-simplify]: Simplify 0 into 0
15.622 * [backup-simplify]: Simplify 0 into 0
15.623 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.624 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
15.626 * [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
15.626 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
15.627 * [backup-simplify]: Simplify (+ 0 0) into 0
15.627 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
15.628 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
15.629 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
15.631 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
15.631 * [taylor]: Taking taylor expansion of 0 in k
15.631 * [backup-simplify]: Simplify 0 into 0
15.631 * [backup-simplify]: Simplify 0 into 0
15.631 * [backup-simplify]: Simplify 0 into 0
15.631 * [backup-simplify]: Simplify 0 into 0
15.632 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.633 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
15.636 * [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
15.636 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
15.637 * [backup-simplify]: Simplify (+ 0 0) into 0
15.637 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
15.638 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
15.639 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
15.641 * [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
15.641 * [taylor]: Taking taylor expansion of 0 in k
15.641 * [backup-simplify]: Simplify 0 into 0
15.641 * [backup-simplify]: Simplify 0 into 0
15.642 * [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))))))
15.643 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
15.643 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
15.643 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
15.643 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
15.643 * [taylor]: Taking taylor expansion of 2 in n
15.643 * [backup-simplify]: Simplify 2 into 2
15.643 * [taylor]: Taking taylor expansion of (* n PI) in n
15.643 * [taylor]: Taking taylor expansion of n in n
15.643 * [backup-simplify]: Simplify 0 into 0
15.643 * [backup-simplify]: Simplify 1 into 1
15.643 * [taylor]: Taking taylor expansion of PI in n
15.643 * [backup-simplify]: Simplify PI into PI
15.643 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
15.644 * [taylor]: Taking taylor expansion of 2 in n
15.644 * [backup-simplify]: Simplify 2 into 2
15.644 * [taylor]: Taking taylor expansion of (* n PI) in n
15.644 * [taylor]: Taking taylor expansion of n in n
15.644 * [backup-simplify]: Simplify 0 into 0
15.644 * [backup-simplify]: Simplify 1 into 1
15.644 * [taylor]: Taking taylor expansion of PI in n
15.644 * [backup-simplify]: Simplify PI into PI
15.644 * [backup-simplify]: Simplify (* 0 PI) into 0
15.645 * [backup-simplify]: Simplify (* 2 0) into 0
15.645 * [backup-simplify]: Simplify 0 into 0
15.646 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.648 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
15.648 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
15.650 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
15.651 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
15.651 * [backup-simplify]: Simplify 0 into 0
15.652 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
15.653 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
15.653 * [backup-simplify]: Simplify 0 into 0
15.655 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
15.657 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
15.657 * [backup-simplify]: Simplify 0 into 0
15.658 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
15.660 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
15.660 * [backup-simplify]: Simplify 0 into 0
15.662 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
15.664 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
15.664 * [backup-simplify]: Simplify 0 into 0
15.666 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
15.668 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
15.668 * [backup-simplify]: Simplify 0 into 0
15.669 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
15.669 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
15.669 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
15.669 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
15.669 * [taylor]: Taking taylor expansion of 2 in n
15.669 * [backup-simplify]: Simplify 2 into 2
15.669 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.669 * [taylor]: Taking taylor expansion of PI in n
15.669 * [backup-simplify]: Simplify PI into PI
15.669 * [taylor]: Taking taylor expansion of n in n
15.669 * [backup-simplify]: Simplify 0 into 0
15.669 * [backup-simplify]: Simplify 1 into 1
15.670 * [backup-simplify]: Simplify (/ PI 1) into PI
15.670 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
15.670 * [taylor]: Taking taylor expansion of 2 in n
15.670 * [backup-simplify]: Simplify 2 into 2
15.670 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.670 * [taylor]: Taking taylor expansion of PI in n
15.670 * [backup-simplify]: Simplify PI into PI
15.670 * [taylor]: Taking taylor expansion of n in n
15.670 * [backup-simplify]: Simplify 0 into 0
15.670 * [backup-simplify]: Simplify 1 into 1
15.670 * [backup-simplify]: Simplify (/ PI 1) into PI
15.671 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
15.671 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
15.671 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
15.672 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
15.672 * [backup-simplify]: Simplify 0 into 0
15.673 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.673 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
15.673 * [backup-simplify]: Simplify 0 into 0
15.674 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.675 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
15.675 * [backup-simplify]: Simplify 0 into 0
15.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.676 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
15.676 * [backup-simplify]: Simplify 0 into 0
15.677 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.678 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
15.678 * [backup-simplify]: Simplify 0 into 0
15.678 * [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
15.679 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
15.679 * [backup-simplify]: Simplify 0 into 0
15.680 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
15.680 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n))
15.680 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
15.680 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
15.680 * [taylor]: Taking taylor expansion of -2 in n
15.680 * [backup-simplify]: Simplify -2 into -2
15.680 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.680 * [taylor]: Taking taylor expansion of PI in n
15.680 * [backup-simplify]: Simplify PI into PI
15.680 * [taylor]: Taking taylor expansion of n in n
15.680 * [backup-simplify]: Simplify 0 into 0
15.680 * [backup-simplify]: Simplify 1 into 1
15.681 * [backup-simplify]: Simplify (/ PI 1) into PI
15.681 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
15.681 * [taylor]: Taking taylor expansion of -2 in n
15.681 * [backup-simplify]: Simplify -2 into -2
15.681 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.681 * [taylor]: Taking taylor expansion of PI in n
15.681 * [backup-simplify]: Simplify PI into PI
15.681 * [taylor]: Taking taylor expansion of n in n
15.681 * [backup-simplify]: Simplify 0 into 0
15.681 * [backup-simplify]: Simplify 1 into 1
15.681 * [backup-simplify]: Simplify (/ PI 1) into PI
15.681 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
15.682 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
15.682 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
15.683 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
15.683 * [backup-simplify]: Simplify 0 into 0
15.683 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.684 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
15.684 * [backup-simplify]: Simplify 0 into 0
15.685 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.686 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
15.686 * [backup-simplify]: Simplify 0 into 0
15.686 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.687 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
15.687 * [backup-simplify]: Simplify 0 into 0
15.688 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.689 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
15.689 * [backup-simplify]: Simplify 0 into 0
15.689 * [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
15.690 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
15.690 * [backup-simplify]: Simplify 0 into 0
15.691 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
15.691 * * * * [progress]: [ 3 / 4 ] generating series at (2 1)
15.691 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
15.691 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0
15.691 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
15.691 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.691 * [taylor]: Taking taylor expansion of k in k
15.691 * [backup-simplify]: Simplify 0 into 0
15.691 * [backup-simplify]: Simplify 1 into 1
15.691 * [backup-simplify]: Simplify (/ 1 1) into 1
15.692 * [backup-simplify]: Simplify (sqrt 0) into 0
15.693 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.693 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
15.693 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.693 * [taylor]: Taking taylor expansion of k in k
15.693 * [backup-simplify]: Simplify 0 into 0
15.693 * [backup-simplify]: Simplify 1 into 1
15.693 * [backup-simplify]: Simplify (/ 1 1) into 1
15.693 * [backup-simplify]: Simplify (sqrt 0) into 0
15.694 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.694 * [backup-simplify]: Simplify 0 into 0
15.694 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.695 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
15.696 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
15.696 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.697 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.700 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
15.700 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.700 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
15.700 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
15.700 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0
15.700 * [taylor]: Taking taylor expansion of (sqrt k) in k
15.700 * [taylor]: Taking taylor expansion of k in k
15.700 * [backup-simplify]: Simplify 0 into 0
15.700 * [backup-simplify]: Simplify 1 into 1
15.700 * [backup-simplify]: Simplify (sqrt 0) into 0
15.701 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.701 * [taylor]: Taking taylor expansion of (sqrt k) in k
15.701 * [taylor]: Taking taylor expansion of k in k
15.701 * [backup-simplify]: Simplify 0 into 0
15.701 * [backup-simplify]: Simplify 1 into 1
15.701 * [backup-simplify]: Simplify (sqrt 0) into 0
15.702 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.702 * [backup-simplify]: Simplify 0 into 0
15.702 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.704 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
15.704 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.707 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
15.707 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.707 * [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))))))))
15.707 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k)))
15.707 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0
15.707 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
15.707 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
15.707 * [taylor]: Taking taylor expansion of (/ -1 k) in k
15.707 * [taylor]: Taking taylor expansion of -1 in k
15.707 * [backup-simplify]: Simplify -1 into -1
15.707 * [taylor]: Taking taylor expansion of k in k
15.707 * [backup-simplify]: Simplify 0 into 0
15.707 * [backup-simplify]: Simplify 1 into 1
15.707 * [backup-simplify]: Simplify (/ -1 1) into -1
15.708 * [backup-simplify]: Simplify (sqrt 0) into 0
15.708 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
15.709 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
15.709 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
15.709 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
15.709 * [taylor]: Taking taylor expansion of (/ -1 k) in k
15.709 * [taylor]: Taking taylor expansion of -1 in k
15.709 * [backup-simplify]: Simplify -1 into -1
15.709 * [taylor]: Taking taylor expansion of k in k
15.709 * [backup-simplify]: Simplify 0 into 0
15.709 * [backup-simplify]: Simplify 1 into 1
15.709 * [backup-simplify]: Simplify (/ -1 1) into -1
15.709 * [backup-simplify]: Simplify (sqrt 0) into 0
15.710 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
15.711 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
15.711 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
15.719 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
15.721 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
15.721 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
15.722 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.725 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
15.729 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
15.729 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
15.730 * [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)))))
15.730 * * * * [progress]: [ 4 / 4 ] generating series at (2)
15.731 * [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)))
15.731 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0
15.731 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
15.731 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
15.731 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
15.731 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
15.731 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
15.731 * [taylor]: Taking taylor expansion of 1/2 in n
15.731 * [backup-simplify]: Simplify 1/2 into 1/2
15.731 * [taylor]: Taking taylor expansion of (- 1 k) in n
15.731 * [taylor]: Taking taylor expansion of 1 in n
15.731 * [backup-simplify]: Simplify 1 into 1
15.731 * [taylor]: Taking taylor expansion of k in n
15.731 * [backup-simplify]: Simplify k into k
15.731 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
15.731 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
15.731 * [taylor]: Taking taylor expansion of 2 in n
15.731 * [backup-simplify]: Simplify 2 into 2
15.731 * [taylor]: Taking taylor expansion of (* n PI) in n
15.732 * [taylor]: Taking taylor expansion of n in n
15.732 * [backup-simplify]: Simplify 0 into 0
15.732 * [backup-simplify]: Simplify 1 into 1
15.732 * [taylor]: Taking taylor expansion of PI in n
15.732 * [backup-simplify]: Simplify PI into PI
15.732 * [backup-simplify]: Simplify (* 0 PI) into 0
15.732 * [backup-simplify]: Simplify (* 2 0) into 0
15.734 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.736 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
15.737 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
15.737 * [backup-simplify]: Simplify (- k) into (- k)
15.737 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
15.737 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
15.738 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
15.739 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
15.740 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
15.740 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
15.740 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.740 * [taylor]: Taking taylor expansion of k in n
15.740 * [backup-simplify]: Simplify k into k
15.741 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.741 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
15.741 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
15.741 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
15.741 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
15.741 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
15.741 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
15.741 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
15.741 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
15.741 * [taylor]: Taking taylor expansion of 1/2 in k
15.741 * [backup-simplify]: Simplify 1/2 into 1/2
15.741 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.741 * [taylor]: Taking taylor expansion of 1 in k
15.741 * [backup-simplify]: Simplify 1 into 1
15.741 * [taylor]: Taking taylor expansion of k in k
15.741 * [backup-simplify]: Simplify 0 into 0
15.741 * [backup-simplify]: Simplify 1 into 1
15.741 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
15.741 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
15.741 * [taylor]: Taking taylor expansion of 2 in k
15.741 * [backup-simplify]: Simplify 2 into 2
15.741 * [taylor]: Taking taylor expansion of (* n PI) in k
15.741 * [taylor]: Taking taylor expansion of n in k
15.741 * [backup-simplify]: Simplify n into n
15.741 * [taylor]: Taking taylor expansion of PI in k
15.741 * [backup-simplify]: Simplify PI into PI
15.741 * [backup-simplify]: Simplify (* n PI) into (* n PI)
15.741 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
15.742 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
15.742 * [backup-simplify]: Simplify (- 0) into 0
15.742 * [backup-simplify]: Simplify (+ 1 0) into 1
15.743 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.743 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
15.743 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
15.743 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
15.743 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.743 * [taylor]: Taking taylor expansion of k in k
15.743 * [backup-simplify]: Simplify 0 into 0
15.743 * [backup-simplify]: Simplify 1 into 1
15.743 * [backup-simplify]: Simplify (/ 1 1) into 1
15.744 * [backup-simplify]: Simplify (sqrt 0) into 0
15.745 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.745 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
15.745 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
15.745 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
15.745 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
15.745 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
15.745 * [taylor]: Taking taylor expansion of 1/2 in k
15.745 * [backup-simplify]: Simplify 1/2 into 1/2
15.745 * [taylor]: Taking taylor expansion of (- 1 k) in k
15.745 * [taylor]: Taking taylor expansion of 1 in k
15.745 * [backup-simplify]: Simplify 1 into 1
15.745 * [taylor]: Taking taylor expansion of k in k
15.745 * [backup-simplify]: Simplify 0 into 0
15.745 * [backup-simplify]: Simplify 1 into 1
15.745 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
15.745 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
15.745 * [taylor]: Taking taylor expansion of 2 in k
15.745 * [backup-simplify]: Simplify 2 into 2
15.746 * [taylor]: Taking taylor expansion of (* n PI) in k
15.746 * [taylor]: Taking taylor expansion of n in k
15.746 * [backup-simplify]: Simplify n into n
15.746 * [taylor]: Taking taylor expansion of PI in k
15.746 * [backup-simplify]: Simplify PI into PI
15.746 * [backup-simplify]: Simplify (* n PI) into (* n PI)
15.746 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
15.746 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
15.746 * [backup-simplify]: Simplify (- 0) into 0
15.747 * [backup-simplify]: Simplify (+ 1 0) into 1
15.747 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.747 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
15.747 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
15.747 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
15.747 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.747 * [taylor]: Taking taylor expansion of k in k
15.747 * [backup-simplify]: Simplify 0 into 0
15.747 * [backup-simplify]: Simplify 1 into 1
15.748 * [backup-simplify]: Simplify (/ 1 1) into 1
15.748 * [backup-simplify]: Simplify (sqrt 0) into 0
15.749 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.749 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0
15.750 * [taylor]: Taking taylor expansion of 0 in n
15.750 * [backup-simplify]: Simplify 0 into 0
15.750 * [backup-simplify]: Simplify 0 into 0
15.750 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
15.751 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
15.751 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
15.752 * [backup-simplify]: Simplify (- 1) into -1
15.752 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.753 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
15.753 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
15.754 * [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)))))
15.754 * [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)))))
15.754 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
15.754 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
15.754 * [taylor]: Taking taylor expansion of +nan.0 in n
15.754 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.754 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
15.754 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.754 * [taylor]: Taking taylor expansion of 2 in n
15.754 * [backup-simplify]: Simplify 2 into 2
15.755 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.755 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.755 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.755 * [taylor]: Taking taylor expansion of (* n PI) in n
15.755 * [taylor]: Taking taylor expansion of n in n
15.755 * [backup-simplify]: Simplify 0 into 0
15.755 * [backup-simplify]: Simplify 1 into 1
15.755 * [taylor]: Taking taylor expansion of PI in n
15.755 * [backup-simplify]: Simplify PI into PI
15.756 * [backup-simplify]: Simplify (* 0 PI) into 0
15.757 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.758 * [backup-simplify]: Simplify (sqrt 0) into 0
15.759 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.760 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
15.760 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.760 * [backup-simplify]: Simplify (- 0) into 0
15.760 * [backup-simplify]: Simplify 0 into 0
15.760 * [backup-simplify]: Simplify 0 into 0
15.761 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
15.764 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
15.765 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
15.766 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
15.767 * [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
15.768 * [backup-simplify]: Simplify (- 0) into 0
15.768 * [backup-simplify]: Simplify (+ 0 0) into 0
15.769 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
15.770 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
15.771 * [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)))
15.772 * [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)))))))
15.772 * [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
15.772 * [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
15.772 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
15.772 * [taylor]: Taking taylor expansion of +nan.0 in n
15.772 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.772 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
15.772 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
15.772 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.772 * [taylor]: Taking taylor expansion of 2 in n
15.773 * [backup-simplify]: Simplify 2 into 2
15.773 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.774 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.774 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
15.774 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
15.774 * [taylor]: Taking taylor expansion of 2 in n
15.774 * [backup-simplify]: Simplify 2 into 2
15.774 * [taylor]: Taking taylor expansion of (* n PI) in n
15.774 * [taylor]: Taking taylor expansion of n in n
15.774 * [backup-simplify]: Simplify 0 into 0
15.774 * [backup-simplify]: Simplify 1 into 1
15.774 * [taylor]: Taking taylor expansion of PI in n
15.774 * [backup-simplify]: Simplify PI into PI
15.775 * [backup-simplify]: Simplify (* 0 PI) into 0
15.775 * [backup-simplify]: Simplify (* 2 0) into 0
15.777 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.778 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
15.779 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
15.780 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.780 * [taylor]: Taking taylor expansion of (* n PI) in n
15.780 * [taylor]: Taking taylor expansion of n in n
15.780 * [backup-simplify]: Simplify 0 into 0
15.780 * [backup-simplify]: Simplify 1 into 1
15.780 * [taylor]: Taking taylor expansion of PI in n
15.780 * [backup-simplify]: Simplify PI into PI
15.780 * [backup-simplify]: Simplify (* 0 PI) into 0
15.782 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.782 * [backup-simplify]: Simplify (sqrt 0) into 0
15.784 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.784 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
15.784 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
15.784 * [taylor]: Taking taylor expansion of +nan.0 in n
15.784 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.784 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
15.784 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.784 * [taylor]: Taking taylor expansion of 2 in n
15.784 * [backup-simplify]: Simplify 2 into 2
15.785 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.785 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.786 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.786 * [taylor]: Taking taylor expansion of (* n PI) in n
15.786 * [taylor]: Taking taylor expansion of n in n
15.786 * [backup-simplify]: Simplify 0 into 0
15.786 * [backup-simplify]: Simplify 1 into 1
15.786 * [taylor]: Taking taylor expansion of PI in n
15.786 * [backup-simplify]: Simplify PI into PI
15.786 * [backup-simplify]: Simplify (* 0 PI) into 0
15.788 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.788 * [backup-simplify]: Simplify (sqrt 0) into 0
15.790 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.791 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
15.793 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
15.794 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
15.795 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.795 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
15.796 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.796 * [backup-simplify]: Simplify (- 0) into 0
15.797 * [backup-simplify]: Simplify (+ 0 0) into 0
15.797 * [backup-simplify]: Simplify (- 0) into 0
15.797 * [backup-simplify]: Simplify 0 into 0
15.800 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
15.806 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
15.810 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
15.812 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
15.813 * [backup-simplify]: Simplify 0 into 0
15.813 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.818 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
15.819 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
15.820 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
15.823 * [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
15.824 * [backup-simplify]: Simplify (- 0) into 0
15.824 * [backup-simplify]: Simplify (+ 0 0) into 0
15.826 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
15.827 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
15.829 * [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)))
15.830 * [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)))))))))
15.830 * [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
15.830 * [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
15.830 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
15.830 * [taylor]: Taking taylor expansion of +nan.0 in n
15.830 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.830 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
15.830 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
15.830 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.830 * [taylor]: Taking taylor expansion of 2 in n
15.830 * [backup-simplify]: Simplify 2 into 2
15.831 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.832 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.832 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
15.832 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
15.832 * [taylor]: Taking taylor expansion of 2 in n
15.832 * [backup-simplify]: Simplify 2 into 2
15.832 * [taylor]: Taking taylor expansion of (* n PI) in n
15.832 * [taylor]: Taking taylor expansion of n in n
15.832 * [backup-simplify]: Simplify 0 into 0
15.832 * [backup-simplify]: Simplify 1 into 1
15.832 * [taylor]: Taking taylor expansion of PI in n
15.832 * [backup-simplify]: Simplify PI into PI
15.832 * [backup-simplify]: Simplify (* 0 PI) into 0
15.833 * [backup-simplify]: Simplify (* 2 0) into 0
15.835 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.836 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
15.837 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
15.837 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.837 * [taylor]: Taking taylor expansion of (* n PI) in n
15.837 * [taylor]: Taking taylor expansion of n in n
15.837 * [backup-simplify]: Simplify 0 into 0
15.838 * [backup-simplify]: Simplify 1 into 1
15.838 * [taylor]: Taking taylor expansion of PI in n
15.838 * [backup-simplify]: Simplify PI into PI
15.838 * [backup-simplify]: Simplify (* 0 PI) into 0
15.840 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.840 * [backup-simplify]: Simplify (sqrt 0) into 0
15.842 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.842 * [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
15.842 * [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
15.842 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
15.842 * [taylor]: Taking taylor expansion of +nan.0 in n
15.842 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.842 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
15.842 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.842 * [taylor]: Taking taylor expansion of 2 in n
15.842 * [backup-simplify]: Simplify 2 into 2
15.842 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.843 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.843 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.843 * [taylor]: Taking taylor expansion of (* n PI) in n
15.843 * [taylor]: Taking taylor expansion of n in n
15.843 * [backup-simplify]: Simplify 0 into 0
15.843 * [backup-simplify]: Simplify 1 into 1
15.843 * [taylor]: Taking taylor expansion of PI in n
15.843 * [backup-simplify]: Simplify PI into PI
15.844 * [backup-simplify]: Simplify (* 0 PI) into 0
15.845 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.846 * [backup-simplify]: Simplify (sqrt 0) into 0
15.847 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.847 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n
15.847 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
15.847 * [taylor]: Taking taylor expansion of +nan.0 in n
15.847 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.847 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
15.847 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
15.847 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.847 * [taylor]: Taking taylor expansion of 2 in n
15.847 * [backup-simplify]: Simplify 2 into 2
15.848 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.848 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.848 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
15.848 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
15.848 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
15.849 * [taylor]: Taking taylor expansion of 2 in n
15.849 * [backup-simplify]: Simplify 2 into 2
15.849 * [taylor]: Taking taylor expansion of (* n PI) in n
15.849 * [taylor]: Taking taylor expansion of n in n
15.849 * [backup-simplify]: Simplify 0 into 0
15.849 * [backup-simplify]: Simplify 1 into 1
15.849 * [taylor]: Taking taylor expansion of PI in n
15.849 * [backup-simplify]: Simplify PI into PI
15.849 * [backup-simplify]: Simplify (* 0 PI) into 0
15.850 * [backup-simplify]: Simplify (* 2 0) into 0
15.851 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.853 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
15.854 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
15.856 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
15.856 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.856 * [taylor]: Taking taylor expansion of (* n PI) in n
15.856 * [taylor]: Taking taylor expansion of n in n
15.856 * [backup-simplify]: Simplify 0 into 0
15.856 * [backup-simplify]: Simplify 1 into 1
15.856 * [taylor]: Taking taylor expansion of PI in n
15.856 * [backup-simplify]: Simplify PI into PI
15.856 * [backup-simplify]: Simplify (* 0 PI) into 0
15.863 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.864 * [backup-simplify]: Simplify (sqrt 0) into 0
15.866 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.867 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
15.869 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
15.870 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
15.871 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.871 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
15.872 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.873 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
15.875 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
15.877 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
15.878 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
15.880 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
15.880 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.881 * [backup-simplify]: Simplify (- 0) into 0
15.881 * [backup-simplify]: Simplify (+ 0 0) into 0
15.881 * [backup-simplify]: Simplify (- 0) into 0
15.882 * [backup-simplify]: Simplify (+ 0 0) into 0
15.882 * [backup-simplify]: Simplify (- 0) into 0
15.882 * [backup-simplify]: Simplify 0 into 0
15.883 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
15.884 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
15.886 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
15.888 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
15.890 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
15.892 * [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))))))))
15.898 * [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))))))))
15.900 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
15.903 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
15.906 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
15.911 * [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))))))))))
15.916 * [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)))))))
15.921 * [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)))))))
15.921 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
15.924 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
15.925 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
15.928 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
15.936 * [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))))
15.941 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
15.945 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
15.959 * [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)))))))))))))
15.960 * [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))
15.960 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0
15.960 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
15.960 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
15.960 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
15.960 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
15.960 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
15.960 * [taylor]: Taking taylor expansion of 1/2 in n
15.960 * [backup-simplify]: Simplify 1/2 into 1/2
15.960 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
15.960 * [taylor]: Taking taylor expansion of 1 in n
15.961 * [backup-simplify]: Simplify 1 into 1
15.961 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.961 * [taylor]: Taking taylor expansion of k in n
15.961 * [backup-simplify]: Simplify k into k
15.961 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.961 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
15.961 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
15.961 * [taylor]: Taking taylor expansion of 2 in n
15.961 * [backup-simplify]: Simplify 2 into 2
15.961 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.961 * [taylor]: Taking taylor expansion of PI in n
15.961 * [backup-simplify]: Simplify PI into PI
15.961 * [taylor]: Taking taylor expansion of n in n
15.961 * [backup-simplify]: Simplify 0 into 0
15.961 * [backup-simplify]: Simplify 1 into 1
15.961 * [backup-simplify]: Simplify (/ PI 1) into PI
15.962 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
15.963 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
15.963 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
15.963 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
15.963 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
15.965 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
15.966 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
15.967 * [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)))))
15.968 * [taylor]: Taking taylor expansion of (sqrt k) in n
15.968 * [taylor]: Taking taylor expansion of k in n
15.968 * [backup-simplify]: Simplify k into k
15.968 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
15.968 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
15.968 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
15.968 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
15.968 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
15.968 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
15.968 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
15.968 * [taylor]: Taking taylor expansion of 1/2 in k
15.968 * [backup-simplify]: Simplify 1/2 into 1/2
15.968 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
15.968 * [taylor]: Taking taylor expansion of 1 in k
15.968 * [backup-simplify]: Simplify 1 into 1
15.968 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.968 * [taylor]: Taking taylor expansion of k in k
15.968 * [backup-simplify]: Simplify 0 into 0
15.968 * [backup-simplify]: Simplify 1 into 1
15.969 * [backup-simplify]: Simplify (/ 1 1) into 1
15.969 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
15.969 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
15.969 * [taylor]: Taking taylor expansion of 2 in k
15.969 * [backup-simplify]: Simplify 2 into 2
15.969 * [taylor]: Taking taylor expansion of (/ PI n) in k
15.969 * [taylor]: Taking taylor expansion of PI in k
15.969 * [backup-simplify]: Simplify PI into PI
15.969 * [taylor]: Taking taylor expansion of n in k
15.969 * [backup-simplify]: Simplify n into n
15.969 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
15.969 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
15.969 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
15.969 * [backup-simplify]: Simplify (- 1) into -1
15.970 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.970 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
15.971 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
15.971 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
15.971 * [taylor]: Taking taylor expansion of (sqrt k) in k
15.971 * [taylor]: Taking taylor expansion of k in k
15.971 * [backup-simplify]: Simplify 0 into 0
15.971 * [backup-simplify]: Simplify 1 into 1
15.971 * [backup-simplify]: Simplify (sqrt 0) into 0
15.973 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.973 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
15.973 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
15.973 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
15.973 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
15.973 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
15.973 * [taylor]: Taking taylor expansion of 1/2 in k
15.973 * [backup-simplify]: Simplify 1/2 into 1/2
15.973 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
15.973 * [taylor]: Taking taylor expansion of 1 in k
15.973 * [backup-simplify]: Simplify 1 into 1
15.973 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.973 * [taylor]: Taking taylor expansion of k in k
15.973 * [backup-simplify]: Simplify 0 into 0
15.973 * [backup-simplify]: Simplify 1 into 1
15.974 * [backup-simplify]: Simplify (/ 1 1) into 1
15.974 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
15.974 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
15.974 * [taylor]: Taking taylor expansion of 2 in k
15.974 * [backup-simplify]: Simplify 2 into 2
15.974 * [taylor]: Taking taylor expansion of (/ PI n) in k
15.974 * [taylor]: Taking taylor expansion of PI in k
15.974 * [backup-simplify]: Simplify PI into PI
15.974 * [taylor]: Taking taylor expansion of n in k
15.974 * [backup-simplify]: Simplify n into n
15.974 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
15.974 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
15.974 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
15.975 * [backup-simplify]: Simplify (- 1) into -1
15.975 * [backup-simplify]: Simplify (+ 0 -1) into -1
15.976 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
15.976 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
15.976 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
15.976 * [taylor]: Taking taylor expansion of (sqrt k) in k
15.976 * [taylor]: Taking taylor expansion of k in k
15.976 * [backup-simplify]: Simplify 0 into 0
15.976 * [backup-simplify]: Simplify 1 into 1
15.977 * [backup-simplify]: Simplify (sqrt 0) into 0
15.978 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.978 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0
15.978 * [taylor]: Taking taylor expansion of 0 in n
15.978 * [backup-simplify]: Simplify 0 into 0
15.978 * [backup-simplify]: Simplify 0 into 0
15.979 * [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))))))))
15.979 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
15.979 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
15.979 * [taylor]: Taking taylor expansion of +nan.0 in n
15.979 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.979 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
15.979 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
15.979 * [taylor]: Taking taylor expansion of 1/2 in n
15.979 * [backup-simplify]: Simplify 1/2 into 1/2
15.979 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
15.979 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
15.979 * [taylor]: Taking taylor expansion of 1 in n
15.979 * [backup-simplify]: Simplify 1 into 1
15.979 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.980 * [taylor]: Taking taylor expansion of k in n
15.980 * [backup-simplify]: Simplify k into k
15.980 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.980 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
15.980 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
15.980 * [taylor]: Taking taylor expansion of 2 in n
15.980 * [backup-simplify]: Simplify 2 into 2
15.980 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.980 * [taylor]: Taking taylor expansion of PI in n
15.980 * [backup-simplify]: Simplify PI into PI
15.980 * [taylor]: Taking taylor expansion of n in n
15.980 * [backup-simplify]: Simplify 0 into 0
15.980 * [backup-simplify]: Simplify 1 into 1
15.987 * [backup-simplify]: Simplify (/ PI 1) into PI
15.988 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
15.989 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
15.989 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
15.990 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
15.991 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
15.992 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
15.994 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
15.995 * [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)))))
15.996 * [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))))))
15.997 * [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)))))))
15.999 * [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)))))))
15.999 * [backup-simplify]: Simplify 0 into 0
16.002 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
16.002 * [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))))))))
16.003 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
16.003 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
16.003 * [taylor]: Taking taylor expansion of +nan.0 in n
16.003 * [backup-simplify]: Simplify +nan.0 into +nan.0
16.003 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
16.003 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
16.003 * [taylor]: Taking taylor expansion of 1/2 in n
16.003 * [backup-simplify]: Simplify 1/2 into 1/2
16.003 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
16.003 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
16.003 * [taylor]: Taking taylor expansion of 1 in n
16.003 * [backup-simplify]: Simplify 1 into 1
16.003 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.003 * [taylor]: Taking taylor expansion of k in n
16.003 * [backup-simplify]: Simplify k into k
16.003 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.003 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
16.003 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.003 * [taylor]: Taking taylor expansion of 2 in n
16.003 * [backup-simplify]: Simplify 2 into 2
16.003 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.003 * [taylor]: Taking taylor expansion of PI in n
16.003 * [backup-simplify]: Simplify PI into PI
16.003 * [taylor]: Taking taylor expansion of n in n
16.003 * [backup-simplify]: Simplify 0 into 0
16.003 * [backup-simplify]: Simplify 1 into 1
16.004 * [backup-simplify]: Simplify (/ PI 1) into PI
16.004 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.005 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.005 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
16.005 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
16.007 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.008 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
16.009 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
16.010 * [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)))))
16.011 * [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))))))
16.012 * [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)))))))
16.014 * [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)))))))
16.015 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.015 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
16.017 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.017 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.018 * [backup-simplify]: Simplify (- 0) into 0
16.018 * [backup-simplify]: Simplify (+ 0 0) into 0
16.019 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.021 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
16.022 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
16.024 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.025 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
16.026 * [backup-simplify]: Simplify (- 0) into 0
16.026 * [backup-simplify]: Simplify 0 into 0
16.026 * [backup-simplify]: Simplify 0 into 0
16.029 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
16.030 * [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))))))))
16.030 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
16.030 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
16.030 * [taylor]: Taking taylor expansion of +nan.0 in n
16.030 * [backup-simplify]: Simplify +nan.0 into +nan.0
16.030 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
16.030 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
16.030 * [taylor]: Taking taylor expansion of 1/2 in n
16.030 * [backup-simplify]: Simplify 1/2 into 1/2
16.030 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
16.030 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
16.030 * [taylor]: Taking taylor expansion of 1 in n
16.030 * [backup-simplify]: Simplify 1 into 1
16.030 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.030 * [taylor]: Taking taylor expansion of k in n
16.030 * [backup-simplify]: Simplify k into k
16.030 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.030 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
16.030 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.030 * [taylor]: Taking taylor expansion of 2 in n
16.030 * [backup-simplify]: Simplify 2 into 2
16.030 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.030 * [taylor]: Taking taylor expansion of PI in n
16.030 * [backup-simplify]: Simplify PI into PI
16.030 * [taylor]: Taking taylor expansion of n in n
16.030 * [backup-simplify]: Simplify 0 into 0
16.030 * [backup-simplify]: Simplify 1 into 1
16.031 * [backup-simplify]: Simplify (/ PI 1) into PI
16.031 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.032 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.032 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
16.032 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
16.033 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.033 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
16.034 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
16.035 * [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)))))
16.036 * [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))))))
16.036 * [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)))))))
16.037 * [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)))))))
16.040 * [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))))))))
16.040 * [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)))
16.040 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0
16.040 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
16.040 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
16.040 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
16.041 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
16.041 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
16.041 * [taylor]: Taking taylor expansion of 1/2 in n
16.041 * [backup-simplify]: Simplify 1/2 into 1/2
16.041 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.041 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.041 * [taylor]: Taking taylor expansion of k in n
16.041 * [backup-simplify]: Simplify k into k
16.041 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.041 * [taylor]: Taking taylor expansion of 1 in n
16.041 * [backup-simplify]: Simplify 1 into 1
16.041 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
16.041 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.041 * [taylor]: Taking taylor expansion of -2 in n
16.041 * [backup-simplify]: Simplify -2 into -2
16.041 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.041 * [taylor]: Taking taylor expansion of PI in n
16.041 * [backup-simplify]: Simplify PI into PI
16.041 * [taylor]: Taking taylor expansion of n in n
16.041 * [backup-simplify]: Simplify 0 into 0
16.041 * [backup-simplify]: Simplify 1 into 1
16.041 * [backup-simplify]: Simplify (/ PI 1) into PI
16.042 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.042 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.042 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.042 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
16.043 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.044 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
16.045 * [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)))))
16.045 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
16.045 * [taylor]: Taking taylor expansion of (/ -1 k) in n
16.045 * [taylor]: Taking taylor expansion of -1 in n
16.045 * [backup-simplify]: Simplify -1 into -1
16.045 * [taylor]: Taking taylor expansion of k in n
16.045 * [backup-simplify]: Simplify k into k
16.045 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
16.045 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
16.045 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
16.045 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
16.046 * [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)))
16.046 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
16.046 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
16.046 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
16.046 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
16.046 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
16.046 * [taylor]: Taking taylor expansion of 1/2 in k
16.046 * [backup-simplify]: Simplify 1/2 into 1/2
16.046 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
16.046 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.046 * [taylor]: Taking taylor expansion of k in k
16.046 * [backup-simplify]: Simplify 0 into 0
16.046 * [backup-simplify]: Simplify 1 into 1
16.046 * [backup-simplify]: Simplify (/ 1 1) into 1
16.046 * [taylor]: Taking taylor expansion of 1 in k
16.046 * [backup-simplify]: Simplify 1 into 1
16.046 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
16.046 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
16.046 * [taylor]: Taking taylor expansion of -2 in k
16.046 * [backup-simplify]: Simplify -2 into -2
16.046 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.046 * [taylor]: Taking taylor expansion of PI in k
16.046 * [backup-simplify]: Simplify PI into PI
16.047 * [taylor]: Taking taylor expansion of n in k
16.047 * [backup-simplify]: Simplify n into n
16.047 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.047 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
16.047 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
16.047 * [backup-simplify]: Simplify (+ 1 0) into 1
16.047 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.047 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
16.047 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
16.047 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
16.047 * [taylor]: Taking taylor expansion of (/ -1 k) in k
16.047 * [taylor]: Taking taylor expansion of -1 in k
16.047 * [backup-simplify]: Simplify -1 into -1
16.048 * [taylor]: Taking taylor expansion of k in k
16.048 * [backup-simplify]: Simplify 0 into 0
16.048 * [backup-simplify]: Simplify 1 into 1
16.048 * [backup-simplify]: Simplify (/ -1 1) into -1
16.048 * [backup-simplify]: Simplify (sqrt 0) into 0
16.049 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
16.049 * [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)))))
16.049 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
16.049 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
16.049 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
16.050 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
16.050 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
16.050 * [taylor]: Taking taylor expansion of 1/2 in k
16.050 * [backup-simplify]: Simplify 1/2 into 1/2
16.050 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
16.050 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.050 * [taylor]: Taking taylor expansion of k in k
16.050 * [backup-simplify]: Simplify 0 into 0
16.050 * [backup-simplify]: Simplify 1 into 1
16.050 * [backup-simplify]: Simplify (/ 1 1) into 1
16.050 * [taylor]: Taking taylor expansion of 1 in k
16.050 * [backup-simplify]: Simplify 1 into 1
16.050 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
16.050 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
16.050 * [taylor]: Taking taylor expansion of -2 in k
16.050 * [backup-simplify]: Simplify -2 into -2
16.050 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.050 * [taylor]: Taking taylor expansion of PI in k
16.050 * [backup-simplify]: Simplify PI into PI
16.050 * [taylor]: Taking taylor expansion of n in k
16.050 * [backup-simplify]: Simplify n into n
16.051 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.051 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
16.051 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
16.051 * [backup-simplify]: Simplify (+ 1 0) into 1
16.052 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.052 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
16.052 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
16.052 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
16.052 * [taylor]: Taking taylor expansion of (/ -1 k) in k
16.052 * [taylor]: Taking taylor expansion of -1 in k
16.052 * [backup-simplify]: Simplify -1 into -1
16.052 * [taylor]: Taking taylor expansion of k in k
16.052 * [backup-simplify]: Simplify 0 into 0
16.052 * [backup-simplify]: Simplify 1 into 1
16.053 * [backup-simplify]: Simplify (/ -1 1) into -1
16.053 * [backup-simplify]: Simplify (sqrt 0) into 0
16.055 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
16.055 * [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)))))
16.055 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
16.055 * [taylor]: Taking taylor expansion of +nan.0 in n
16.055 * [backup-simplify]: Simplify +nan.0 into +nan.0
16.055 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
16.055 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
16.055 * [taylor]: Taking taylor expansion of 1/2 in n
16.055 * [backup-simplify]: Simplify 1/2 into 1/2
16.055 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
16.055 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
16.055 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.055 * [taylor]: Taking taylor expansion of -2 in n
16.055 * [backup-simplify]: Simplify -2 into -2
16.055 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.055 * [taylor]: Taking taylor expansion of PI in n
16.055 * [backup-simplify]: Simplify PI into PI
16.055 * [taylor]: Taking taylor expansion of n in n
16.055 * [backup-simplify]: Simplify 0 into 0
16.055 * [backup-simplify]: Simplify 1 into 1
16.056 * [backup-simplify]: Simplify (/ PI 1) into PI
16.056 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.057 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.058 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.058 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.058 * [taylor]: Taking taylor expansion of k in n
16.058 * [backup-simplify]: Simplify k into k
16.058 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.058 * [taylor]: Taking taylor expansion of 1 in n
16.058 * [backup-simplify]: Simplify 1 into 1
16.059 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.059 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.060 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
16.062 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
16.063 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
16.064 * [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))))))
16.065 * [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))))))
16.066 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
16.068 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
16.069 * [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))))))
16.069 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
16.069 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
16.069 * [taylor]: Taking taylor expansion of +nan.0 in n
16.069 * [backup-simplify]: Simplify +nan.0 into +nan.0
16.069 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
16.070 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
16.070 * [taylor]: Taking taylor expansion of 1/2 in n
16.070 * [backup-simplify]: Simplify 1/2 into 1/2
16.070 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
16.070 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
16.070 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.070 * [taylor]: Taking taylor expansion of -2 in n
16.070 * [backup-simplify]: Simplify -2 into -2
16.070 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.070 * [taylor]: Taking taylor expansion of PI in n
16.070 * [backup-simplify]: Simplify PI into PI
16.070 * [taylor]: Taking taylor expansion of n in n
16.070 * [backup-simplify]: Simplify 0 into 0
16.070 * [backup-simplify]: Simplify 1 into 1
16.070 * [backup-simplify]: Simplify (/ PI 1) into PI
16.071 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.072 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.072 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.072 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.072 * [taylor]: Taking taylor expansion of k in n
16.072 * [backup-simplify]: Simplify k into k
16.072 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.072 * [taylor]: Taking taylor expansion of 1 in n
16.072 * [backup-simplify]: Simplify 1 into 1
16.073 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.073 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.075 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
16.076 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
16.077 * [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)))))
16.078 * [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))))))
16.079 * [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)))))))
16.079 * [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)))))))
16.080 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.080 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.081 * [backup-simplify]: Simplify (+ 0 0) into 0
16.081 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.082 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
16.083 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
16.084 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
16.085 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
16.086 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.087 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
16.087 * [backup-simplify]: Simplify 0 into 0
16.088 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.090 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
16.091 * [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))))))
16.091 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
16.091 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
16.091 * [taylor]: Taking taylor expansion of +nan.0 in n
16.091 * [backup-simplify]: Simplify +nan.0 into +nan.0
16.091 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
16.091 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
16.091 * [taylor]: Taking taylor expansion of 1/2 in n
16.091 * [backup-simplify]: Simplify 1/2 into 1/2
16.091 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
16.091 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
16.091 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.091 * [taylor]: Taking taylor expansion of -2 in n
16.091 * [backup-simplify]: Simplify -2 into -2
16.091 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.091 * [taylor]: Taking taylor expansion of PI in n
16.091 * [backup-simplify]: Simplify PI into PI
16.091 * [taylor]: Taking taylor expansion of n in n
16.091 * [backup-simplify]: Simplify 0 into 0
16.091 * [backup-simplify]: Simplify 1 into 1
16.092 * [backup-simplify]: Simplify (/ PI 1) into PI
16.092 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.093 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.093 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.093 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.093 * [taylor]: Taking taylor expansion of k in n
16.093 * [backup-simplify]: Simplify k into k
16.093 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.093 * [taylor]: Taking taylor expansion of 1 in n
16.093 * [backup-simplify]: Simplify 1 into 1
16.094 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.094 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.095 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
16.095 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
16.096 * [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)))))
16.097 * [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))))))
16.098 * [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)))))))
16.099 * [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)))))))
16.105 * [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))))))))))))
16.106 * * * [progress]: simplifying candidates
16.106 * * * * [progress]: [ 1 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
16.106 * * * * [progress]: [ 2 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
16.106 * * * * [progress]: [ 3 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
16.106 * * * * [progress]: [ 4 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
16.106 * * * * [progress]: [ 5 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
16.106 * * * * [progress]: [ 6 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
16.106 * * * * [progress]: [ 7 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
16.106 * * * * [progress]: [ 8 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))>
16.106 * * * * [progress]: [ 9 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2)))))>
16.106 * * * * [progress]: [ 10 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2)))))>
16.106 * * * * [progress]: [ 11 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2)))))>
16.106 * * * * [progress]: [ 12 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2)))))>
16.106 * * * * [progress]: [ 13 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2))))>
16.106 * * * * [progress]: [ 14 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2)))))>
16.106 * * * * [progress]: [ 15 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2)))))>
16.106 * * * * [progress]: [ 16 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2))))>
16.106 * * * * [progress]: [ 17 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
16.106 * * * * [progress]: [ 18 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
16.106 * * * * [progress]: [ 19 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
16.106 * * * * [progress]: [ 20 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2)))))>
16.106 * * * * [progress]: [ 21 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2)))))>
16.107 * * * * [progress]: [ 22 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2))))>
16.107 * * * * [progress]: [ 23 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2)))))>
16.107 * * * * [progress]: [ 24 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2)))))>
16.107 * * * * [progress]: [ 25 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))))>
16.107 * * * * [progress]: [ 26 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
16.107 * * * * [progress]: [ 27 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
16.107 * * * * [progress]: [ 28 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
16.107 * * * * [progress]: [ 29 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
16.107 * * * * [progress]: [ 30 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) (/ 1 2))))>
16.107 * * * * [progress]: [ 31 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))))>
16.107 * * * * [progress]: [ 32 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1)))>
16.107 * * * * [progress]: [ 33 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.107 * * * * [progress]: [ 34 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (log (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.107 * * * * [progress]: [ 35 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.107 * * * * [progress]: [ 36 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (cbrt (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.107 * * * * [progress]: [ 37 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.107 * * * * [progress]: [ 38 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.107 * * * * [progress]: [ 39 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
16.107 * * * * [progress]: [ 40 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (posit16->real (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.107 * * * * [progress]: [ 41 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
16.107 * * * * [progress]: [ 42 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
16.107 * * * * [progress]: [ 43 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
16.107 * * * * [progress]: [ 44 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (+ (log 2) (log PI)) (log n))) (/ (- 1 k) 2))))>
16.107 * * * * [progress]: [ 45 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (log (* 2 PI)) (log n))) (/ (- 1 k) 2))))>
16.107 * * * * [progress]: [ 46 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (log (* (* 2 PI) n))) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 47 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (log (exp (* (* 2 PI) n))) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 48 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 49 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 50 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) (cbrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 51 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 52 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 53 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 1 (* (* 2 PI) n)) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 54 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 55 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 56 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) 1) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 57 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 58 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (posit16->real (real->posit16 (* (* 2 PI) n))) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 59 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 60 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 61 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 62 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) (- 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 63 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- (/ 1 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 64 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 65 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 66 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- 0 (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 67 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log 1) (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 68 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 69 / 188 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 70 / 188 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 71 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.108 * * * * [progress]: [ 72 / 188 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 73 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 74 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (- 1) (- (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 75 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 76 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1) (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 77 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 78 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 79 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 80 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 81 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1) (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 82 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1) (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 83 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 84 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 85 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 86 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 87 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 88 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 89 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 90 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt 1)) (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 91 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 92 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 1) (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 93 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.109 * * * * [progress]: [ 94 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.110 * * * * [progress]: [ 95 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.110 * * * * [progress]: [ 96 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.110 * * * * [progress]: [ 97 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.110 * * * * [progress]: [ 98 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.110 * * * * [progress]: [ 99 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt 1)) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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16.110 * * * * [progress]: [ 101 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.110 * * * * [progress]: [ 102 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (cbrt 1))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.110 * * * * [progress]: [ 103 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt k) (sqrt 1))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.110 * * * * [progress]: [ 104 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.110 * * * * [progress]: [ 105 / 188 ] simplifiying candidate #<alt (λ (k n) (* (posit16->real (real->posit16 (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.110 * * * * [progress]: [ 106 / 188 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1))>
16.110 * * * * [progress]: [ 107 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
16.110 * * * * [progress]: [ 108 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
16.110 * * * * [progress]: [ 109 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
16.110 * * * * [progress]: [ 110 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
16.111 * * * * [progress]: [ 111 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.111 * * * * [progress]: [ 112 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
16.111 * * * * [progress]: [ 113 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
16.111 * * * * [progress]: [ 114 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
16.111 * * * * [progress]: [ 115 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
16.111 * * * * [progress]: [ 116 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.111 * * * * [progress]: [ 117 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
16.111 * * * * [progress]: [ 118 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
16.111 * * * * [progress]: [ 119 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
16.111 * * * * [progress]: [ 120 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
16.111 * * * * [progress]: [ 121 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.111 * * * * [progress]: [ 122 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
16.111 * * * * [progress]: [ 123 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
16.111 * * * * [progress]: [ 124 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
16.111 * * * * [progress]: [ 125 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
16.112 * * * * [progress]: [ 126 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.112 * * * * [progress]: [ 127 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.112 * * * * [progress]: [ 128 / 188 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.112 * * * * [progress]: [ 129 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.112 * * * * [progress]: [ 130 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.112 * * * * [progress]: [ 131 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.112 * * * * [progress]: [ 132 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.112 * * * * [progress]: [ 133 / 188 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.112 * * * * [progress]: [ 134 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))))>
16.112 * * * * [progress]: [ 135 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.112 * * * * [progress]: [ 136 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.112 * * * * [progress]: [ 137 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
16.112 * * * * [progress]: [ 138 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.112 * * * * [progress]: [ 139 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
16.112 * * * * [progress]: [ 140 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.113 * * * * [progress]: [ 141 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
16.113 * * * * [progress]: [ 142 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.113 * * * * [progress]: [ 143 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
16.113 * * * * [progress]: [ 144 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.113 * * * * [progress]: [ 145 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
16.113 * * * * [progress]: [ 146 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))))>
16.113 * * * * [progress]: [ 147 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.113 * * * * [progress]: [ 148 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.113 * * * * [progress]: [ 149 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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16.113 * * * * [progress]: [ 151 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.113 * * * * [progress]: [ 152 / 188 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.113 * * * * [progress]: [ 153 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.113 * * * * [progress]: [ 154 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.113 * * * * [progress]: [ 155 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.114 * * * * [progress]: [ 156 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.114 * * * * [progress]: [ 157 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.114 * * * * [progress]: [ 158 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) 1) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.114 * * * * [progress]: [ 159 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.114 * * * * [progress]: [ 160 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.114 * * * * [progress]: [ 161 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
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16.114 * * * * [progress]: [ 163 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.114 * * * * [progress]: [ 164 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.114 * * * * [progress]: [ 165 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.114 * * * * [progress]: [ 166 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
16.114 * * * * [progress]: [ 167 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
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16.115 * * * * [progress]: [ 170 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
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16.115 * * * * [progress]: [ 173 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* (* 2 PI) n) (/ k 2))))>
16.115 * * * * [progress]: [ 174 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))>
16.115 * * * * [progress]: [ 175 / 188 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
16.115 * * * * [progress]: [ 176 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
16.115 * * * * [progress]: [ 177 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))))>
16.115 * * * * [progress]: [ 178 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))>
16.115 * * * * [progress]: [ 179 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))>
16.115 * * * * [progress]: [ 180 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
16.115 * * * * [progress]: [ 181 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
16.115 * * * * [progress]: [ 182 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
16.115 * * * * [progress]: [ 183 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.115 * * * * [progress]: [ 184 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.115 * * * * [progress]: [ 185 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
16.116 * * * * [progress]: [ 186 / 188 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))>
16.116 * * * * [progress]: [ 187 / 188 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
16.116 * * * * [progress]: [ 188 / 188 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
16.119 * [simplify]: Simplifying:
  (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2))
  (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))
  (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
  (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* (* 2 PI) n) (/ 1 2))
  (pow (* (* 2 PI) n) (/ k 2))
  (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1))
  (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2 PI) n) (/ 1 1))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1))
  (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2 PI) n) (/ 1 1))
  (pow (* (* 2 PI) n) 1)
  (pow (* (* 2 PI) n) (- 1 k))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
  (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (+ (+ (log 2) (log PI)) (log n))
  (+ (log (* 2 PI)) (log n))
  (log (* (* 2 PI) n))
  (exp (* (* 2 PI) n))
  (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))
  (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n)))
  (cbrt (* (* 2 PI) n))
  (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (* (* 2 PI) (* (cbrt n) (cbrt n)))
  (* (* 2 PI) (sqrt n))
  (* (* 2 PI) 1)
  (* PI n)
  (real->posit16 (* (* 2 PI) n))
  (- 1/2)
  (- 1)
  (- (/ 1 2))
  (- (log (sqrt k)))
  (- 0 (log (sqrt k)))
  (- (log 1) (log (sqrt k)))
  (log (/ 1 (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (- 1)
  (- (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1) (cbrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1) (sqrt (cbrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))
  (/ (cbrt 1) (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) 1)
  (/ (cbrt 1) (sqrt k))
  (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1) (cbrt (sqrt k)))
  (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1) (sqrt (cbrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt 1))
  (/ (sqrt 1) (sqrt k))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) 1)
  (/ (sqrt 1) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1)
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ (sqrt k) (cbrt 1))
  (/ (sqrt k) (sqrt 1))
  (/ (sqrt k) 1)
  (real->posit16 (/ 1 (sqrt k)))
  (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (- (log 1) (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (log (/ 1 (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
  (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* 1 (pow (* (* 2 PI) n) (/ 1 2)))
  (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
  (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt k)) 1)
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2)))
  (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
16.125 * * [simplify]: iteration 1: (345 enodes)
16.373 * * [simplify]: iteration 2: (922 enodes)
17.140 * * [simplify]: Extracting #0: cost 94 inf + 0
17.142 * * [simplify]: Extracting #1: cost 421 inf + 3
17.147 * * [simplify]: Extracting #2: cost 699 inf + 5459
17.161 * * [simplify]: Extracting #3: cost 633 inf + 50506
17.183 * * [simplify]: Extracting #4: cost 314 inf + 163558
17.224 * * [simplify]: Extracting #5: cost 151 inf + 230840
17.302 * * [simplify]: Extracting #6: cost 58 inf + 265745
17.389 * * [simplify]: Extracting #7: cost 33 inf + 274956
17.470 * * [simplify]: Extracting #8: cost 5 inf + 291468
17.533 * * [simplify]: Extracting #9: cost 0 inf + 293017
17.603 * * [simplify]: Extracting #10: cost 0 inf + 292497
17.678 * [simplify]: Simplified to:
  (* (/ (- 1 k) 2) (log (* n (* 2 PI))))
  (* (/ (- 1 k) 2) (log (* n (* 2 PI))))
  (* (/ (- 1 k) 2) (log (* n (* 2 PI))))
  (* (/ (- 1 k) 2) (log (* n (* 2 PI))))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (sqrt (* n (* 2 PI)))
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* n (* 2 PI)) (* (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt (- 1 k))))
  (pow (* n (* 2 PI)) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (sqrt (- 1 k)))
  (pow (* n (* 2 PI)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (* n (* 2 PI))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* n (* 2 PI)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (+ (sqrt k) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* n (* 2 PI)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (+ (sqrt k) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (pow (* n (* 2 PI)) (- 1 k))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* n (* 2 PI))))
  (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (- 1 k) 4))
  (pow (* n (* 2 PI)) (/ (- 1 k) 4))
  (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (log (* n (* 2 PI)))
  (log (* n (* 2 PI)))
  (log (* n (* 2 PI)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* n (* (* (* (* PI PI) PI) 8) (* n n)))
  (* (* PI n) (* 2 (* (* (* PI n) (* PI n)) 4)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* PI n) (* 2 (* (* (* PI n) (* PI n)) 4)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* (* 2 PI) (* (cbrt n) (cbrt n)))
  (* (* 2 PI) (sqrt n))
  (* 2 PI)
  (* PI n)
  (real->posit16 (* n (* 2 PI)))
  -1/2
  -1
  -1/2
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ 1 (* (sqrt k) k))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (/ (/ 1 (sqrt k)) (sqrt k)) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  -1
  (- (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (sqrt k)
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt (sqrt k)))
  1
  (sqrt k)
  (sqrt k)
  (sqrt k)
  (real->posit16 (/ 1 (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (exp (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (/ (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 3) (* (sqrt k) k))
  (* (/ (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) (sqrt k)) (/ (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))
  (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (* (/ (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) (sqrt k)) (/ (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (* n (* 2 PI)))
  (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt k))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (/ 1 (sqrt k))))
  (* (sqrt (/ 1 (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (sqrt (* n (* 2 PI))) (sqrt k))
  (pow (* n (* 2 PI)) (/ (- 1 k) 2))
  (real->posit16 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (+ (+ (+ (sqrt (* n (* 2 PI))) (* (* (* (log n) (* k k)) (log n)) (* 1/8 (sqrt (* n (* 2 PI)))))) (* 1/8 (* (* (log (* 2 PI)) (log (* 2 PI))) (* (sqrt (* n (* 2 PI))) (* k k))))) (+ (* (* (log (* 2 PI)) 1/4) (* (log n) (* (sqrt (* n (* 2 PI))) (* k k)))) (* -1/2 (* k (+ (* (sqrt (* n (* 2 PI))) (log n)) (* (log (* 2 PI)) (sqrt (* n (* 2 PI)))))))))
  (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI)))))
  (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n)))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (* +nan.0 (- (* k k))) (- +nan.0 (* k +nan.0)))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* (* k k) k))))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) +nan.0))
  (+ (- (* (* (* n PI) k) (* (sqrt 2) +nan.0))) (+ (- (* (* (sqrt 2) +nan.0) (* PI n)) (* (* (* (* n PI) k) (* (sqrt 2) +nan.0)) (log (* 2 PI)))) (* (* (sqrt 2) +nan.0) (- (* (* n PI) (* k (log n))) (* (* n PI) (* n PI))))))
  (+ (* (/ (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI))))) k) (- +nan.0)) (* +nan.0 (- (/ (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI))))) (* k k)) (/ (/ (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI))))) (* k k)) k))))
  (- (- (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) (/ k +nan.0)) (* +nan.0 (- (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k)) (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n)))))))))
17.699 * * * [progress]: adding candidates to table
19.042 * * [progress]: iteration 4 / 4
19.042 * * * [progress]: picking best candidate
19.072 * * * * [pick]: Picked  #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
19.072 * * * [progress]: localizing error
19.126 * * * [progress]: generating rewritten candidates
19.126 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2)
19.156 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1)
19.186 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1)
19.263 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 1)
19.294 * * * [progress]: generating series expansions
19.294 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2)
19.296 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))
19.296 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
19.296 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
19.296 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
19.296 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
19.296 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
19.296 * [taylor]: Taking taylor expansion of 1/2 in k
19.296 * [backup-simplify]: Simplify 1/2 into 1/2
19.296 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
19.296 * [taylor]: Taking taylor expansion of 1/2 in k
19.296 * [backup-simplify]: Simplify 1/2 into 1/2
19.296 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
19.296 * [taylor]: Taking taylor expansion of 1/2 in k
19.296 * [backup-simplify]: Simplify 1/2 into 1/2
19.296 * [taylor]: Taking taylor expansion of k in k
19.296 * [backup-simplify]: Simplify 0 into 0
19.296 * [backup-simplify]: Simplify 1 into 1
19.296 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
19.296 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
19.296 * [taylor]: Taking taylor expansion of 2 in k
19.296 * [backup-simplify]: Simplify 2 into 2
19.296 * [taylor]: Taking taylor expansion of (* n PI) in k
19.296 * [taylor]: Taking taylor expansion of n in k
19.296 * [backup-simplify]: Simplify n into n
19.296 * [taylor]: Taking taylor expansion of PI in k
19.296 * [backup-simplify]: Simplify PI into PI
19.296 * [backup-simplify]: Simplify (* n PI) into (* n PI)
19.297 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
19.297 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
19.297 * [backup-simplify]: Simplify (* 1/2 0) into 0
19.298 * [backup-simplify]: Simplify (- 0) into 0
19.298 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.299 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
19.299 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
19.299 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
19.299 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
19.299 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
19.299 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
19.299 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
19.299 * [taylor]: Taking taylor expansion of 1/2 in n
19.299 * [backup-simplify]: Simplify 1/2 into 1/2
19.299 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
19.299 * [taylor]: Taking taylor expansion of 1/2 in n
19.299 * [backup-simplify]: Simplify 1/2 into 1/2
19.299 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
19.299 * [taylor]: Taking taylor expansion of 1/2 in n
19.299 * [backup-simplify]: Simplify 1/2 into 1/2
19.299 * [taylor]: Taking taylor expansion of k in n
19.299 * [backup-simplify]: Simplify k into k
19.299 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
19.299 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
19.299 * [taylor]: Taking taylor expansion of 2 in n
19.299 * [backup-simplify]: Simplify 2 into 2
19.299 * [taylor]: Taking taylor expansion of (* n PI) in n
19.299 * [taylor]: Taking taylor expansion of n in n
19.299 * [backup-simplify]: Simplify 0 into 0
19.299 * [backup-simplify]: Simplify 1 into 1
19.299 * [taylor]: Taking taylor expansion of PI in n
19.299 * [backup-simplify]: Simplify PI into PI
19.300 * [backup-simplify]: Simplify (* 0 PI) into 0
19.301 * [backup-simplify]: Simplify (* 2 0) into 0
19.303 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.304 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
19.306 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.306 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
19.306 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
19.306 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
19.306 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
19.308 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.309 * [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)))))
19.310 * [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))))))
19.310 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
19.310 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
19.310 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
19.310 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
19.310 * [taylor]: Taking taylor expansion of 1/2 in n
19.311 * [backup-simplify]: Simplify 1/2 into 1/2
19.311 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
19.311 * [taylor]: Taking taylor expansion of 1/2 in n
19.311 * [backup-simplify]: Simplify 1/2 into 1/2
19.311 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
19.311 * [taylor]: Taking taylor expansion of 1/2 in n
19.311 * [backup-simplify]: Simplify 1/2 into 1/2
19.311 * [taylor]: Taking taylor expansion of k in n
19.311 * [backup-simplify]: Simplify k into k
19.311 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
19.311 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
19.311 * [taylor]: Taking taylor expansion of 2 in n
19.311 * [backup-simplify]: Simplify 2 into 2
19.311 * [taylor]: Taking taylor expansion of (* n PI) in n
19.311 * [taylor]: Taking taylor expansion of n in n
19.311 * [backup-simplify]: Simplify 0 into 0
19.311 * [backup-simplify]: Simplify 1 into 1
19.311 * [taylor]: Taking taylor expansion of PI in n
19.311 * [backup-simplify]: Simplify PI into PI
19.312 * [backup-simplify]: Simplify (* 0 PI) into 0
19.312 * [backup-simplify]: Simplify (* 2 0) into 0
19.313 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.315 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
19.316 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.316 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
19.316 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
19.316 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
19.317 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
19.318 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.319 * [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)))))
19.319 * [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))))))
19.319 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
19.319 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
19.319 * [taylor]: Taking taylor expansion of 1/2 in k
19.319 * [backup-simplify]: Simplify 1/2 into 1/2
19.319 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
19.320 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
19.320 * [taylor]: Taking taylor expansion of 1/2 in k
19.320 * [backup-simplify]: Simplify 1/2 into 1/2
19.320 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
19.320 * [taylor]: Taking taylor expansion of 1/2 in k
19.320 * [backup-simplify]: Simplify 1/2 into 1/2
19.320 * [taylor]: Taking taylor expansion of k in k
19.320 * [backup-simplify]: Simplify 0 into 0
19.320 * [backup-simplify]: Simplify 1 into 1
19.320 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
19.320 * [taylor]: Taking taylor expansion of (log n) in k
19.320 * [taylor]: Taking taylor expansion of n in k
19.320 * [backup-simplify]: Simplify n into n
19.320 * [backup-simplify]: Simplify (log n) into (log n)
19.320 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
19.320 * [taylor]: Taking taylor expansion of (* 2 PI) in k
19.320 * [taylor]: Taking taylor expansion of 2 in k
19.320 * [backup-simplify]: Simplify 2 into 2
19.320 * [taylor]: Taking taylor expansion of PI in k
19.320 * [backup-simplify]: Simplify PI into PI
19.320 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.321 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.321 * [backup-simplify]: Simplify (* 1/2 0) into 0
19.321 * [backup-simplify]: Simplify (- 0) into 0
19.322 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.326 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.327 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
19.327 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
19.328 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
19.329 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
19.329 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
19.330 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
19.331 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
19.332 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
19.332 * [backup-simplify]: Simplify (- 0) into 0
19.332 * [backup-simplify]: Simplify (+ 0 0) into 0
19.332 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
19.333 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.334 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
19.335 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.335 * [taylor]: Taking taylor expansion of 0 in k
19.335 * [backup-simplify]: Simplify 0 into 0
19.335 * [backup-simplify]: Simplify 0 into 0
19.336 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
19.336 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
19.338 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
19.338 * [backup-simplify]: Simplify (+ 0 0) into 0
19.338 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
19.338 * [backup-simplify]: Simplify (- 1/2) into -1/2
19.339 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
19.340 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
19.342 * [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)))))
19.344 * [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)))))))
19.346 * [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)))))))
19.348 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
19.349 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
19.352 * [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
19.353 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
19.353 * [backup-simplify]: Simplify (- 0) into 0
19.354 * [backup-simplify]: Simplify (+ 0 0) into 0
19.355 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
19.356 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.357 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
19.360 * [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
19.360 * [taylor]: Taking taylor expansion of 0 in k
19.360 * [backup-simplify]: Simplify 0 into 0
19.360 * [backup-simplify]: Simplify 0 into 0
19.360 * [backup-simplify]: Simplify 0 into 0
19.361 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
19.362 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
19.365 * [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
19.366 * [backup-simplify]: Simplify (+ 0 0) into 0
19.367 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
19.368 * [backup-simplify]: Simplify (- 0) into 0
19.368 * [backup-simplify]: Simplify (+ 0 0) into 0
19.370 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
19.374 * [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
19.378 * [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)))))
19.383 * [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)))))
19.392 * [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)))))))
19.393 * [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)))))
19.393 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
19.393 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
19.393 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
19.393 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
19.393 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
19.393 * [taylor]: Taking taylor expansion of 1/2 in k
19.393 * [backup-simplify]: Simplify 1/2 into 1/2
19.393 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
19.393 * [taylor]: Taking taylor expansion of 1/2 in k
19.393 * [backup-simplify]: Simplify 1/2 into 1/2
19.393 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
19.393 * [taylor]: Taking taylor expansion of 1/2 in k
19.394 * [backup-simplify]: Simplify 1/2 into 1/2
19.394 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.394 * [taylor]: Taking taylor expansion of k in k
19.394 * [backup-simplify]: Simplify 0 into 0
19.394 * [backup-simplify]: Simplify 1 into 1
19.394 * [backup-simplify]: Simplify (/ 1 1) into 1
19.394 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
19.394 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
19.394 * [taylor]: Taking taylor expansion of 2 in k
19.394 * [backup-simplify]: Simplify 2 into 2
19.394 * [taylor]: Taking taylor expansion of (/ PI n) in k
19.394 * [taylor]: Taking taylor expansion of PI in k
19.394 * [backup-simplify]: Simplify PI into PI
19.394 * [taylor]: Taking taylor expansion of n in k
19.394 * [backup-simplify]: Simplify n into n
19.394 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
19.394 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
19.394 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
19.395 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
19.395 * [backup-simplify]: Simplify (- 1/2) into -1/2
19.396 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
19.396 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
19.396 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
19.396 * [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))))))
19.396 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
19.396 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
19.396 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
19.396 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
19.397 * [taylor]: Taking taylor expansion of 1/2 in n
19.397 * [backup-simplify]: Simplify 1/2 into 1/2
19.397 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
19.397 * [taylor]: Taking taylor expansion of 1/2 in n
19.397 * [backup-simplify]: Simplify 1/2 into 1/2
19.397 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
19.397 * [taylor]: Taking taylor expansion of 1/2 in n
19.397 * [backup-simplify]: Simplify 1/2 into 1/2
19.397 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.397 * [taylor]: Taking taylor expansion of k in n
19.397 * [backup-simplify]: Simplify k into k
19.397 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.397 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
19.397 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
19.397 * [taylor]: Taking taylor expansion of 2 in n
19.397 * [backup-simplify]: Simplify 2 into 2
19.397 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.397 * [taylor]: Taking taylor expansion of PI in n
19.397 * [backup-simplify]: Simplify PI into PI
19.397 * [taylor]: Taking taylor expansion of n in n
19.397 * [backup-simplify]: Simplify 0 into 0
19.397 * [backup-simplify]: Simplify 1 into 1
19.398 * [backup-simplify]: Simplify (/ PI 1) into PI
19.398 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.399 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.399 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
19.399 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
19.399 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
19.399 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
19.401 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.402 * [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))))
19.403 * [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)))))
19.403 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
19.403 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
19.403 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
19.403 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
19.403 * [taylor]: Taking taylor expansion of 1/2 in n
19.403 * [backup-simplify]: Simplify 1/2 into 1/2
19.403 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
19.403 * [taylor]: Taking taylor expansion of 1/2 in n
19.403 * [backup-simplify]: Simplify 1/2 into 1/2
19.403 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
19.403 * [taylor]: Taking taylor expansion of 1/2 in n
19.404 * [backup-simplify]: Simplify 1/2 into 1/2
19.404 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.404 * [taylor]: Taking taylor expansion of k in n
19.404 * [backup-simplify]: Simplify k into k
19.404 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.404 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
19.404 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
19.404 * [taylor]: Taking taylor expansion of 2 in n
19.404 * [backup-simplify]: Simplify 2 into 2
19.404 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.404 * [taylor]: Taking taylor expansion of PI in n
19.404 * [backup-simplify]: Simplify PI into PI
19.404 * [taylor]: Taking taylor expansion of n in n
19.404 * [backup-simplify]: Simplify 0 into 0
19.404 * [backup-simplify]: Simplify 1 into 1
19.404 * [backup-simplify]: Simplify (/ PI 1) into PI
19.405 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.406 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.406 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
19.406 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
19.406 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
19.406 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
19.407 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.408 * [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))))
19.408 * [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)))))
19.409 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
19.409 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
19.409 * [taylor]: Taking taylor expansion of 1/2 in k
19.409 * [backup-simplify]: Simplify 1/2 into 1/2
19.409 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
19.409 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
19.409 * [taylor]: Taking taylor expansion of 1/2 in k
19.409 * [backup-simplify]: Simplify 1/2 into 1/2
19.409 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
19.409 * [taylor]: Taking taylor expansion of 1/2 in k
19.409 * [backup-simplify]: Simplify 1/2 into 1/2
19.409 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.409 * [taylor]: Taking taylor expansion of k in k
19.409 * [backup-simplify]: Simplify 0 into 0
19.409 * [backup-simplify]: Simplify 1 into 1
19.409 * [backup-simplify]: Simplify (/ 1 1) into 1
19.409 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
19.409 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
19.409 * [taylor]: Taking taylor expansion of (* 2 PI) in k
19.409 * [taylor]: Taking taylor expansion of 2 in k
19.409 * [backup-simplify]: Simplify 2 into 2
19.409 * [taylor]: Taking taylor expansion of PI in k
19.409 * [backup-simplify]: Simplify PI into PI
19.410 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.410 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.410 * [taylor]: Taking taylor expansion of (log n) in k
19.410 * [taylor]: Taking taylor expansion of n in k
19.410 * [backup-simplify]: Simplify n into n
19.410 * [backup-simplify]: Simplify (log n) into (log n)
19.411 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
19.411 * [backup-simplify]: Simplify (- 1/2) into -1/2
19.411 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
19.411 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
19.412 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
19.413 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
19.413 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
19.414 * [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)))))
19.415 * [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)))))
19.415 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.416 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
19.417 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
19.417 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
19.418 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
19.418 * [backup-simplify]: Simplify (- 0) into 0
19.418 * [backup-simplify]: Simplify (+ 0 0) into 0
19.419 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
19.420 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.420 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
19.422 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.422 * [taylor]: Taking taylor expansion of 0 in k
19.422 * [backup-simplify]: Simplify 0 into 0
19.422 * [backup-simplify]: Simplify 0 into 0
19.422 * [backup-simplify]: Simplify 0 into 0
19.423 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.423 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
19.425 * [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
19.425 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.426 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
19.426 * [backup-simplify]: Simplify (- 0) into 0
19.427 * [backup-simplify]: Simplify (+ 0 0) into 0
19.427 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
19.428 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.429 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
19.431 * [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
19.431 * [taylor]: Taking taylor expansion of 0 in k
19.431 * [backup-simplify]: Simplify 0 into 0
19.431 * [backup-simplify]: Simplify 0 into 0
19.431 * [backup-simplify]: Simplify 0 into 0
19.431 * [backup-simplify]: Simplify 0 into 0
19.432 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.433 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.441 * [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
19.441 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.442 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
19.443 * [backup-simplify]: Simplify (- 0) into 0
19.443 * [backup-simplify]: Simplify (+ 0 0) into 0
19.444 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
19.445 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.446 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
19.448 * [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
19.448 * [taylor]: Taking taylor expansion of 0 in k
19.448 * [backup-simplify]: Simplify 0 into 0
19.448 * [backup-simplify]: Simplify 0 into 0
19.449 * [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))))))
19.449 * [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)))
19.449 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
19.449 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
19.449 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
19.449 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
19.449 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
19.449 * [taylor]: Taking taylor expansion of 1/2 in k
19.449 * [backup-simplify]: Simplify 1/2 into 1/2
19.449 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
19.449 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
19.449 * [taylor]: Taking taylor expansion of 1/2 in k
19.449 * [backup-simplify]: Simplify 1/2 into 1/2
19.449 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.449 * [taylor]: Taking taylor expansion of k in k
19.449 * [backup-simplify]: Simplify 0 into 0
19.449 * [backup-simplify]: Simplify 1 into 1
19.450 * [backup-simplify]: Simplify (/ 1 1) into 1
19.450 * [taylor]: Taking taylor expansion of 1/2 in k
19.450 * [backup-simplify]: Simplify 1/2 into 1/2
19.450 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
19.450 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
19.450 * [taylor]: Taking taylor expansion of -2 in k
19.450 * [backup-simplify]: Simplify -2 into -2
19.450 * [taylor]: Taking taylor expansion of (/ PI n) in k
19.450 * [taylor]: Taking taylor expansion of PI in k
19.450 * [backup-simplify]: Simplify PI into PI
19.450 * [taylor]: Taking taylor expansion of n in k
19.450 * [backup-simplify]: Simplify n into n
19.450 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
19.450 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
19.450 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
19.450 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
19.451 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.451 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
19.451 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
19.451 * [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))))
19.451 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
19.451 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
19.451 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
19.451 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
19.451 * [taylor]: Taking taylor expansion of 1/2 in n
19.451 * [backup-simplify]: Simplify 1/2 into 1/2
19.451 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
19.451 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
19.451 * [taylor]: Taking taylor expansion of 1/2 in n
19.451 * [backup-simplify]: Simplify 1/2 into 1/2
19.451 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.451 * [taylor]: Taking taylor expansion of k in n
19.451 * [backup-simplify]: Simplify k into k
19.451 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.451 * [taylor]: Taking taylor expansion of 1/2 in n
19.451 * [backup-simplify]: Simplify 1/2 into 1/2
19.451 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
19.451 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
19.451 * [taylor]: Taking taylor expansion of -2 in n
19.451 * [backup-simplify]: Simplify -2 into -2
19.451 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.451 * [taylor]: Taking taylor expansion of PI in n
19.451 * [backup-simplify]: Simplify PI into PI
19.451 * [taylor]: Taking taylor expansion of n in n
19.452 * [backup-simplify]: Simplify 0 into 0
19.452 * [backup-simplify]: Simplify 1 into 1
19.452 * [backup-simplify]: Simplify (/ PI 1) into PI
19.452 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
19.453 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
19.453 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
19.453 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
19.453 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
19.454 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
19.455 * [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))))
19.456 * [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)))))
19.456 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
19.456 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
19.456 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
19.456 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
19.456 * [taylor]: Taking taylor expansion of 1/2 in n
19.456 * [backup-simplify]: Simplify 1/2 into 1/2
19.456 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
19.456 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
19.456 * [taylor]: Taking taylor expansion of 1/2 in n
19.456 * [backup-simplify]: Simplify 1/2 into 1/2
19.456 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.456 * [taylor]: Taking taylor expansion of k in n
19.456 * [backup-simplify]: Simplify k into k
19.456 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.456 * [taylor]: Taking taylor expansion of 1/2 in n
19.456 * [backup-simplify]: Simplify 1/2 into 1/2
19.456 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
19.456 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
19.456 * [taylor]: Taking taylor expansion of -2 in n
19.456 * [backup-simplify]: Simplify -2 into -2
19.456 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.456 * [taylor]: Taking taylor expansion of PI in n
19.456 * [backup-simplify]: Simplify PI into PI
19.456 * [taylor]: Taking taylor expansion of n in n
19.456 * [backup-simplify]: Simplify 0 into 0
19.456 * [backup-simplify]: Simplify 1 into 1
19.456 * [backup-simplify]: Simplify (/ PI 1) into PI
19.457 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
19.458 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
19.458 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
19.458 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
19.458 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
19.459 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
19.459 * [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))))
19.460 * [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)))))
19.460 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
19.460 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
19.460 * [taylor]: Taking taylor expansion of 1/2 in k
19.460 * [backup-simplify]: Simplify 1/2 into 1/2
19.460 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
19.460 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
19.460 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
19.460 * [taylor]: Taking taylor expansion of 1/2 in k
19.460 * [backup-simplify]: Simplify 1/2 into 1/2
19.460 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.460 * [taylor]: Taking taylor expansion of k in k
19.460 * [backup-simplify]: Simplify 0 into 0
19.460 * [backup-simplify]: Simplify 1 into 1
19.461 * [backup-simplify]: Simplify (/ 1 1) into 1
19.461 * [taylor]: Taking taylor expansion of 1/2 in k
19.461 * [backup-simplify]: Simplify 1/2 into 1/2
19.461 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
19.461 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
19.461 * [taylor]: Taking taylor expansion of (* -2 PI) in k
19.461 * [taylor]: Taking taylor expansion of -2 in k
19.461 * [backup-simplify]: Simplify -2 into -2
19.461 * [taylor]: Taking taylor expansion of PI in k
19.461 * [backup-simplify]: Simplify PI into PI
19.461 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
19.462 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
19.462 * [taylor]: Taking taylor expansion of (log n) in k
19.462 * [taylor]: Taking taylor expansion of n in k
19.462 * [backup-simplify]: Simplify n into n
19.462 * [backup-simplify]: Simplify (log n) into (log n)
19.462 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
19.463 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.463 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
19.463 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
19.464 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
19.465 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
19.465 * [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)))))
19.466 * [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)))))
19.467 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.467 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
19.469 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
19.469 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
19.469 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
19.469 * [backup-simplify]: Simplify (+ 0 0) into 0
19.470 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
19.471 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
19.471 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
19.473 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.473 * [taylor]: Taking taylor expansion of 0 in k
19.473 * [backup-simplify]: Simplify 0 into 0
19.473 * [backup-simplify]: Simplify 0 into 0
19.473 * [backup-simplify]: Simplify 0 into 0
19.473 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.474 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
19.476 * [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
19.476 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.477 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
19.477 * [backup-simplify]: Simplify (+ 0 0) into 0
19.478 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
19.479 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
19.480 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
19.481 * [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
19.481 * [taylor]: Taking taylor expansion of 0 in k
19.481 * [backup-simplify]: Simplify 0 into 0
19.482 * [backup-simplify]: Simplify 0 into 0
19.482 * [backup-simplify]: Simplify 0 into 0
19.482 * [backup-simplify]: Simplify 0 into 0
19.482 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.483 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.486 * [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
19.487 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.487 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
19.488 * [backup-simplify]: Simplify (+ 0 0) into 0
19.489 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
19.490 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
19.491 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
19.493 * [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
19.493 * [taylor]: Taking taylor expansion of 0 in k
19.493 * [backup-simplify]: Simplify 0 into 0
19.493 * [backup-simplify]: Simplify 0 into 0
19.494 * [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))))))
19.494 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1)
19.494 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))
19.494 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
19.494 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
19.495 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
19.495 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
19.495 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
19.495 * [taylor]: Taking taylor expansion of 1/2 in k
19.495 * [backup-simplify]: Simplify 1/2 into 1/2
19.495 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
19.495 * [taylor]: Taking taylor expansion of 1/2 in k
19.495 * [backup-simplify]: Simplify 1/2 into 1/2
19.495 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
19.495 * [taylor]: Taking taylor expansion of 1/2 in k
19.495 * [backup-simplify]: Simplify 1/2 into 1/2
19.495 * [taylor]: Taking taylor expansion of k in k
19.495 * [backup-simplify]: Simplify 0 into 0
19.495 * [backup-simplify]: Simplify 1 into 1
19.495 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
19.495 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
19.495 * [taylor]: Taking taylor expansion of 2 in k
19.495 * [backup-simplify]: Simplify 2 into 2
19.495 * [taylor]: Taking taylor expansion of (* n PI) in k
19.495 * [taylor]: Taking taylor expansion of n in k
19.495 * [backup-simplify]: Simplify n into n
19.495 * [taylor]: Taking taylor expansion of PI in k
19.495 * [backup-simplify]: Simplify PI into PI
19.495 * [backup-simplify]: Simplify (* n PI) into (* n PI)
19.495 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
19.496 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
19.496 * [backup-simplify]: Simplify (* 1/2 0) into 0
19.496 * [backup-simplify]: Simplify (- 0) into 0
19.497 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.497 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
19.497 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
19.498 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
19.498 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
19.498 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
19.498 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
19.498 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
19.498 * [taylor]: Taking taylor expansion of 1/2 in n
19.498 * [backup-simplify]: Simplify 1/2 into 1/2
19.498 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
19.498 * [taylor]: Taking taylor expansion of 1/2 in n
19.498 * [backup-simplify]: Simplify 1/2 into 1/2
19.498 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
19.498 * [taylor]: Taking taylor expansion of 1/2 in n
19.498 * [backup-simplify]: Simplify 1/2 into 1/2
19.498 * [taylor]: Taking taylor expansion of k in n
19.498 * [backup-simplify]: Simplify k into k
19.498 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
19.498 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
19.498 * [taylor]: Taking taylor expansion of 2 in n
19.498 * [backup-simplify]: Simplify 2 into 2
19.498 * [taylor]: Taking taylor expansion of (* n PI) in n
19.498 * [taylor]: Taking taylor expansion of n in n
19.498 * [backup-simplify]: Simplify 0 into 0
19.498 * [backup-simplify]: Simplify 1 into 1
19.498 * [taylor]: Taking taylor expansion of PI in n
19.498 * [backup-simplify]: Simplify PI into PI
19.499 * [backup-simplify]: Simplify (* 0 PI) into 0
19.499 * [backup-simplify]: Simplify (* 2 0) into 0
19.501 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.503 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
19.504 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.504 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
19.504 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
19.504 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
19.504 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
19.506 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.506 * [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)))))
19.507 * [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))))))
19.507 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
19.507 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
19.507 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
19.507 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
19.507 * [taylor]: Taking taylor expansion of 1/2 in n
19.507 * [backup-simplify]: Simplify 1/2 into 1/2
19.507 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
19.507 * [taylor]: Taking taylor expansion of 1/2 in n
19.507 * [backup-simplify]: Simplify 1/2 into 1/2
19.507 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
19.507 * [taylor]: Taking taylor expansion of 1/2 in n
19.507 * [backup-simplify]: Simplify 1/2 into 1/2
19.507 * [taylor]: Taking taylor expansion of k in n
19.507 * [backup-simplify]: Simplify k into k
19.507 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
19.507 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
19.507 * [taylor]: Taking taylor expansion of 2 in n
19.507 * [backup-simplify]: Simplify 2 into 2
19.507 * [taylor]: Taking taylor expansion of (* n PI) in n
19.507 * [taylor]: Taking taylor expansion of n in n
19.507 * [backup-simplify]: Simplify 0 into 0
19.507 * [backup-simplify]: Simplify 1 into 1
19.507 * [taylor]: Taking taylor expansion of PI in n
19.507 * [backup-simplify]: Simplify PI into PI
19.508 * [backup-simplify]: Simplify (* 0 PI) into 0
19.508 * [backup-simplify]: Simplify (* 2 0) into 0
19.509 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.510 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
19.511 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.511 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
19.511 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
19.511 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
19.511 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
19.512 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.513 * [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)))))
19.513 * [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))))))
19.513 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
19.514 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
19.514 * [taylor]: Taking taylor expansion of 1/2 in k
19.514 * [backup-simplify]: Simplify 1/2 into 1/2
19.514 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
19.514 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
19.514 * [taylor]: Taking taylor expansion of 1/2 in k
19.514 * [backup-simplify]: Simplify 1/2 into 1/2
19.514 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
19.514 * [taylor]: Taking taylor expansion of 1/2 in k
19.514 * [backup-simplify]: Simplify 1/2 into 1/2
19.514 * [taylor]: Taking taylor expansion of k in k
19.514 * [backup-simplify]: Simplify 0 into 0
19.514 * [backup-simplify]: Simplify 1 into 1
19.514 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
19.514 * [taylor]: Taking taylor expansion of (log n) in k
19.514 * [taylor]: Taking taylor expansion of n in k
19.514 * [backup-simplify]: Simplify n into n
19.514 * [backup-simplify]: Simplify (log n) into (log n)
19.514 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
19.514 * [taylor]: Taking taylor expansion of (* 2 PI) in k
19.514 * [taylor]: Taking taylor expansion of 2 in k
19.514 * [backup-simplify]: Simplify 2 into 2
19.514 * [taylor]: Taking taylor expansion of PI in k
19.514 * [backup-simplify]: Simplify PI into PI
19.514 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.515 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.515 * [backup-simplify]: Simplify (* 1/2 0) into 0
19.515 * [backup-simplify]: Simplify (- 0) into 0
19.516 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.516 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.517 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
19.518 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
19.519 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
19.519 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
19.520 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
19.521 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
19.522 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
19.522 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
19.522 * [backup-simplify]: Simplify (- 0) into 0
19.523 * [backup-simplify]: Simplify (+ 0 0) into 0
19.523 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
19.524 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.525 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
19.526 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.526 * [taylor]: Taking taylor expansion of 0 in k
19.526 * [backup-simplify]: Simplify 0 into 0
19.526 * [backup-simplify]: Simplify 0 into 0
19.526 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
19.527 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
19.528 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
19.528 * [backup-simplify]: Simplify (+ 0 0) into 0
19.529 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
19.529 * [backup-simplify]: Simplify (- 1/2) into -1/2
19.530 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
19.531 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
19.533 * [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)))))
19.535 * [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)))))))
19.542 * [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)))))))
19.543 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
19.543 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
19.545 * [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
19.546 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
19.546 * [backup-simplify]: Simplify (- 0) into 0
19.546 * [backup-simplify]: Simplify (+ 0 0) into 0
19.547 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
19.548 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.549 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
19.551 * [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
19.551 * [taylor]: Taking taylor expansion of 0 in k
19.551 * [backup-simplify]: Simplify 0 into 0
19.551 * [backup-simplify]: Simplify 0 into 0
19.551 * [backup-simplify]: Simplify 0 into 0
19.552 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
19.553 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
19.556 * [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
19.556 * [backup-simplify]: Simplify (+ 0 0) into 0
19.557 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
19.558 * [backup-simplify]: Simplify (- 0) into 0
19.558 * [backup-simplify]: Simplify (+ 0 0) into 0
19.560 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
19.564 * [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
19.568 * [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)))))
19.574 * [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)))))
19.584 * [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)))))))
19.585 * [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)))))
19.585 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
19.585 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
19.585 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
19.585 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
19.585 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
19.586 * [taylor]: Taking taylor expansion of 1/2 in k
19.586 * [backup-simplify]: Simplify 1/2 into 1/2
19.586 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
19.586 * [taylor]: Taking taylor expansion of 1/2 in k
19.586 * [backup-simplify]: Simplify 1/2 into 1/2
19.586 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
19.586 * [taylor]: Taking taylor expansion of 1/2 in k
19.586 * [backup-simplify]: Simplify 1/2 into 1/2
19.586 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.586 * [taylor]: Taking taylor expansion of k in k
19.586 * [backup-simplify]: Simplify 0 into 0
19.586 * [backup-simplify]: Simplify 1 into 1
19.586 * [backup-simplify]: Simplify (/ 1 1) into 1
19.586 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
19.586 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
19.586 * [taylor]: Taking taylor expansion of 2 in k
19.586 * [backup-simplify]: Simplify 2 into 2
19.586 * [taylor]: Taking taylor expansion of (/ PI n) in k
19.586 * [taylor]: Taking taylor expansion of PI in k
19.586 * [backup-simplify]: Simplify PI into PI
19.586 * [taylor]: Taking taylor expansion of n in k
19.586 * [backup-simplify]: Simplify n into n
19.587 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
19.587 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
19.587 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
19.587 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
19.588 * [backup-simplify]: Simplify (- 1/2) into -1/2
19.588 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
19.588 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
19.589 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
19.589 * [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))))))
19.589 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
19.589 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
19.589 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
19.589 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
19.589 * [taylor]: Taking taylor expansion of 1/2 in n
19.589 * [backup-simplify]: Simplify 1/2 into 1/2
19.589 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
19.589 * [taylor]: Taking taylor expansion of 1/2 in n
19.589 * [backup-simplify]: Simplify 1/2 into 1/2
19.589 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
19.589 * [taylor]: Taking taylor expansion of 1/2 in n
19.589 * [backup-simplify]: Simplify 1/2 into 1/2
19.589 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.589 * [taylor]: Taking taylor expansion of k in n
19.589 * [backup-simplify]: Simplify k into k
19.589 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.589 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
19.589 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
19.589 * [taylor]: Taking taylor expansion of 2 in n
19.590 * [backup-simplify]: Simplify 2 into 2
19.590 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.590 * [taylor]: Taking taylor expansion of PI in n
19.590 * [backup-simplify]: Simplify PI into PI
19.590 * [taylor]: Taking taylor expansion of n in n
19.590 * [backup-simplify]: Simplify 0 into 0
19.590 * [backup-simplify]: Simplify 1 into 1
19.590 * [backup-simplify]: Simplify (/ PI 1) into PI
19.591 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.592 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.592 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
19.592 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
19.592 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
19.592 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
19.594 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.595 * [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))))
19.596 * [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)))))
19.596 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
19.596 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
19.597 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
19.597 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
19.597 * [taylor]: Taking taylor expansion of 1/2 in n
19.597 * [backup-simplify]: Simplify 1/2 into 1/2
19.597 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
19.597 * [taylor]: Taking taylor expansion of 1/2 in n
19.597 * [backup-simplify]: Simplify 1/2 into 1/2
19.597 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
19.597 * [taylor]: Taking taylor expansion of 1/2 in n
19.597 * [backup-simplify]: Simplify 1/2 into 1/2
19.597 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.597 * [taylor]: Taking taylor expansion of k in n
19.597 * [backup-simplify]: Simplify k into k
19.597 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.597 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
19.597 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
19.597 * [taylor]: Taking taylor expansion of 2 in n
19.597 * [backup-simplify]: Simplify 2 into 2
19.597 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.597 * [taylor]: Taking taylor expansion of PI in n
19.597 * [backup-simplify]: Simplify PI into PI
19.597 * [taylor]: Taking taylor expansion of n in n
19.597 * [backup-simplify]: Simplify 0 into 0
19.597 * [backup-simplify]: Simplify 1 into 1
19.598 * [backup-simplify]: Simplify (/ PI 1) into PI
19.598 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.599 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.599 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
19.600 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
19.600 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
19.600 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
19.601 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.603 * [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))))
19.604 * [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)))))
19.604 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
19.604 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
19.604 * [taylor]: Taking taylor expansion of 1/2 in k
19.604 * [backup-simplify]: Simplify 1/2 into 1/2
19.604 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
19.604 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
19.604 * [taylor]: Taking taylor expansion of 1/2 in k
19.604 * [backup-simplify]: Simplify 1/2 into 1/2
19.604 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
19.604 * [taylor]: Taking taylor expansion of 1/2 in k
19.604 * [backup-simplify]: Simplify 1/2 into 1/2
19.604 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.604 * [taylor]: Taking taylor expansion of k in k
19.604 * [backup-simplify]: Simplify 0 into 0
19.604 * [backup-simplify]: Simplify 1 into 1
19.605 * [backup-simplify]: Simplify (/ 1 1) into 1
19.605 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
19.605 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
19.605 * [taylor]: Taking taylor expansion of (* 2 PI) in k
19.605 * [taylor]: Taking taylor expansion of 2 in k
19.605 * [backup-simplify]: Simplify 2 into 2
19.605 * [taylor]: Taking taylor expansion of PI in k
19.605 * [backup-simplify]: Simplify PI into PI
19.605 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.607 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.607 * [taylor]: Taking taylor expansion of (log n) in k
19.607 * [taylor]: Taking taylor expansion of n in k
19.607 * [backup-simplify]: Simplify n into n
19.607 * [backup-simplify]: Simplify (log n) into (log n)
19.607 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
19.608 * [backup-simplify]: Simplify (- 1/2) into -1/2
19.608 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
19.608 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
19.609 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
19.610 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
19.611 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
19.613 * [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)))))
19.614 * [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)))))
19.615 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.616 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
19.618 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
19.618 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
19.618 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
19.619 * [backup-simplify]: Simplify (- 0) into 0
19.619 * [backup-simplify]: Simplify (+ 0 0) into 0
19.620 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
19.621 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.623 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
19.625 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.625 * [taylor]: Taking taylor expansion of 0 in k
19.625 * [backup-simplify]: Simplify 0 into 0
19.625 * [backup-simplify]: Simplify 0 into 0
19.625 * [backup-simplify]: Simplify 0 into 0
19.626 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.627 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
19.631 * [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
19.631 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.632 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
19.632 * [backup-simplify]: Simplify (- 0) into 0
19.633 * [backup-simplify]: Simplify (+ 0 0) into 0
19.634 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
19.635 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.637 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
19.640 * [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
19.640 * [taylor]: Taking taylor expansion of 0 in k
19.640 * [backup-simplify]: Simplify 0 into 0
19.640 * [backup-simplify]: Simplify 0 into 0
19.640 * [backup-simplify]: Simplify 0 into 0
19.640 * [backup-simplify]: Simplify 0 into 0
19.640 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.641 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.645 * [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
19.645 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.646 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
19.646 * [backup-simplify]: Simplify (- 0) into 0
19.646 * [backup-simplify]: Simplify (+ 0 0) into 0
19.647 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
19.648 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.649 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
19.651 * [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
19.651 * [taylor]: Taking taylor expansion of 0 in k
19.651 * [backup-simplify]: Simplify 0 into 0
19.651 * [backup-simplify]: Simplify 0 into 0
19.652 * [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))))))
19.653 * [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)))
19.653 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
19.653 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
19.653 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
19.653 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
19.653 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
19.653 * [taylor]: Taking taylor expansion of 1/2 in k
19.653 * [backup-simplify]: Simplify 1/2 into 1/2
19.653 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
19.653 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
19.653 * [taylor]: Taking taylor expansion of 1/2 in k
19.653 * [backup-simplify]: Simplify 1/2 into 1/2
19.653 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.653 * [taylor]: Taking taylor expansion of k in k
19.653 * [backup-simplify]: Simplify 0 into 0
19.653 * [backup-simplify]: Simplify 1 into 1
19.653 * [backup-simplify]: Simplify (/ 1 1) into 1
19.653 * [taylor]: Taking taylor expansion of 1/2 in k
19.653 * [backup-simplify]: Simplify 1/2 into 1/2
19.653 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
19.653 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
19.653 * [taylor]: Taking taylor expansion of -2 in k
19.653 * [backup-simplify]: Simplify -2 into -2
19.653 * [taylor]: Taking taylor expansion of (/ PI n) in k
19.653 * [taylor]: Taking taylor expansion of PI in k
19.653 * [backup-simplify]: Simplify PI into PI
19.653 * [taylor]: Taking taylor expansion of n in k
19.653 * [backup-simplify]: Simplify n into n
19.653 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
19.653 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
19.653 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
19.654 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
19.654 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.654 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
19.654 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
19.655 * [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))))
19.655 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
19.655 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
19.655 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
19.655 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
19.655 * [taylor]: Taking taylor expansion of 1/2 in n
19.655 * [backup-simplify]: Simplify 1/2 into 1/2
19.655 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
19.655 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
19.655 * [taylor]: Taking taylor expansion of 1/2 in n
19.655 * [backup-simplify]: Simplify 1/2 into 1/2
19.655 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.655 * [taylor]: Taking taylor expansion of k in n
19.655 * [backup-simplify]: Simplify k into k
19.655 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.655 * [taylor]: Taking taylor expansion of 1/2 in n
19.655 * [backup-simplify]: Simplify 1/2 into 1/2
19.655 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
19.655 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
19.655 * [taylor]: Taking taylor expansion of -2 in n
19.655 * [backup-simplify]: Simplify -2 into -2
19.655 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.655 * [taylor]: Taking taylor expansion of PI in n
19.655 * [backup-simplify]: Simplify PI into PI
19.655 * [taylor]: Taking taylor expansion of n in n
19.655 * [backup-simplify]: Simplify 0 into 0
19.655 * [backup-simplify]: Simplify 1 into 1
19.655 * [backup-simplify]: Simplify (/ PI 1) into PI
19.656 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
19.656 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
19.656 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
19.656 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
19.656 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
19.657 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
19.658 * [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))))
19.659 * [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)))))
19.659 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
19.659 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
19.659 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
19.659 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
19.659 * [taylor]: Taking taylor expansion of 1/2 in n
19.659 * [backup-simplify]: Simplify 1/2 into 1/2
19.659 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
19.659 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
19.659 * [taylor]: Taking taylor expansion of 1/2 in n
19.659 * [backup-simplify]: Simplify 1/2 into 1/2
19.659 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.659 * [taylor]: Taking taylor expansion of k in n
19.659 * [backup-simplify]: Simplify k into k
19.659 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.659 * [taylor]: Taking taylor expansion of 1/2 in n
19.659 * [backup-simplify]: Simplify 1/2 into 1/2
19.659 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
19.659 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
19.659 * [taylor]: Taking taylor expansion of -2 in n
19.659 * [backup-simplify]: Simplify -2 into -2
19.659 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.659 * [taylor]: Taking taylor expansion of PI in n
19.659 * [backup-simplify]: Simplify PI into PI
19.659 * [taylor]: Taking taylor expansion of n in n
19.659 * [backup-simplify]: Simplify 0 into 0
19.659 * [backup-simplify]: Simplify 1 into 1
19.660 * [backup-simplify]: Simplify (/ PI 1) into PI
19.660 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
19.661 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
19.661 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
19.661 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
19.661 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
19.662 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
19.663 * [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))))
19.669 * [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)))))
19.669 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
19.669 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
19.670 * [taylor]: Taking taylor expansion of 1/2 in k
19.670 * [backup-simplify]: Simplify 1/2 into 1/2
19.670 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
19.670 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
19.670 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
19.670 * [taylor]: Taking taylor expansion of 1/2 in k
19.670 * [backup-simplify]: Simplify 1/2 into 1/2
19.670 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.670 * [taylor]: Taking taylor expansion of k in k
19.670 * [backup-simplify]: Simplify 0 into 0
19.670 * [backup-simplify]: Simplify 1 into 1
19.670 * [backup-simplify]: Simplify (/ 1 1) into 1
19.670 * [taylor]: Taking taylor expansion of 1/2 in k
19.670 * [backup-simplify]: Simplify 1/2 into 1/2
19.670 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
19.670 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
19.670 * [taylor]: Taking taylor expansion of (* -2 PI) in k
19.670 * [taylor]: Taking taylor expansion of -2 in k
19.670 * [backup-simplify]: Simplify -2 into -2
19.670 * [taylor]: Taking taylor expansion of PI in k
19.670 * [backup-simplify]: Simplify PI into PI
19.670 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
19.671 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
19.671 * [taylor]: Taking taylor expansion of (log n) in k
19.671 * [taylor]: Taking taylor expansion of n in k
19.671 * [backup-simplify]: Simplify n into n
19.671 * [backup-simplify]: Simplify (log n) into (log n)
19.671 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
19.672 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.672 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
19.673 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
19.673 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
19.674 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
19.676 * [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)))))
19.677 * [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)))))
19.678 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.679 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
19.681 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
19.681 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
19.681 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
19.682 * [backup-simplify]: Simplify (+ 0 0) into 0
19.682 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
19.683 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
19.685 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
19.687 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.687 * [taylor]: Taking taylor expansion of 0 in k
19.687 * [backup-simplify]: Simplify 0 into 0
19.687 * [backup-simplify]: Simplify 0 into 0
19.687 * [backup-simplify]: Simplify 0 into 0
19.688 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.689 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
19.692 * [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
19.693 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.694 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
19.694 * [backup-simplify]: Simplify (+ 0 0) into 0
19.695 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
19.696 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
19.698 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
19.701 * [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
19.701 * [taylor]: Taking taylor expansion of 0 in k
19.701 * [backup-simplify]: Simplify 0 into 0
19.701 * [backup-simplify]: Simplify 0 into 0
19.701 * [backup-simplify]: Simplify 0 into 0
19.701 * [backup-simplify]: Simplify 0 into 0
19.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.703 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.710 * [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
19.710 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.712 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
19.712 * [backup-simplify]: Simplify (+ 0 0) into 0
19.713 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
19.716 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
19.718 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
19.721 * [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
19.721 * [taylor]: Taking taylor expansion of 0 in k
19.721 * [backup-simplify]: Simplify 0 into 0
19.721 * [backup-simplify]: Simplify 0 into 0
19.722 * [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))))))
19.722 * * * * [progress]: [ 3 / 4 ] generating series at (2 1)
19.724 * [backup-simplify]: Simplify (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) into (pow (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) 2)
19.724 * [approximate]: Taking taylor expansion of (pow (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) 2) in (n k) around 0
19.724 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) 2) in k
19.724 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
19.724 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
19.724 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
19.724 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
19.724 * [taylor]: Taking taylor expansion of 1/2 in k
19.724 * [backup-simplify]: Simplify 1/2 into 1/2
19.724 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
19.724 * [taylor]: Taking taylor expansion of 1/2 in k
19.724 * [backup-simplify]: Simplify 1/2 into 1/2
19.724 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
19.724 * [taylor]: Taking taylor expansion of 1/2 in k
19.724 * [backup-simplify]: Simplify 1/2 into 1/2
19.724 * [taylor]: Taking taylor expansion of k in k
19.724 * [backup-simplify]: Simplify 0 into 0
19.724 * [backup-simplify]: Simplify 1 into 1
19.724 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
19.724 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
19.724 * [taylor]: Taking taylor expansion of 2 in k
19.724 * [backup-simplify]: Simplify 2 into 2
19.724 * [taylor]: Taking taylor expansion of (* n PI) in k
19.724 * [taylor]: Taking taylor expansion of n in k
19.724 * [backup-simplify]: Simplify n into n
19.724 * [taylor]: Taking taylor expansion of PI in k
19.724 * [backup-simplify]: Simplify PI into PI
19.724 * [backup-simplify]: Simplify (* n PI) into (* n PI)
19.725 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
19.725 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
19.725 * [backup-simplify]: Simplify (* 1/2 0) into 0
19.725 * [backup-simplify]: Simplify (- 0) into 0
19.726 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.726 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
19.726 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
19.727 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
19.727 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) 2) in n
19.727 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
19.727 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
19.727 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
19.727 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
19.727 * [taylor]: Taking taylor expansion of 1/2 in n
19.727 * [backup-simplify]: Simplify 1/2 into 1/2
19.727 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
19.727 * [taylor]: Taking taylor expansion of 1/2 in n
19.727 * [backup-simplify]: Simplify 1/2 into 1/2
19.727 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
19.727 * [taylor]: Taking taylor expansion of 1/2 in n
19.727 * [backup-simplify]: Simplify 1/2 into 1/2
19.727 * [taylor]: Taking taylor expansion of k in n
19.727 * [backup-simplify]: Simplify k into k
19.727 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
19.727 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
19.727 * [taylor]: Taking taylor expansion of 2 in n
19.727 * [backup-simplify]: Simplify 2 into 2
19.727 * [taylor]: Taking taylor expansion of (* n PI) in n
19.727 * [taylor]: Taking taylor expansion of n in n
19.727 * [backup-simplify]: Simplify 0 into 0
19.727 * [backup-simplify]: Simplify 1 into 1
19.727 * [taylor]: Taking taylor expansion of PI in n
19.727 * [backup-simplify]: Simplify PI into PI
19.728 * [backup-simplify]: Simplify (* 0 PI) into 0
19.728 * [backup-simplify]: Simplify (* 2 0) into 0
19.730 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.731 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
19.733 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.733 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
19.733 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
19.733 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
19.733 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
19.734 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.736 * [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)))))
19.737 * [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))))))
19.737 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) 2) in n
19.737 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
19.737 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
19.737 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
19.737 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
19.737 * [taylor]: Taking taylor expansion of 1/2 in n
19.737 * [backup-simplify]: Simplify 1/2 into 1/2
19.737 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
19.737 * [taylor]: Taking taylor expansion of 1/2 in n
19.737 * [backup-simplify]: Simplify 1/2 into 1/2
19.737 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
19.737 * [taylor]: Taking taylor expansion of 1/2 in n
19.737 * [backup-simplify]: Simplify 1/2 into 1/2
19.737 * [taylor]: Taking taylor expansion of k in n
19.737 * [backup-simplify]: Simplify k into k
19.737 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
19.737 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
19.737 * [taylor]: Taking taylor expansion of 2 in n
19.737 * [backup-simplify]: Simplify 2 into 2
19.737 * [taylor]: Taking taylor expansion of (* n PI) in n
19.737 * [taylor]: Taking taylor expansion of n in n
19.737 * [backup-simplify]: Simplify 0 into 0
19.737 * [backup-simplify]: Simplify 1 into 1
19.738 * [taylor]: Taking taylor expansion of PI in n
19.738 * [backup-simplify]: Simplify PI into PI
19.738 * [backup-simplify]: Simplify (* 0 PI) into 0
19.739 * [backup-simplify]: Simplify (* 2 0) into 0
19.740 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.742 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
19.743 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.743 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
19.743 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
19.743 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
19.743 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
19.745 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.746 * [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)))))
19.747 * [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))))))
19.751 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into (pow (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 2)
19.751 * [taylor]: Taking taylor expansion of (pow (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 2) in k
19.751 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
19.751 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
19.751 * [taylor]: Taking taylor expansion of 1/2 in k
19.751 * [backup-simplify]: Simplify 1/2 into 1/2
19.751 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
19.751 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
19.751 * [taylor]: Taking taylor expansion of 1/2 in k
19.751 * [backup-simplify]: Simplify 1/2 into 1/2
19.751 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
19.751 * [taylor]: Taking taylor expansion of 1/2 in k
19.751 * [backup-simplify]: Simplify 1/2 into 1/2
19.751 * [taylor]: Taking taylor expansion of k in k
19.751 * [backup-simplify]: Simplify 0 into 0
19.751 * [backup-simplify]: Simplify 1 into 1
19.751 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
19.751 * [taylor]: Taking taylor expansion of (log n) in k
19.751 * [taylor]: Taking taylor expansion of n in k
19.751 * [backup-simplify]: Simplify n into n
19.751 * [backup-simplify]: Simplify (log n) into (log n)
19.751 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
19.751 * [taylor]: Taking taylor expansion of (* 2 PI) in k
19.751 * [taylor]: Taking taylor expansion of 2 in k
19.751 * [backup-simplify]: Simplify 2 into 2
19.751 * [taylor]: Taking taylor expansion of PI in k
19.751 * [backup-simplify]: Simplify PI into PI
19.752 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.753 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.754 * [backup-simplify]: Simplify (* 1/2 0) into 0
19.754 * [backup-simplify]: Simplify (- 0) into 0
19.754 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.755 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.756 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
19.757 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
19.759 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
19.761 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) into (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)
19.762 * [backup-simplify]: Simplify (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) into (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)
19.763 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
19.764 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
19.766 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
19.767 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
19.767 * [backup-simplify]: Simplify (- 0) into 0
19.768 * [backup-simplify]: Simplify (+ 0 0) into 0
19.768 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
19.770 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.771 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
19.773 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.776 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
19.776 * [taylor]: Taking taylor expansion of 0 in k
19.776 * [backup-simplify]: Simplify 0 into 0
19.776 * [backup-simplify]: Simplify 0 into 0
19.777 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
19.778 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
19.780 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
19.780 * [backup-simplify]: Simplify (+ 0 0) into 0
19.781 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
19.781 * [backup-simplify]: Simplify (- 1/2) into -1/2
19.782 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
19.784 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
19.787 * [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)))))
19.791 * [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)))))))
19.800 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log n))) (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log (* 2 PI))))))
19.804 * [backup-simplify]: Simplify (- (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log n))) (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log (* 2 PI)))))) into (- (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log n))) (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log (* 2 PI))))))
19.805 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
19.807 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
19.810 * [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
19.811 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
19.819 * [backup-simplify]: Simplify (- 0) into 0
19.820 * [backup-simplify]: Simplify (+ 0 0) into 0
19.821 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
19.823 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.824 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
19.827 * [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
19.831 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0
19.831 * [taylor]: Taking taylor expansion of 0 in k
19.831 * [backup-simplify]: Simplify 0 into 0
19.831 * [backup-simplify]: Simplify 0 into 0
19.831 * [backup-simplify]: Simplify 0 into 0
19.833 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
19.834 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
19.838 * [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
19.839 * [backup-simplify]: Simplify (+ 0 0) into 0
19.840 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
19.840 * [backup-simplify]: Simplify (- 0) into 0
19.841 * [backup-simplify]: Simplify (+ 0 0) into 0
19.843 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
19.846 * [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
19.851 * [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)))))
19.872 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) into (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log n) 2))) (+ (* 1/4 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI))))) (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))))
19.879 * [backup-simplify]: Simplify (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log n) 2))) (+ (* 1/4 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI))))) (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2))))) into (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log n) 2))) (+ (* 1/4 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI))))) (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))))
19.893 * [backup-simplify]: Simplify (+ (* (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log n) 2))) (+ (* 1/4 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI))))) (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log n))) (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log (* 2 PI)))))) (* k 1)) (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2))) into (- (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/4 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI)))))) (+ (* 1/8 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))) (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)))) (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) k)))))
19.894 * [backup-simplify]: Simplify (* (pow (* (/ 1 n) (* 2 PI)) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) (pow (* (/ 1 n) (* 2 PI)) (/ (- 1/2 (/ (/ 1 k) 2)) 2))) into (pow (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) 2)
19.894 * [approximate]: Taking taylor expansion of (pow (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) 2) in (n k) around 0
19.894 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) 2) in k
19.894 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
19.894 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
19.894 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
19.894 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
19.895 * [taylor]: Taking taylor expansion of 1/2 in k
19.895 * [backup-simplify]: Simplify 1/2 into 1/2
19.895 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
19.895 * [taylor]: Taking taylor expansion of 1/2 in k
19.895 * [backup-simplify]: Simplify 1/2 into 1/2
19.895 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
19.895 * [taylor]: Taking taylor expansion of 1/2 in k
19.895 * [backup-simplify]: Simplify 1/2 into 1/2
19.895 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.895 * [taylor]: Taking taylor expansion of k in k
19.895 * [backup-simplify]: Simplify 0 into 0
19.895 * [backup-simplify]: Simplify 1 into 1
19.895 * [backup-simplify]: Simplify (/ 1 1) into 1
19.895 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
19.895 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
19.895 * [taylor]: Taking taylor expansion of 2 in k
19.895 * [backup-simplify]: Simplify 2 into 2
19.896 * [taylor]: Taking taylor expansion of (/ PI n) in k
19.896 * [taylor]: Taking taylor expansion of PI in k
19.896 * [backup-simplify]: Simplify PI into PI
19.896 * [taylor]: Taking taylor expansion of n in k
19.896 * [backup-simplify]: Simplify n into n
19.896 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
19.896 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
19.896 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
19.896 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
19.897 * [backup-simplify]: Simplify (- 1/2) into -1/2
19.897 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
19.898 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
19.898 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
19.898 * [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))))))
19.898 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) 2) in n
19.898 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
19.898 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
19.898 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
19.898 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
19.898 * [taylor]: Taking taylor expansion of 1/2 in n
19.898 * [backup-simplify]: Simplify 1/2 into 1/2
19.898 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
19.898 * [taylor]: Taking taylor expansion of 1/2 in n
19.898 * [backup-simplify]: Simplify 1/2 into 1/2
19.898 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
19.898 * [taylor]: Taking taylor expansion of 1/2 in n
19.898 * [backup-simplify]: Simplify 1/2 into 1/2
19.898 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.898 * [taylor]: Taking taylor expansion of k in n
19.899 * [backup-simplify]: Simplify k into k
19.899 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.899 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
19.899 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
19.899 * [taylor]: Taking taylor expansion of 2 in n
19.899 * [backup-simplify]: Simplify 2 into 2
19.899 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.899 * [taylor]: Taking taylor expansion of PI in n
19.899 * [backup-simplify]: Simplify PI into PI
19.899 * [taylor]: Taking taylor expansion of n in n
19.899 * [backup-simplify]: Simplify 0 into 0
19.899 * [backup-simplify]: Simplify 1 into 1
19.899 * [backup-simplify]: Simplify (/ PI 1) into PI
19.900 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.901 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.901 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
19.901 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
19.901 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
19.901 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
19.903 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.904 * [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))))
19.905 * [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)))))
19.905 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) 2) in n
19.905 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
19.905 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
19.905 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
19.905 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
19.905 * [taylor]: Taking taylor expansion of 1/2 in n
19.905 * [backup-simplify]: Simplify 1/2 into 1/2
19.905 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
19.906 * [taylor]: Taking taylor expansion of 1/2 in n
19.906 * [backup-simplify]: Simplify 1/2 into 1/2
19.906 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
19.906 * [taylor]: Taking taylor expansion of 1/2 in n
19.906 * [backup-simplify]: Simplify 1/2 into 1/2
19.906 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.906 * [taylor]: Taking taylor expansion of k in n
19.906 * [backup-simplify]: Simplify k into k
19.906 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.906 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
19.906 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
19.906 * [taylor]: Taking taylor expansion of 2 in n
19.906 * [backup-simplify]: Simplify 2 into 2
19.906 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.906 * [taylor]: Taking taylor expansion of PI in n
19.906 * [backup-simplify]: Simplify PI into PI
19.906 * [taylor]: Taking taylor expansion of n in n
19.906 * [backup-simplify]: Simplify 0 into 0
19.906 * [backup-simplify]: Simplify 1 into 1
19.906 * [backup-simplify]: Simplify (/ PI 1) into PI
19.906 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.907 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.907 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
19.907 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
19.907 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
19.907 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
19.908 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.909 * [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))))
19.910 * [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)))))
19.911 * [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 (* 2 PI)) (log n)))))) into (pow (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 2)
19.912 * [taylor]: Taking taylor expansion of (pow (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 2) in k
19.912 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
19.912 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
19.912 * [taylor]: Taking taylor expansion of 1/2 in k
19.912 * [backup-simplify]: Simplify 1/2 into 1/2
19.912 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
19.912 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
19.912 * [taylor]: Taking taylor expansion of 1/2 in k
19.912 * [backup-simplify]: Simplify 1/2 into 1/2
19.912 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
19.912 * [taylor]: Taking taylor expansion of 1/2 in k
19.912 * [backup-simplify]: Simplify 1/2 into 1/2
19.912 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.912 * [taylor]: Taking taylor expansion of k in k
19.912 * [backup-simplify]: Simplify 0 into 0
19.912 * [backup-simplify]: Simplify 1 into 1
19.912 * [backup-simplify]: Simplify (/ 1 1) into 1
19.912 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
19.912 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
19.912 * [taylor]: Taking taylor expansion of (* 2 PI) in k
19.912 * [taylor]: Taking taylor expansion of 2 in k
19.912 * [backup-simplify]: Simplify 2 into 2
19.912 * [taylor]: Taking taylor expansion of PI in k
19.912 * [backup-simplify]: Simplify PI into PI
19.912 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.913 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.913 * [taylor]: Taking taylor expansion of (log n) in k
19.913 * [taylor]: Taking taylor expansion of n in k
19.913 * [backup-simplify]: Simplify n into n
19.913 * [backup-simplify]: Simplify (log n) into (log n)
19.914 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
19.914 * [backup-simplify]: Simplify (- 1/2) into -1/2
19.914 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
19.914 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
19.915 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
19.915 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
19.916 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
19.917 * [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)))))
19.918 * [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 (* 2 PI)) (log n)))))) into (pow (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 2)
19.919 * [backup-simplify]: Simplify (pow (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 2) into (pow (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 2)
19.920 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.921 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
19.922 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
19.922 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
19.922 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
19.922 * [backup-simplify]: Simplify (- 0) into 0
19.923 * [backup-simplify]: Simplify (+ 0 0) into 0
19.923 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
19.924 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.925 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
19.926 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.928 * [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 (* 2 PI)) (log n))))))) into 0
19.928 * [taylor]: Taking taylor expansion of 0 in k
19.928 * [backup-simplify]: Simplify 0 into 0
19.928 * [backup-simplify]: Simplify 0 into 0
19.929 * [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 (* 2 PI)) (log n))))))) into 0
19.929 * [backup-simplify]: Simplify 0 into 0
19.930 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.931 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
19.933 * [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
19.933 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.934 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
19.934 * [backup-simplify]: Simplify (- 0) into 0
19.934 * [backup-simplify]: Simplify (+ 0 0) into 0
19.935 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
19.936 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.937 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
19.938 * [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
19.940 * [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 (* 2 PI)) (log n)))))))) into 0
19.940 * [taylor]: Taking taylor expansion of 0 in k
19.940 * [backup-simplify]: Simplify 0 into 0
19.940 * [backup-simplify]: Simplify 0 into 0
19.940 * [backup-simplify]: Simplify 0 into 0
19.948 * [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 (* 2 PI)) (log n)))))))) into 0
19.948 * [backup-simplify]: Simplify 0 into 0
19.949 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.950 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.954 * [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
19.954 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.955 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
19.955 * [backup-simplify]: Simplify (- 0) into 0
19.956 * [backup-simplify]: Simplify (+ 0 0) into 0
19.957 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
19.958 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
19.959 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
19.961 * [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
19.964 * [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 (* 2 PI)) (log n))))))))) into 0
19.964 * [taylor]: Taking taylor expansion of 0 in k
19.964 * [backup-simplify]: Simplify 0 into 0
19.964 * [backup-simplify]: Simplify 0 into 0
19.965 * [backup-simplify]: Simplify (pow (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) 2) into (pow (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 2)
19.967 * [backup-simplify]: Simplify (* (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2))) into (pow (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) 2)
19.967 * [approximate]: Taking taylor expansion of (pow (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) 2) in (n k) around 0
19.967 * [taylor]: Taking taylor expansion of (pow (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) 2) in k
19.967 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
19.967 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
19.967 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
19.967 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
19.967 * [taylor]: Taking taylor expansion of 1/2 in k
19.967 * [backup-simplify]: Simplify 1/2 into 1/2
19.967 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
19.967 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
19.967 * [taylor]: Taking taylor expansion of 1/2 in k
19.967 * [backup-simplify]: Simplify 1/2 into 1/2
19.967 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.967 * [taylor]: Taking taylor expansion of k in k
19.967 * [backup-simplify]: Simplify 0 into 0
19.967 * [backup-simplify]: Simplify 1 into 1
19.968 * [backup-simplify]: Simplify (/ 1 1) into 1
19.968 * [taylor]: Taking taylor expansion of 1/2 in k
19.968 * [backup-simplify]: Simplify 1/2 into 1/2
19.968 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
19.968 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
19.968 * [taylor]: Taking taylor expansion of -2 in k
19.968 * [backup-simplify]: Simplify -2 into -2
19.968 * [taylor]: Taking taylor expansion of (/ PI n) in k
19.968 * [taylor]: Taking taylor expansion of PI in k
19.968 * [backup-simplify]: Simplify PI into PI
19.968 * [taylor]: Taking taylor expansion of n in k
19.968 * [backup-simplify]: Simplify n into n
19.968 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
19.968 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
19.968 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
19.969 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
19.969 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.970 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
19.970 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
19.970 * [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))))
19.970 * [taylor]: Taking taylor expansion of (pow (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) 2) in n
19.970 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
19.970 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
19.970 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
19.970 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
19.970 * [taylor]: Taking taylor expansion of 1/2 in n
19.970 * [backup-simplify]: Simplify 1/2 into 1/2
19.970 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
19.971 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
19.971 * [taylor]: Taking taylor expansion of 1/2 in n
19.971 * [backup-simplify]: Simplify 1/2 into 1/2
19.971 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.971 * [taylor]: Taking taylor expansion of k in n
19.971 * [backup-simplify]: Simplify k into k
19.971 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.971 * [taylor]: Taking taylor expansion of 1/2 in n
19.971 * [backup-simplify]: Simplify 1/2 into 1/2
19.971 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
19.971 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
19.971 * [taylor]: Taking taylor expansion of -2 in n
19.971 * [backup-simplify]: Simplify -2 into -2
19.971 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.971 * [taylor]: Taking taylor expansion of PI in n
19.971 * [backup-simplify]: Simplify PI into PI
19.971 * [taylor]: Taking taylor expansion of n in n
19.971 * [backup-simplify]: Simplify 0 into 0
19.971 * [backup-simplify]: Simplify 1 into 1
19.972 * [backup-simplify]: Simplify (/ PI 1) into PI
19.972 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
19.974 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
19.974 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
19.974 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
19.974 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
19.976 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
19.977 * [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))))
19.978 * [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)))))
19.979 * [taylor]: Taking taylor expansion of (pow (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) 2) in n
19.979 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
19.979 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
19.979 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
19.979 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
19.979 * [taylor]: Taking taylor expansion of 1/2 in n
19.979 * [backup-simplify]: Simplify 1/2 into 1/2
19.979 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
19.979 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
19.979 * [taylor]: Taking taylor expansion of 1/2 in n
19.979 * [backup-simplify]: Simplify 1/2 into 1/2
19.979 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.979 * [taylor]: Taking taylor expansion of k in n
19.979 * [backup-simplify]: Simplify k into k
19.979 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.979 * [taylor]: Taking taylor expansion of 1/2 in n
19.979 * [backup-simplify]: Simplify 1/2 into 1/2
19.979 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
19.979 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
19.979 * [taylor]: Taking taylor expansion of -2 in n
19.980 * [backup-simplify]: Simplify -2 into -2
19.980 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.980 * [taylor]: Taking taylor expansion of PI in n
19.980 * [backup-simplify]: Simplify PI into PI
19.980 * [taylor]: Taking taylor expansion of n in n
19.980 * [backup-simplify]: Simplify 0 into 0
19.980 * [backup-simplify]: Simplify 1 into 1
19.980 * [backup-simplify]: Simplify (/ PI 1) into PI
19.981 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
19.982 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
19.982 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
19.982 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
19.982 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
19.984 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
19.985 * [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))))
19.987 * [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)))))
19.989 * [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 (* -2 PI)) (log n)))))) into (pow (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2)
19.989 * [taylor]: Taking taylor expansion of (pow (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2) in k
19.990 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
19.990 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
19.990 * [taylor]: Taking taylor expansion of 1/2 in k
19.990 * [backup-simplify]: Simplify 1/2 into 1/2
19.990 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
19.990 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
19.990 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
19.990 * [taylor]: Taking taylor expansion of 1/2 in k
19.990 * [backup-simplify]: Simplify 1/2 into 1/2
19.990 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.990 * [taylor]: Taking taylor expansion of k in k
19.990 * [backup-simplify]: Simplify 0 into 0
19.990 * [backup-simplify]: Simplify 1 into 1
19.990 * [backup-simplify]: Simplify (/ 1 1) into 1
19.990 * [taylor]: Taking taylor expansion of 1/2 in k
19.990 * [backup-simplify]: Simplify 1/2 into 1/2
19.990 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
19.990 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
19.990 * [taylor]: Taking taylor expansion of (* -2 PI) in k
19.990 * [taylor]: Taking taylor expansion of -2 in k
19.990 * [backup-simplify]: Simplify -2 into -2
19.990 * [taylor]: Taking taylor expansion of PI in k
19.990 * [backup-simplify]: Simplify PI into PI
19.990 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
19.991 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
19.991 * [taylor]: Taking taylor expansion of (log n) in k
19.991 * [taylor]: Taking taylor expansion of n in k
19.991 * [backup-simplify]: Simplify n into n
19.991 * [backup-simplify]: Simplify (log n) into (log n)
19.992 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
19.992 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.992 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
19.993 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
19.993 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
19.994 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
19.995 * [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)))))
19.996 * [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 (* -2 PI)) (log n)))))) into (pow (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2)
19.997 * [backup-simplify]: Simplify (pow (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2) into (pow (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2)
19.998 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.998 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
19.999 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
20.000 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.000 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
20.000 * [backup-simplify]: Simplify (+ 0 0) into 0
20.001 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
20.002 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.002 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
20.004 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.005 * [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 (* -2 PI)) (log n))))))) into 0
20.005 * [taylor]: Taking taylor expansion of 0 in k
20.005 * [backup-simplify]: Simplify 0 into 0
20.005 * [backup-simplify]: Simplify 0 into 0
20.007 * [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 (* -2 PI)) (log n))))))) into 0
20.007 * [backup-simplify]: Simplify 0 into 0
20.008 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.009 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
20.011 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
20.011 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.012 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
20.012 * [backup-simplify]: Simplify (+ 0 0) into 0
20.013 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
20.014 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.015 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
20.016 * [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
20.018 * [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 (* -2 PI)) (log n)))))))) into 0
20.018 * [taylor]: Taking taylor expansion of 0 in k
20.018 * [backup-simplify]: Simplify 0 into 0
20.018 * [backup-simplify]: Simplify 0 into 0
20.018 * [backup-simplify]: Simplify 0 into 0
20.020 * [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 (* -2 PI)) (log n)))))))) into 0
20.020 * [backup-simplify]: Simplify 0 into 0
20.021 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.022 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.026 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
20.026 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.027 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
20.028 * [backup-simplify]: Simplify (+ 0 0) into 0
20.029 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
20.031 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.033 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
20.036 * [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
20.039 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))))) into 0
20.040 * [taylor]: Taking taylor expansion of 0 in k
20.040 * [backup-simplify]: Simplify 0 into 0
20.040 * [backup-simplify]: Simplify 0 into 0
20.041 * [backup-simplify]: Simplify (pow (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) 2) into (pow (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 2)
20.041 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 1)
20.042 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
20.042 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
20.042 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
20.042 * [taylor]: Taking taylor expansion of 2 in n
20.042 * [backup-simplify]: Simplify 2 into 2
20.042 * [taylor]: Taking taylor expansion of (* n PI) in n
20.042 * [taylor]: Taking taylor expansion of n in n
20.042 * [backup-simplify]: Simplify 0 into 0
20.042 * [backup-simplify]: Simplify 1 into 1
20.042 * [taylor]: Taking taylor expansion of PI in n
20.042 * [backup-simplify]: Simplify PI into PI
20.042 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
20.042 * [taylor]: Taking taylor expansion of 2 in n
20.042 * [backup-simplify]: Simplify 2 into 2
20.042 * [taylor]: Taking taylor expansion of (* n PI) in n
20.042 * [taylor]: Taking taylor expansion of n in n
20.042 * [backup-simplify]: Simplify 0 into 0
20.042 * [backup-simplify]: Simplify 1 into 1
20.042 * [taylor]: Taking taylor expansion of PI in n
20.042 * [backup-simplify]: Simplify PI into PI
20.043 * [backup-simplify]: Simplify (* 0 PI) into 0
20.044 * [backup-simplify]: Simplify (* 2 0) into 0
20.044 * [backup-simplify]: Simplify 0 into 0
20.045 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.047 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
20.048 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.049 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
20.050 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
20.050 * [backup-simplify]: Simplify 0 into 0
20.051 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
20.053 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
20.053 * [backup-simplify]: Simplify 0 into 0
20.054 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.055 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
20.055 * [backup-simplify]: Simplify 0 into 0
20.056 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.057 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
20.057 * [backup-simplify]: Simplify 0 into 0
20.058 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.059 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
20.059 * [backup-simplify]: Simplify 0 into 0
20.060 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
20.062 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
20.062 * [backup-simplify]: Simplify 0 into 0
20.062 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
20.063 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
20.063 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
20.063 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
20.063 * [taylor]: Taking taylor expansion of 2 in n
20.063 * [backup-simplify]: Simplify 2 into 2
20.063 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.063 * [taylor]: Taking taylor expansion of PI in n
20.063 * [backup-simplify]: Simplify PI into PI
20.063 * [taylor]: Taking taylor expansion of n in n
20.063 * [backup-simplify]: Simplify 0 into 0
20.063 * [backup-simplify]: Simplify 1 into 1
20.063 * [backup-simplify]: Simplify (/ PI 1) into PI
20.063 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
20.063 * [taylor]: Taking taylor expansion of 2 in n
20.063 * [backup-simplify]: Simplify 2 into 2
20.063 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.063 * [taylor]: Taking taylor expansion of PI in n
20.063 * [backup-simplify]: Simplify PI into PI
20.063 * [taylor]: Taking taylor expansion of n in n
20.063 * [backup-simplify]: Simplify 0 into 0
20.063 * [backup-simplify]: Simplify 1 into 1
20.064 * [backup-simplify]: Simplify (/ PI 1) into PI
20.064 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.064 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.065 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.072 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
20.072 * [backup-simplify]: Simplify 0 into 0
20.073 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.074 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
20.074 * [backup-simplify]: Simplify 0 into 0
20.075 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.076 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.076 * [backup-simplify]: Simplify 0 into 0
20.077 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.077 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.077 * [backup-simplify]: Simplify 0 into 0
20.078 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.079 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.079 * [backup-simplify]: Simplify 0 into 0
20.080 * [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
20.081 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.081 * [backup-simplify]: Simplify 0 into 0
20.081 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
20.082 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
20.082 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
20.082 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
20.082 * [taylor]: Taking taylor expansion of -2 in n
20.082 * [backup-simplify]: Simplify -2 into -2
20.082 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.082 * [taylor]: Taking taylor expansion of PI in n
20.082 * [backup-simplify]: Simplify PI into PI
20.082 * [taylor]: Taking taylor expansion of n in n
20.082 * [backup-simplify]: Simplify 0 into 0
20.082 * [backup-simplify]: Simplify 1 into 1
20.082 * [backup-simplify]: Simplify (/ PI 1) into PI
20.082 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
20.082 * [taylor]: Taking taylor expansion of -2 in n
20.082 * [backup-simplify]: Simplify -2 into -2
20.082 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.082 * [taylor]: Taking taylor expansion of PI in n
20.082 * [backup-simplify]: Simplify PI into PI
20.082 * [taylor]: Taking taylor expansion of n in n
20.082 * [backup-simplify]: Simplify 0 into 0
20.083 * [backup-simplify]: Simplify 1 into 1
20.083 * [backup-simplify]: Simplify (/ PI 1) into PI
20.083 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.084 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.084 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.085 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
20.085 * [backup-simplify]: Simplify 0 into 0
20.086 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.087 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
20.087 * [backup-simplify]: Simplify 0 into 0
20.088 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.089 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.089 * [backup-simplify]: Simplify 0 into 0
20.090 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.092 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.092 * [backup-simplify]: Simplify 0 into 0
20.093 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.095 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.095 * [backup-simplify]: Simplify 0 into 0
20.096 * [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
20.098 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.098 * [backup-simplify]: Simplify 0 into 0
20.099 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
20.099 * * * [progress]: simplifying candidates
20.099 * * * * [progress]: [ 1 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.099 * * * * [progress]: [ 2 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.099 * * * * [progress]: [ 3 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.099 * * * * [progress]: [ 4 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.099 * * * * [progress]: [ 5 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.100 * * * * [progress]: [ 6 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.100 * * * * [progress]: [ 7 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.100 * * * * [progress]: [ 8 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2)))) (sqrt k)))>
20.100 * * * * [progress]: [ 9 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (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)))>
20.100 * * * * [progress]: [ 10 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.100 * * * * [progress]: [ 11 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (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)))>
20.100 * * * * [progress]: [ 12 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (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)))>
20.100 * * * * [progress]: [ 13 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (/ (cbrt (- 1/2 (/ k 2))) 2))) (sqrt k)))>
20.100 * * * * [progress]: [ 14 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2)))) (sqrt k)))>
20.100 * * * * [progress]: [ 15 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))) (sqrt k)))>
20.100 * * * * [progress]: [ 16 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2))) (sqrt k)))>
20.100 * * * * [progress]: [ 17 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2)))) (sqrt k)))>
20.101 * * * * [progress]: [ 18 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2)))) (sqrt k)))>
20.101 * * * * [progress]: [ 19 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.101 * * * * [progress]: [ 20 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (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)))>
20.101 * * * * [progress]: [ 21 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))) (sqrt k)))>
20.101 * * * * [progress]: [ 22 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (/ (- (sqrt 1/2) (sqrt (/ k 2))) 2))) (sqrt k)))>
20.101 * * * * [progress]: [ 23 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (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)))>
20.101 * * * * [progress]: [ 24 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (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)))>
20.101 * * * * [progress]: [ 25 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 2))) (sqrt k)))>
20.101 * * * * [progress]: [ 26 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2)))) (sqrt k)))>
20.101 * * * * [progress]: [ 27 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2)))) (sqrt k)))>
20.101 * * * * [progress]: [ 28 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.102 * * * * [progress]: [ 29 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.102 * * * * [progress]: [ 30 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2))) (sqrt k)))>
20.102 * * * * [progress]: [ 31 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.102 * * * * [progress]: [ 32 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1)) (sqrt k)))>
20.102 * * * * [progress]: [ 33 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (exp (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.102 * * * * [progress]: [ 34 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (log (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.102 * * * * [progress]: [ 35 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (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))))) (sqrt k)))>
20.102 * * * * [progress]: [ 36 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (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))))) (sqrt k)))>
20.102 * * * * [progress]: [ 37 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (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))))) (sqrt k)))>
20.102 * * * * [progress]: [ 38 / 172 ] 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)))>
20.102 * * * * [progress]: [ 39 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (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)))) (sqrt k)))>
20.102 * * * * [progress]: [ 40 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.102 * * * * [progress]: [ 41 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 42 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 43 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 44 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 45 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 46 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 47 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 48 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 49 / 172 ] 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))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 50 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 51 / 172 ] 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))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 52 / 172 ] 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))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 53 / 172 ] 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)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.103 * * * * [progress]: [ 54 / 172 ] 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))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.104 * * * * [progress]: [ 55 / 172 ] 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))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.104 * * * * [progress]: [ 56 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.104 * * * * [progress]: [ 57 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.104 * * * * [progress]: [ 58 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.104 * * * * [progress]: [ 59 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.104 * * * * [progress]: [ 60 / 172 ] 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))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.104 * * * * [progress]: [ 61 / 172 ] 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))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.104 * * * * [progress]: [ 62 / 172 ] 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)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.104 * * * * [progress]: [ 63 / 172 ] 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))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.104 * * * * [progress]: [ 64 / 172 ] 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))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.104 * * * * [progress]: [ 65 / 172 ] 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)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 66 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 67 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 68 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 69 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 70 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 71 / 172 ] 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)))>
20.105 * * * * [progress]: [ 72 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 73 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 74 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (log (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 75 / 172 ] 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)))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 76 / 172 ] 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)))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 77 / 172 ] 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)))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 78 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (* 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.105 * * * * [progress]: [ 79 / 172 ] 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))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.106 * * * * [progress]: [ 80 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.106 * * * * [progress]: [ 81 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (+ (/ (- 1/2 (/ k 2)) 2) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.106 * * * * [progress]: [ 82 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n (* 2 PI)) (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))>
20.106 * * * * [progress]: [ 83 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 2) (sqrt k)))>
20.106 * * * * [progress]: [ 84 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) 1) (sqrt k)))>
20.106 * * * * [progress]: [ 85 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.106 * * * * [progress]: [ 86 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.106 * * * * [progress]: [ 87 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.106 * * * * [progress]: [ 88 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.106 * * * * [progress]: [ 89 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.106 * * * * [progress]: [ 90 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.106 * * * * [progress]: [ 91 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.106 * * * * [progress]: [ 92 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.106 * * * * [progress]: [ 93 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.107 * * * * [progress]: [ 94 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.107 * * * * [progress]: [ 95 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.107 * * * * [progress]: [ 96 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.107 * * * * [progress]: [ 97 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.107 * * * * [progress]: [ 98 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.107 * * * * [progress]: [ 99 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.107 * * * * [progress]: [ 100 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.107 * * * * [progress]: [ 101 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.107 * * * * [progress]: [ 102 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.107 * * * * [progress]: [ 103 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.107 * * * * [progress]: [ 104 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.107 * * * * [progress]: [ 105 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.107 * * * * [progress]: [ 106 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.107 * * * * [progress]: [ 107 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.108 * * * * [progress]: [ 108 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.108 * * * * [progress]: [ 109 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.108 * * * * [progress]: [ 110 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.108 * * * * [progress]: [ 111 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.108 * * * * [progress]: [ 112 / 172 ] 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))) (* (* (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)))>
20.108 * * * * [progress]: [ 113 / 172 ] 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)))) (cbrt (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (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))))) (sqrt k)))>
20.108 * * * * [progress]: [ 114 / 172 ] 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)) (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)))>
20.108 * * * * [progress]: [ 115 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.108 * * * * [progress]: [ 116 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ 1/2 2))) (* (pow (* n (* 2 PI)) (/ (/ k 2) 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2)))) (sqrt k)))>
20.108 * * * * [progress]: [ 117 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.108 * * * * [progress]: [ 118 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (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)))) (sqrt k)))>
20.108 * * * * [progress]: [ 119 / 172 ] 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))) (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)))>
20.108 * * * * [progress]: [ 120 / 172 ] 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)))) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.109 * * * * [progress]: [ 121 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (* 1 1) (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.109 * * * * [progress]: [ 122 / 172 ] 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))) (* (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)))) (sqrt k)))>
20.109 * * * * [progress]: [ 123 / 172 ] 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)))) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.109 * * * * [progress]: [ 124 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2))) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)))) (sqrt k)))>
20.109 * * * * [progress]: [ 125 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (* (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.109 * * * * [progress]: [ 126 / 172 ] 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))) (* (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)))) (sqrt k)))>
20.109 * * * * [progress]: [ 127 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 2 (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.109 * * * * [progress]: [ 128 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow n (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.109 * * * * [progress]: [ 129 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (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)))) (sqrt k)))>
20.109 * * * * [progress]: [ 130 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (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)))) (sqrt k)))>
20.109 * * * * [progress]: [ 131 / 172 ] 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)))>
20.109 * * * * [progress]: [ 132 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (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))) (sqrt k)))>
20.109 * * * * [progress]: [ 133 / 172 ] 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)))>
20.110 * * * * [progress]: [ 134 / 172 ] 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))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.110 * * * * [progress]: [ 135 / 172 ] 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))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.110 * * * * [progress]: [ 136 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.110 * * * * [progress]: [ 137 / 172 ] 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)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
20.110 * * * * [progress]: [ 138 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ 1/2 2))) (pow (* n (* 2 PI)) (/ (/ k 2) 2))) (sqrt k)))>
20.110 * * * * [progress]: [ 139 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (/ k 2) 2))) (sqrt k)))>
20.110 * * * * [progress]: [ 140 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))) (sqrt k)))>
20.110 * * * * [progress]: [ 141 / 172 ] 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)))>
20.110 * * * * [progress]: [ 142 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.110 * * * * [progress]: [ 143 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.110 * * * * [progress]: [ 144 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.111 * * * * [progress]: [ 145 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.111 * * * * [progress]: [ 146 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.111 * * * * [progress]: [ 147 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (exp (log (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.111 * * * * [progress]: [ 148 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (log (exp (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.111 * * * * [progress]: [ 149 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.111 * * * * [progress]: [ 150 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.111 * * * * [progress]: [ 151 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.111 * * * * [progress]: [ 152 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.111 * * * * [progress]: [ 153 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.111 * * * * [progress]: [ 154 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.111 * * * * [progress]: [ 155 / 172 ] 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)))>
20.111 * * * * [progress]: [ 156 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.111 * * * * [progress]: [ 157 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.112 * * * * [progress]: [ 158 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.112 * * * * [progress]: [ 159 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.112 * * * * [progress]: [ 160 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* 2 PI) n) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.112 * * * * [progress]: [ 161 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))) (sqrt k)))>
20.112 * * * * [progress]: [ 162 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))) (sqrt k)))>
20.112 * * * * [progress]: [ 163 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))) (sqrt k)))>
20.112 * * * * [progress]: [ 164 / 172 ] 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))))))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.112 * * * * [progress]: [ 165 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.112 * * * * [progress]: [ 166 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.112 * * * * [progress]: [ 167 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/4 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI)))))) (+ (* 1/8 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))) (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)))) (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) k))))) (sqrt k)))>
20.112 * * * * [progress]: [ 168 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 2) (sqrt k)))>
20.112 * * * * [progress]: [ 169 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 2) (sqrt k)))>
20.112 * * * * [progress]: [ 170 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.113 * * * * [progress]: [ 171 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.113 * * * * [progress]: [ 172 / 172 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
20.116 * [simplify]: Simplifying:
  (* (+ (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)))
  (* (+ (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)))
  (+ (/ (- 1/2 (/ k 2)) 2) (/ (- 1/2 (/ k 2)) 2))
  (* (* n (* 2 PI)) (* n (* 2 PI)))
  (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (+ (log 2) (log 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) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))
  (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))
  (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (+ (* (+ (log n) (log (* 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) (log (* 2 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) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))
  (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (+ (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)))
  (+ (* (log (* n (* 2 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)))
  (+ (* (log (* n (* 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)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (+ (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)))
  (+ (* (log (* n (* 2 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)))
  (+ (* (log (* n (* 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)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (+ (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)))
  (+ (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))
  (+ (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))
  (+ (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))
  (+ (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (log (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (exp (* (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))) (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))))
  (* (cbrt (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (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)))))
  (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))) (* (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)) (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))))
  (* (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ 1/2 2)))
  (* (pow (* n (* 2 PI)) (/ (/ k 2) 2)) (pow (* n (* 2 PI)) (/ (/ 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)))
  (* (* (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))) (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 (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))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (* 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) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)))
  (* (sqrt (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))) (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)))
  (* (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)) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 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)))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)))
  (* 2 (/ (- 1/2 (/ k 2)) 2))
  (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow n (/ (- 1/2 (/ k 2)) 2)))
  (* (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)) (sqrt (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)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)))
  (* (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (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)))
  (* (sqrt (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)))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 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 2)))
  (* (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (real->posit16 (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (+ (* 1/16 (* (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))))))
  (- (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/4 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI)))))) (+ (* 1/8 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))) (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)))) (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) k)))))
  (pow (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 2)
  (pow (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 2)
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
20.120 * * [simplify]: iteration 1: (232 enodes)
20.199 * * [simplify]: iteration 2: (653 enodes)
21.435 * * [simplify]: Extracting #0: cost 72 inf + 0
21.437 * * [simplify]: Extracting #1: cost 361 inf + 1
21.441 * * [simplify]: Extracting #2: cost 598 inf + 4252
21.455 * * [simplify]: Extracting #3: cost 527 inf + 46749
21.474 * * [simplify]: Extracting #4: cost 276 inf + 150702
21.530 * * [simplify]: Extracting #5: cost 71 inf + 246988
21.576 * * [simplify]: Extracting #6: cost 26 inf + 272440
21.634 * * [simplify]: Extracting #7: cost 21 inf + 271703
21.691 * * [simplify]: Extracting #8: cost 6 inf + 276817
21.747 * * [simplify]: Extracting #9: cost 0 inf + 279580
21.799 * * [simplify]: Extracting #10: cost 0 inf + 279410
21.850 * [simplify]: Simplified to:
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (exp (* 1/4 (log (* 2 (* PI n)))))
  (pow (* 2 (* PI n)) (/ k 4))
  (pow (* 2 (* PI n)) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4)))))
  (pow (* 2 (* PI n)) (sqrt (- 1/4 (/ k 4))))
  (pow (* 2 (* PI n)) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2)))
  (pow (* 2 (* PI n)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 (* PI n)) (/ (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* 2 (* PI n)) (sqrt (- 1/2 (/ k 2))))
  (pow (* 2 (* PI n)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ 1 (sqrt 2)))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (/ (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* 2 (* PI n)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* 2 (* PI n)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2)))
  (pow (* 2 (* PI n)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* 2 (* PI n)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ 1 (sqrt 2)))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))
  (pow n (- 1/4 (/ k 4)))
  (pow (* PI 2) (- 1/4 (/ k 4)))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (exp (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))) (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))))
  (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (* (pow (* 2 (* PI n)) (- 1/4 (/ k 4))) (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))) (* (pow (* 2 (* PI n)) (- 1/4 (/ k 4))) (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))))
  (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (pow (* 2 (* PI n)) (- 1/8 (/ k 8)))
  (pow (* 2 (* PI n)) (- 1/8 (/ k 8)))
  (real->posit16 (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (exp (* 1/4 (log (* 2 (* PI n)))))
  (pow (* 2 (* PI n)) (/ k 4))
  (pow (* 2 (* PI n)) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4)))))
  (pow (* 2 (* PI n)) (sqrt (- 1/4 (/ k 4))))
  (pow (* 2 (* PI n)) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2)))
  (pow (* 2 (* PI n)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 (* PI n)) (/ (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* 2 (* PI n)) (sqrt (- 1/2 (/ k 2))))
  (pow (* 2 (* PI n)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ 1 (sqrt 2)))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (/ (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* 2 (* PI n)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* 2 (* PI n)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2)))
  (pow (* 2 (* PI n)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* 2 (* PI n)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ 1 (sqrt 2)))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))
  (pow n (- 1/4 (/ k 4)))
  (pow (* PI 2) (- 1/4 (/ k 4)))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (exp (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))) (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))))
  (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (* (pow (* 2 (* PI n)) (- 1/4 (/ k 4))) (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))) (* (pow (* 2 (* PI n)) (- 1/4 (/ k 4))) (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))))
  (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (pow (* 2 (* PI n)) (- 1/8 (/ k 8)))
  (pow (* 2 (* PI n)) (- 1/8 (/ k 8)))
  (real->posit16 (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4)))
  (* (* 2 (* PI n)) (* 2 (* PI n)))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (* (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))) (log (* 2 (* PI n))))
  (exp (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* (pow (* 2 (* PI n)) (- 1/2 (/ k 2))) (* (pow (* 2 (* PI n)) (- 1/2 (/ k 2))) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))
  (* (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* (pow (* 2 (* PI n)) (- 1/2 (/ k 2))) (* (pow (* 2 (* PI n)) (- 1/2 (/ k 2))) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))
  (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (sqrt (* 2 (* PI n)))
  (* (pow (* 2 (* PI n)) (/ k 4)) (pow (* 2 (* PI n)) (/ k 4)))
  (pow n (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4))))
  (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow (* PI 2) (- 1/4 (/ k 4))))
  (* (* (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))) (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))) (* (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))) (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))))
  (* (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))) (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  1
  (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (* (sqrt (pow (* 2 (* PI n)) (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 (* PI n)) (/ (- 1/2 (/ k 2)) 4)))
  (* (sqrt (pow (* 2 (* PI n)) (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 (* PI n)) (/ (- 1/2 (/ k 2)) 4)))
  (* (sqrt (pow (* 2 (* PI n)) (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 (* PI n)) (/ (- 1/2 (/ k 2)) 4)))
  (* (sqrt (pow (* 2 (* PI n)) (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 (* PI n)) (/ (- 1/2 (/ k 2)) 4)))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (+ (- 1/4 (/ k 4)) (- 1/4 (/ k 4)))
  (* (pow n (- 1/4 (/ k 4))) (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))) (* (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))) (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))))
  (* (pow (* 2 (* PI n)) (- 1/4 (/ k 4))) (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (* (pow (* 2 (* PI n)) (- 1/8 (/ k 8))) (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (pow (* PI 2) (- 1/4 (/ k 4))) (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))) (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (pow (* 2 (* PI n)) (- 1/4 (/ k 4))) (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))))
  (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))
  (* (pow (* 2 (* PI n)) (- 1/8 (/ k 8))) (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (pow (* 2 (* PI n)) (- 1/4 (/ k 4))) (exp (* 1/4 (log (* 2 (* PI n))))))
  (* (pow (* 2 (* PI n)) (- 1/4 (/ k 4))) (exp (* 1/4 (log (* 2 (* PI n))))))
  (real->posit16 (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* 8 (* (* PI (* PI PI)) (* (* n n) n)))
  (* (* 2 (* PI n)) (* (* 2 (* PI n)) (* 2 (* PI 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)))
  (* n 2)
  (* (* PI 2) (cbrt n))
  (* (* PI 2) (sqrt n))
  (* 2 (* PI n))
  (real->posit16 (* 2 (* PI n)))
  (- (+ (* (* (* k k) (+ (* (exp (* 1/4 (log (* 2 (* PI n))))) (* (log n) (log n))) (* (exp (* 1/4 (log (* 2 (* PI n))))) (* (log (* PI 2)) (log (* PI 2)))))) 1/32) (+ (exp (* 1/4 (log (* 2 (* PI n))))) (* (* (* 1/16 (log (* PI 2))) (* (* k k) (log n))) (exp (* 1/4 (log (* 2 (* PI n)))))))) (* (* k (+ (* (exp (* 1/4 (log (* 2 (* PI n))))) (log n)) (* (exp (* 1/4 (log (* 2 (* PI n))))) (log (* PI 2))))) 1/4))
  (exp (* (* 1/2 (- 1/2 (* k 1/2))) (log (* 2 (* PI n)))))
  (exp (* (* 1/2 (- 1/2 (* k 1/2))) (- (log (* PI -2)) (log (/ -1 n)))))
  (- (+ (* (* (* k k) (+ (* (exp (* 1/4 (log (* 2 (* PI n))))) (* (log n) (log n))) (* (exp (* 1/4 (log (* 2 (* PI n))))) (* (log (* PI 2)) (log (* PI 2)))))) 1/32) (+ (exp (* 1/4 (log (* 2 (* PI n))))) (* (* (* 1/16 (log (* PI 2))) (* (* k k) (log n))) (exp (* 1/4 (log (* 2 (* PI n)))))))) (* (* k (+ (* (exp (* 1/4 (log (* 2 (* PI n))))) (log n)) (* (exp (* 1/4 (log (* 2 (* PI n))))) (log (* PI 2))))) 1/4))
  (exp (* (* 1/2 (- 1/2 (* k 1/2))) (log (* 2 (* PI n)))))
  (exp (* (* 1/2 (- 1/2 (* k 1/2))) (- (log (* PI -2)) (log (/ -1 n)))))
  (+ (+ (* 1/8 (* (* (log (* PI 2)) (* (log (* PI 2)) (sqrt (* 2 (* PI n))))) (* k k))) (+ (sqrt (* 2 (* PI n))) (* (* 1/4 (* k k)) (* (sqrt (* 2 (* PI n))) (* (log (* PI 2)) (log n)))))) (+ (* (* (sqrt (* 2 (* PI n))) (* (log n) (log n))) (* (* k k) 1/8)) (* -1/2 (+ (* (log (* PI 2)) (* k (sqrt (* 2 (* PI n))))) (* (* k (sqrt (* 2 (* PI n)))) (log n))))))
  (exp (+ (* (* 1/2 (- 1/2 (* k 1/2))) (log (* 2 (* PI n)))) (* (* 1/2 (- 1/2 (* k 1/2))) (log (* 2 (* PI n))))))
  (* (exp (* (* 1/2 (- 1/2 (* k 1/2))) (- (log (* PI -2)) (log (/ -1 n))))) (exp (* (* 1/2 (- 1/2 (* k 1/2))) (- (log (* PI -2)) (log (/ -1 n))))))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
21.864 * * * [progress]: adding candidates to table
23.476 * [progress]: [Phase 3 of 3] Extracting.
23.477 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))> #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))> #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))> #<alt (λ (k n) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (fabs (cbrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))> #<alt (λ (k n) (/ 1 (* (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>)
23.478 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2 PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) n k)
23.478 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))> #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))> #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))> #<alt (λ (k n) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (fabs (cbrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))> #<alt (λ (k n) (/ 1 (* (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>)
23.560 * * * * [regimes]: Trying to branch on (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) from (#<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))> #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))> #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))> #<alt (λ (k n) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (fabs (cbrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))> #<alt (λ (k n) (/ 1 (* (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>)
23.649 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))> #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))> #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))> #<alt (λ (k n) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (fabs (cbrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))> #<alt (λ (k n) (/ 1 (* (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>)
23.725 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))> #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))> #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))> #<alt (λ (k n) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (fabs (cbrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))> #<alt (λ (k n) (/ 1 (* (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>)
23.796 * * * [regime]: Found split indices: #<option (#s(si 0 255))>
23.797 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
23.797 * * [simplify]: iteration 1: (13 enodes)
23.798 * * [simplify]: iteration 2: (16 enodes)
23.799 * * [simplify]: Extracting #0: cost 1 inf + 0
23.799 * * [simplify]: Extracting #1: cost 3 inf + 0
23.799 * * [simplify]: Extracting #2: cost 7 inf + 0
23.799 * * [simplify]: Extracting #3: cost 11 inf + 1
23.799 * * [simplify]: Extracting #4: cost 5 inf + 252
23.799 * * [simplify]: Extracting #5: cost 4 inf + 253
23.800 * * [simplify]: Extracting #6: cost 1 inf + 753
23.800 * * [simplify]: Extracting #7: cost 0 inf + 1248
23.800 * [simplify]: Simplified to:
  (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
33.274 * [regime-testing]: Baseline error score: 0.37701794678329476
33.278 * [regime-testing]: Oracle error score: 0.025399415552124306
33.287 * [regime-testing]: End program error score: 0.37701794678329476