63.145 * [progress]: [Phase 1 of 3] Setting up.
0.001 * * * [progress]: [1/2] Preparing points
0.206 * * * [progress]: [2/2] Setting up program.
0.210 * [progress]: [Phase 2 of 3] Improving.
0.210 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.210 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.210 * * [simplify]: iteration 1: (13 enodes)
0.214 * * [simplify]: iteration 2: (31 enodes)
0.220 * * [simplify]: iteration 3: (62 enodes)
0.239 * * [simplify]: iteration 4: (124 enodes)
0.315 * * [simplify]: iteration 5: (330 enodes)
0.515 * * [simplify]: iteration 6: (827 enodes)
1.402 * * [simplify]: iteration 7: (1992 enodes)
7.527 * * [simplify]: Extracting #0: cost 1 inf + 0
7.527 * * [simplify]: Extracting #1: cost 116 inf + 0
7.540 * * [simplify]: Extracting #2: cost 506 inf + 1
7.548 * * [simplify]: Extracting #3: cost 588 inf + 50
7.557 * * [simplify]: Extracting #4: cost 591 inf + 1270
7.577 * * [simplify]: Extracting #5: cost 475 inf + 39174
7.739 * * [simplify]: Extracting #6: cost 113 inf + 397134
7.933 * * [simplify]: Extracting #7: cost 0 inf + 509518
8.104 * * [simplify]: Extracting #8: cost 0 inf + 492512
8.278 * * [simplify]: Extracting #9: cost 0 inf + 481384
8.503 * * [simplify]: Extracting #10: cost 0 inf + 480399
8.720 * * [simplify]: Extracting #11: cost 0 inf + 480349
8.912 * [simplify]: Simplified to:
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
8.919 * * [progress]: iteration 1 / 4
8.919 * * * [progress]: picking best candidate
8.930 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))>
8.931 * * * [progress]: localizing error
8.966 * * * [progress]: generating rewritten candidates
8.966 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
8.981 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
9.005 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
9.037 * * * [progress]: generating series expansions
9.037 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
9.038 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
9.038 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
9.038 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
9.038 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
9.038 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
9.038 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
9.038 * [taylor]: Taking taylor expansion of 1/2 in k
9.038 * [backup-simplify]: Simplify 1/2 into 1/2
9.038 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
9.038 * [taylor]: Taking taylor expansion of 1/2 in k
9.038 * [backup-simplify]: Simplify 1/2 into 1/2
9.038 * [taylor]: Taking taylor expansion of k in k
9.038 * [backup-simplify]: Simplify 0 into 0
9.038 * [backup-simplify]: Simplify 1 into 1
9.038 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
9.038 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
9.038 * [taylor]: Taking taylor expansion of 2 in k
9.038 * [backup-simplify]: Simplify 2 into 2
9.038 * [taylor]: Taking taylor expansion of (* n PI) in k
9.038 * [taylor]: Taking taylor expansion of n in k
9.038 * [backup-simplify]: Simplify n into n
9.038 * [taylor]: Taking taylor expansion of PI in k
9.038 * [backup-simplify]: Simplify PI into PI
9.039 * [backup-simplify]: Simplify (* n PI) into (* n PI)
9.039 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
9.039 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
9.039 * [backup-simplify]: Simplify (* 1/2 0) into 0
9.040 * [backup-simplify]: Simplify (- 0) into 0
9.040 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.040 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
9.040 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
9.040 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
9.040 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
9.040 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
9.040 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
9.040 * [taylor]: Taking taylor expansion of 1/2 in n
9.041 * [backup-simplify]: Simplify 1/2 into 1/2
9.041 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
9.041 * [taylor]: Taking taylor expansion of 1/2 in n
9.041 * [backup-simplify]: Simplify 1/2 into 1/2
9.041 * [taylor]: Taking taylor expansion of k in n
9.041 * [backup-simplify]: Simplify k into k
9.041 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.041 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.041 * [taylor]: Taking taylor expansion of 2 in n
9.041 * [backup-simplify]: Simplify 2 into 2
9.041 * [taylor]: Taking taylor expansion of (* n PI) in n
9.041 * [taylor]: Taking taylor expansion of n in n
9.041 * [backup-simplify]: Simplify 0 into 0
9.041 * [backup-simplify]: Simplify 1 into 1
9.041 * [taylor]: Taking taylor expansion of PI in n
9.041 * [backup-simplify]: Simplify PI into PI
9.041 * [backup-simplify]: Simplify (* 0 PI) into 0
9.042 * [backup-simplify]: Simplify (* 2 0) into 0
9.043 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.045 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.046 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.046 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
9.046 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
9.047 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
9.048 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.049 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
9.050 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
9.050 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
9.050 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
9.050 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
9.050 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
9.050 * [taylor]: Taking taylor expansion of 1/2 in n
9.050 * [backup-simplify]: Simplify 1/2 into 1/2
9.050 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
9.050 * [taylor]: Taking taylor expansion of 1/2 in n
9.050 * [backup-simplify]: Simplify 1/2 into 1/2
9.050 * [taylor]: Taking taylor expansion of k in n
9.050 * [backup-simplify]: Simplify k into k
9.051 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.051 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.051 * [taylor]: Taking taylor expansion of 2 in n
9.051 * [backup-simplify]: Simplify 2 into 2
9.051 * [taylor]: Taking taylor expansion of (* n PI) in n
9.051 * [taylor]: Taking taylor expansion of n in n
9.051 * [backup-simplify]: Simplify 0 into 0
9.051 * [backup-simplify]: Simplify 1 into 1
9.051 * [taylor]: Taking taylor expansion of PI in n
9.051 * [backup-simplify]: Simplify PI into PI
9.051 * [backup-simplify]: Simplify (* 0 PI) into 0
9.052 * [backup-simplify]: Simplify (* 2 0) into 0
9.053 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.055 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.056 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.056 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
9.056 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
9.056 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
9.058 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.059 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
9.060 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
9.060 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
9.060 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
9.060 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
9.060 * [taylor]: Taking taylor expansion of 1/2 in k
9.060 * [backup-simplify]: Simplify 1/2 into 1/2
9.060 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
9.060 * [taylor]: Taking taylor expansion of 1/2 in k
9.060 * [backup-simplify]: Simplify 1/2 into 1/2
9.060 * [taylor]: Taking taylor expansion of k in k
9.060 * [backup-simplify]: Simplify 0 into 0
9.060 * [backup-simplify]: Simplify 1 into 1
9.060 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
9.060 * [taylor]: Taking taylor expansion of (log n) in k
9.060 * [taylor]: Taking taylor expansion of n in k
9.060 * [backup-simplify]: Simplify n into n
9.060 * [backup-simplify]: Simplify (log n) into (log n)
9.060 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.061 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.061 * [taylor]: Taking taylor expansion of 2 in k
9.061 * [backup-simplify]: Simplify 2 into 2
9.061 * [taylor]: Taking taylor expansion of PI in k
9.061 * [backup-simplify]: Simplify PI into PI
9.061 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.062 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.063 * [backup-simplify]: Simplify (* 1/2 0) into 0
9.063 * [backup-simplify]: Simplify (- 0) into 0
9.063 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.065 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.066 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
9.067 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.068 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.069 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.070 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.072 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.072 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
9.073 * [backup-simplify]: Simplify (- 0) into 0
9.073 * [backup-simplify]: Simplify (+ 0 0) into 0
9.075 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.076 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
9.078 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.078 * [taylor]: Taking taylor expansion of 0 in k
9.078 * [backup-simplify]: Simplify 0 into 0
9.078 * [backup-simplify]: Simplify 0 into 0
9.079 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
9.080 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.081 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.081 * [backup-simplify]: Simplify (+ 0 0) into 0
9.082 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
9.082 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.082 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.083 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
9.085 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.087 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.087 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.088 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.090 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.091 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
9.091 * [backup-simplify]: Simplify (- 0) into 0
9.091 * [backup-simplify]: Simplify (+ 0 0) into 0
9.092 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.093 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.094 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.094 * [taylor]: Taking taylor expansion of 0 in k
9.094 * [backup-simplify]: Simplify 0 into 0
9.094 * [backup-simplify]: Simplify 0 into 0
9.094 * [backup-simplify]: Simplify 0 into 0
9.095 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
9.096 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.098 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.098 * [backup-simplify]: Simplify (+ 0 0) into 0
9.099 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
9.099 * [backup-simplify]: Simplify (- 0) into 0
9.099 * [backup-simplify]: Simplify (+ 0 0) into 0
9.100 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.102 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.105 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.113 * [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)))))
9.114 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
9.114 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
9.114 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
9.114 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
9.114 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
9.114 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
9.114 * [taylor]: Taking taylor expansion of 1/2 in k
9.114 * [backup-simplify]: Simplify 1/2 into 1/2
9.114 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.114 * [taylor]: Taking taylor expansion of 1/2 in k
9.114 * [backup-simplify]: Simplify 1/2 into 1/2
9.114 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.114 * [taylor]: Taking taylor expansion of k in k
9.114 * [backup-simplify]: Simplify 0 into 0
9.114 * [backup-simplify]: Simplify 1 into 1
9.114 * [backup-simplify]: Simplify (/ 1 1) into 1
9.114 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
9.114 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
9.115 * [taylor]: Taking taylor expansion of 2 in k
9.115 * [backup-simplify]: Simplify 2 into 2
9.115 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.115 * [taylor]: Taking taylor expansion of PI in k
9.115 * [backup-simplify]: Simplify PI into PI
9.115 * [taylor]: Taking taylor expansion of n in k
9.115 * [backup-simplify]: Simplify n into n
9.115 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.115 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
9.115 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
9.115 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.116 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.116 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.116 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
9.117 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
9.117 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
9.117 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.117 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.117 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
9.117 * [taylor]: Taking taylor expansion of 1/2 in n
9.117 * [backup-simplify]: Simplify 1/2 into 1/2
9.117 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.117 * [taylor]: Taking taylor expansion of 1/2 in n
9.117 * [backup-simplify]: Simplify 1/2 into 1/2
9.117 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.117 * [taylor]: Taking taylor expansion of k in n
9.117 * [backup-simplify]: Simplify k into k
9.117 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.117 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.117 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.117 * [taylor]: Taking taylor expansion of 2 in n
9.117 * [backup-simplify]: Simplify 2 into 2
9.117 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.117 * [taylor]: Taking taylor expansion of PI in n
9.117 * [backup-simplify]: Simplify PI into PI
9.117 * [taylor]: Taking taylor expansion of n in n
9.117 * [backup-simplify]: Simplify 0 into 0
9.117 * [backup-simplify]: Simplify 1 into 1
9.118 * [backup-simplify]: Simplify (/ PI 1) into PI
9.118 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.119 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.119 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.119 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
9.119 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
9.121 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.122 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
9.123 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.123 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
9.123 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.123 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.123 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
9.123 * [taylor]: Taking taylor expansion of 1/2 in n
9.123 * [backup-simplify]: Simplify 1/2 into 1/2
9.123 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.123 * [taylor]: Taking taylor expansion of 1/2 in n
9.123 * [backup-simplify]: Simplify 1/2 into 1/2
9.123 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.123 * [taylor]: Taking taylor expansion of k in n
9.123 * [backup-simplify]: Simplify k into k
9.124 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.124 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.124 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.124 * [taylor]: Taking taylor expansion of 2 in n
9.124 * [backup-simplify]: Simplify 2 into 2
9.124 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.124 * [taylor]: Taking taylor expansion of PI in n
9.124 * [backup-simplify]: Simplify PI into PI
9.124 * [taylor]: Taking taylor expansion of n in n
9.124 * [backup-simplify]: Simplify 0 into 0
9.124 * [backup-simplify]: Simplify 1 into 1
9.124 * [backup-simplify]: Simplify (/ PI 1) into PI
9.125 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.126 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.126 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.126 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
9.126 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
9.128 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.129 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
9.130 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.130 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
9.130 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
9.130 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
9.130 * [taylor]: Taking taylor expansion of 1/2 in k
9.130 * [backup-simplify]: Simplify 1/2 into 1/2
9.130 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.130 * [taylor]: Taking taylor expansion of 1/2 in k
9.130 * [backup-simplify]: Simplify 1/2 into 1/2
9.130 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.130 * [taylor]: Taking taylor expansion of k in k
9.130 * [backup-simplify]: Simplify 0 into 0
9.130 * [backup-simplify]: Simplify 1 into 1
9.130 * [backup-simplify]: Simplify (/ 1 1) into 1
9.131 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
9.131 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.131 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.131 * [taylor]: Taking taylor expansion of 2 in k
9.131 * [backup-simplify]: Simplify 2 into 2
9.131 * [taylor]: Taking taylor expansion of PI in k
9.131 * [backup-simplify]: Simplify PI into PI
9.131 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.132 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.132 * [taylor]: Taking taylor expansion of (log n) in k
9.132 * [taylor]: Taking taylor expansion of n in k
9.132 * [backup-simplify]: Simplify n into n
9.132 * [backup-simplify]: Simplify (log n) into (log n)
9.133 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.133 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.133 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.133 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.134 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
9.135 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
9.136 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.138 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.139 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.140 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.142 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.142 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.142 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
9.143 * [backup-simplify]: Simplify (- 0) into 0
9.143 * [backup-simplify]: Simplify (+ 0 0) into 0
9.145 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.146 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
9.148 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.148 * [taylor]: Taking taylor expansion of 0 in k
9.148 * [backup-simplify]: Simplify 0 into 0
9.148 * [backup-simplify]: Simplify 0 into 0
9.148 * [backup-simplify]: Simplify 0 into 0
9.149 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.150 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.153 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.153 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.154 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
9.155 * [backup-simplify]: Simplify (- 0) into 0
9.155 * [backup-simplify]: Simplify (+ 0 0) into 0
9.160 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.162 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
9.164 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.164 * [taylor]: Taking taylor expansion of 0 in k
9.164 * [backup-simplify]: Simplify 0 into 0
9.164 * [backup-simplify]: Simplify 0 into 0
9.164 * [backup-simplify]: Simplify 0 into 0
9.164 * [backup-simplify]: Simplify 0 into 0
9.166 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.167 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.173 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.173 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.174 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
9.175 * [backup-simplify]: Simplify (- 0) into 0
9.175 * [backup-simplify]: Simplify (+ 0 0) into 0
9.177 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.178 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
9.181 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.181 * [taylor]: Taking taylor expansion of 0 in k
9.181 * [backup-simplify]: Simplify 0 into 0
9.181 * [backup-simplify]: Simplify 0 into 0
9.183 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
9.183 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
9.183 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
9.183 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
9.183 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
9.183 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
9.183 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
9.183 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.184 * [taylor]: Taking taylor expansion of 1/2 in k
9.184 * [backup-simplify]: Simplify 1/2 into 1/2
9.184 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.184 * [taylor]: Taking taylor expansion of k in k
9.184 * [backup-simplify]: Simplify 0 into 0
9.184 * [backup-simplify]: Simplify 1 into 1
9.184 * [backup-simplify]: Simplify (/ 1 1) into 1
9.184 * [taylor]: Taking taylor expansion of 1/2 in k
9.184 * [backup-simplify]: Simplify 1/2 into 1/2
9.184 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
9.184 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
9.184 * [taylor]: Taking taylor expansion of -2 in k
9.184 * [backup-simplify]: Simplify -2 into -2
9.184 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.184 * [taylor]: Taking taylor expansion of PI in k
9.184 * [backup-simplify]: Simplify PI into PI
9.184 * [taylor]: Taking taylor expansion of n in k
9.184 * [backup-simplify]: Simplify n into n
9.184 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.184 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
9.185 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
9.185 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.186 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.186 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
9.186 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
9.186 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
9.186 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
9.186 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
9.186 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
9.186 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.187 * [taylor]: Taking taylor expansion of 1/2 in n
9.187 * [backup-simplify]: Simplify 1/2 into 1/2
9.187 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.187 * [taylor]: Taking taylor expansion of k in n
9.187 * [backup-simplify]: Simplify k into k
9.187 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.187 * [taylor]: Taking taylor expansion of 1/2 in n
9.187 * [backup-simplify]: Simplify 1/2 into 1/2
9.187 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.187 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.187 * [taylor]: Taking taylor expansion of -2 in n
9.187 * [backup-simplify]: Simplify -2 into -2
9.187 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.187 * [taylor]: Taking taylor expansion of PI in n
9.187 * [backup-simplify]: Simplify PI into PI
9.187 * [taylor]: Taking taylor expansion of n in n
9.187 * [backup-simplify]: Simplify 0 into 0
9.187 * [backup-simplify]: Simplify 1 into 1
9.188 * [backup-simplify]: Simplify (/ PI 1) into PI
9.188 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.189 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.189 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.189 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
9.191 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.192 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
9.193 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.193 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
9.193 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
9.193 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
9.193 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
9.193 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.193 * [taylor]: Taking taylor expansion of 1/2 in n
9.193 * [backup-simplify]: Simplify 1/2 into 1/2
9.193 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.193 * [taylor]: Taking taylor expansion of k in n
9.193 * [backup-simplify]: Simplify k into k
9.193 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.193 * [taylor]: Taking taylor expansion of 1/2 in n
9.193 * [backup-simplify]: Simplify 1/2 into 1/2
9.193 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.193 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.193 * [taylor]: Taking taylor expansion of -2 in n
9.193 * [backup-simplify]: Simplify -2 into -2
9.193 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.194 * [taylor]: Taking taylor expansion of PI in n
9.194 * [backup-simplify]: Simplify PI into PI
9.194 * [taylor]: Taking taylor expansion of n in n
9.194 * [backup-simplify]: Simplify 0 into 0
9.194 * [backup-simplify]: Simplify 1 into 1
9.194 * [backup-simplify]: Simplify (/ PI 1) into PI
9.195 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.196 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.196 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.196 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
9.197 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.198 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
9.199 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.200 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
9.200 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
9.200 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
9.200 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.200 * [taylor]: Taking taylor expansion of 1/2 in k
9.200 * [backup-simplify]: Simplify 1/2 into 1/2
9.200 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.200 * [taylor]: Taking taylor expansion of k in k
9.200 * [backup-simplify]: Simplify 0 into 0
9.200 * [backup-simplify]: Simplify 1 into 1
9.200 * [backup-simplify]: Simplify (/ 1 1) into 1
9.200 * [taylor]: Taking taylor expansion of 1/2 in k
9.200 * [backup-simplify]: Simplify 1/2 into 1/2
9.200 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
9.200 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
9.200 * [taylor]: Taking taylor expansion of (* -2 PI) in k
9.200 * [taylor]: Taking taylor expansion of -2 in k
9.200 * [backup-simplify]: Simplify -2 into -2
9.200 * [taylor]: Taking taylor expansion of PI in k
9.200 * [backup-simplify]: Simplify PI into PI
9.201 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.202 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.202 * [taylor]: Taking taylor expansion of (log n) in k
9.202 * [taylor]: Taking taylor expansion of n in k
9.202 * [backup-simplify]: Simplify n into n
9.202 * [backup-simplify]: Simplify (log n) into (log n)
9.202 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.203 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.203 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.204 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
9.205 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
9.206 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.207 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.208 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.209 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.211 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
9.211 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.212 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
9.212 * [backup-simplify]: Simplify (+ 0 0) into 0
9.214 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.215 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
9.217 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.217 * [taylor]: Taking taylor expansion of 0 in k
9.217 * [backup-simplify]: Simplify 0 into 0
9.217 * [backup-simplify]: Simplify 0 into 0
9.217 * [backup-simplify]: Simplify 0 into 0
9.218 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.219 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.223 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
9.223 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.224 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
9.225 * [backup-simplify]: Simplify (+ 0 0) into 0
9.226 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.227 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
9.228 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.228 * [taylor]: Taking taylor expansion of 0 in k
9.228 * [backup-simplify]: Simplify 0 into 0
9.228 * [backup-simplify]: Simplify 0 into 0
9.228 * [backup-simplify]: Simplify 0 into 0
9.228 * [backup-simplify]: Simplify 0 into 0
9.229 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.230 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.233 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
9.233 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.234 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
9.234 * [backup-simplify]: Simplify (+ 0 0) into 0
9.235 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.236 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
9.237 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.237 * [taylor]: Taking taylor expansion of 0 in k
9.238 * [backup-simplify]: Simplify 0 into 0
9.238 * [backup-simplify]: Simplify 0 into 0
9.238 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
9.238 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
9.239 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
9.239 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
9.239 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.239 * [taylor]: Taking taylor expansion of 2 in n
9.239 * [backup-simplify]: Simplify 2 into 2
9.239 * [taylor]: Taking taylor expansion of (* n PI) in n
9.239 * [taylor]: Taking taylor expansion of n in n
9.239 * [backup-simplify]: Simplify 0 into 0
9.239 * [backup-simplify]: Simplify 1 into 1
9.239 * [taylor]: Taking taylor expansion of PI in n
9.239 * [backup-simplify]: Simplify PI into PI
9.239 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.239 * [taylor]: Taking taylor expansion of 2 in n
9.239 * [backup-simplify]: Simplify 2 into 2
9.239 * [taylor]: Taking taylor expansion of (* n PI) in n
9.239 * [taylor]: Taking taylor expansion of n in n
9.239 * [backup-simplify]: Simplify 0 into 0
9.239 * [backup-simplify]: Simplify 1 into 1
9.239 * [taylor]: Taking taylor expansion of PI in n
9.239 * [backup-simplify]: Simplify PI into PI
9.239 * [backup-simplify]: Simplify (* 0 PI) into 0
9.240 * [backup-simplify]: Simplify (* 2 0) into 0
9.240 * [backup-simplify]: Simplify 0 into 0
9.240 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.241 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.242 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.242 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.243 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.243 * [backup-simplify]: Simplify 0 into 0
9.244 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.244 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.244 * [backup-simplify]: Simplify 0 into 0
9.245 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.246 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
9.246 * [backup-simplify]: Simplify 0 into 0
9.247 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.248 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
9.248 * [backup-simplify]: Simplify 0 into 0
9.249 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.249 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
9.250 * [backup-simplify]: Simplify 0 into 0
9.251 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
9.252 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
9.252 * [backup-simplify]: Simplify 0 into 0
9.252 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
9.252 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
9.252 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
9.252 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.252 * [taylor]: Taking taylor expansion of 2 in n
9.252 * [backup-simplify]: Simplify 2 into 2
9.252 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.252 * [taylor]: Taking taylor expansion of PI in n
9.252 * [backup-simplify]: Simplify PI into PI
9.252 * [taylor]: Taking taylor expansion of n in n
9.252 * [backup-simplify]: Simplify 0 into 0
9.252 * [backup-simplify]: Simplify 1 into 1
9.253 * [backup-simplify]: Simplify (/ PI 1) into PI
9.253 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.253 * [taylor]: Taking taylor expansion of 2 in n
9.253 * [backup-simplify]: Simplify 2 into 2
9.253 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.253 * [taylor]: Taking taylor expansion of PI in n
9.253 * [backup-simplify]: Simplify PI into PI
9.253 * [taylor]: Taking taylor expansion of n in n
9.253 * [backup-simplify]: Simplify 0 into 0
9.253 * [backup-simplify]: Simplify 1 into 1
9.254 * [backup-simplify]: Simplify (/ PI 1) into PI
9.254 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.255 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.255 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.256 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.256 * [backup-simplify]: Simplify 0 into 0
9.257 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.258 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.258 * [backup-simplify]: Simplify 0 into 0
9.259 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.261 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.261 * [backup-simplify]: Simplify 0 into 0
9.262 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.263 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.263 * [backup-simplify]: Simplify 0 into 0
9.264 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.266 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.266 * [backup-simplify]: Simplify 0 into 0
9.267 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.269 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.269 * [backup-simplify]: Simplify 0 into 0
9.270 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
9.270 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
9.270 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
9.270 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.270 * [taylor]: Taking taylor expansion of -2 in n
9.270 * [backup-simplify]: Simplify -2 into -2
9.271 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.271 * [taylor]: Taking taylor expansion of PI in n
9.271 * [backup-simplify]: Simplify PI into PI
9.271 * [taylor]: Taking taylor expansion of n in n
9.271 * [backup-simplify]: Simplify 0 into 0
9.271 * [backup-simplify]: Simplify 1 into 1
9.271 * [backup-simplify]: Simplify (/ PI 1) into PI
9.271 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.271 * [taylor]: Taking taylor expansion of -2 in n
9.271 * [backup-simplify]: Simplify -2 into -2
9.271 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.271 * [taylor]: Taking taylor expansion of PI in n
9.271 * [backup-simplify]: Simplify PI into PI
9.271 * [taylor]: Taking taylor expansion of n in n
9.271 * [backup-simplify]: Simplify 0 into 0
9.271 * [backup-simplify]: Simplify 1 into 1
9.272 * [backup-simplify]: Simplify (/ PI 1) into PI
9.272 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.273 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.274 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.274 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.275 * [backup-simplify]: Simplify 0 into 0
9.276 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.277 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.277 * [backup-simplify]: Simplify 0 into 0
9.278 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.279 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.279 * [backup-simplify]: Simplify 0 into 0
9.280 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.281 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.281 * [backup-simplify]: Simplify 0 into 0
9.282 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.284 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.284 * [backup-simplify]: Simplify 0 into 0
9.285 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.594 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.594 * [backup-simplify]: Simplify 0 into 0
9.594 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
9.594 * * * * [progress]: [ 3 / 3 ] generating series at (2)
9.595 * [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))))
9.595 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
9.595 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
9.595 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.595 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.595 * [taylor]: Taking taylor expansion of k in k
9.595 * [backup-simplify]: Simplify 0 into 0
9.595 * [backup-simplify]: Simplify 1 into 1
9.595 * [backup-simplify]: Simplify (/ 1 1) into 1
9.595 * [backup-simplify]: Simplify (sqrt 0) into 0
9.596 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.596 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
9.596 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
9.596 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
9.596 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
9.596 * [taylor]: Taking taylor expansion of 1/2 in k
9.596 * [backup-simplify]: Simplify 1/2 into 1/2
9.596 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
9.596 * [taylor]: Taking taylor expansion of 1/2 in k
9.596 * [backup-simplify]: Simplify 1/2 into 1/2
9.596 * [taylor]: Taking taylor expansion of k in k
9.596 * [backup-simplify]: Simplify 0 into 0
9.596 * [backup-simplify]: Simplify 1 into 1
9.597 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
9.597 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
9.597 * [taylor]: Taking taylor expansion of 2 in k
9.597 * [backup-simplify]: Simplify 2 into 2
9.597 * [taylor]: Taking taylor expansion of (* n PI) in k
9.597 * [taylor]: Taking taylor expansion of n in k
9.597 * [backup-simplify]: Simplify n into n
9.597 * [taylor]: Taking taylor expansion of PI in k
9.597 * [backup-simplify]: Simplify PI into PI
9.597 * [backup-simplify]: Simplify (* n PI) into (* n PI)
9.597 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
9.597 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
9.597 * [backup-simplify]: Simplify (* 1/2 0) into 0
9.597 * [backup-simplify]: Simplify (- 0) into 0
9.598 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.598 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
9.598 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
9.598 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
9.598 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
9.598 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.598 * [taylor]: Taking taylor expansion of k in n
9.598 * [backup-simplify]: Simplify k into k
9.598 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.598 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
9.598 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.598 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
9.598 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
9.598 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
9.598 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
9.598 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
9.598 * [taylor]: Taking taylor expansion of 1/2 in n
9.598 * [backup-simplify]: Simplify 1/2 into 1/2
9.598 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
9.598 * [taylor]: Taking taylor expansion of 1/2 in n
9.598 * [backup-simplify]: Simplify 1/2 into 1/2
9.598 * [taylor]: Taking taylor expansion of k in n
9.598 * [backup-simplify]: Simplify k into k
9.598 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.598 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.598 * [taylor]: Taking taylor expansion of 2 in n
9.598 * [backup-simplify]: Simplify 2 into 2
9.598 * [taylor]: Taking taylor expansion of (* n PI) in n
9.598 * [taylor]: Taking taylor expansion of n in n
9.598 * [backup-simplify]: Simplify 0 into 0
9.598 * [backup-simplify]: Simplify 1 into 1
9.598 * [taylor]: Taking taylor expansion of PI in n
9.598 * [backup-simplify]: Simplify PI into PI
9.599 * [backup-simplify]: Simplify (* 0 PI) into 0
9.599 * [backup-simplify]: Simplify (* 2 0) into 0
9.600 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.601 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.601 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.601 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
9.601 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
9.601 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
9.602 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.603 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
9.605 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
9.605 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
9.605 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
9.605 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.605 * [taylor]: Taking taylor expansion of k in n
9.606 * [backup-simplify]: Simplify k into k
9.606 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.606 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
9.606 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.606 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
9.606 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
9.606 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
9.606 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
9.606 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
9.606 * [taylor]: Taking taylor expansion of 1/2 in n
9.606 * [backup-simplify]: Simplify 1/2 into 1/2
9.606 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
9.606 * [taylor]: Taking taylor expansion of 1/2 in n
9.606 * [backup-simplify]: Simplify 1/2 into 1/2
9.606 * [taylor]: Taking taylor expansion of k in n
9.606 * [backup-simplify]: Simplify k into k
9.606 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.606 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.606 * [taylor]: Taking taylor expansion of 2 in n
9.606 * [backup-simplify]: Simplify 2 into 2
9.606 * [taylor]: Taking taylor expansion of (* n PI) in n
9.606 * [taylor]: Taking taylor expansion of n in n
9.606 * [backup-simplify]: Simplify 0 into 0
9.606 * [backup-simplify]: Simplify 1 into 1
9.606 * [taylor]: Taking taylor expansion of PI in n
9.606 * [backup-simplify]: Simplify PI into PI
9.606 * [backup-simplify]: Simplify (* 0 PI) into 0
9.607 * [backup-simplify]: Simplify (* 2 0) into 0
9.608 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.609 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.609 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.609 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
9.609 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
9.610 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
9.610 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.611 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
9.612 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
9.612 * [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)))
9.613 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
9.613 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
9.613 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
9.613 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
9.613 * [taylor]: Taking taylor expansion of 1/2 in k
9.613 * [backup-simplify]: Simplify 1/2 into 1/2
9.613 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
9.613 * [taylor]: Taking taylor expansion of 1/2 in k
9.613 * [backup-simplify]: Simplify 1/2 into 1/2
9.613 * [taylor]: Taking taylor expansion of k in k
9.613 * [backup-simplify]: Simplify 0 into 0
9.613 * [backup-simplify]: Simplify 1 into 1
9.613 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
9.613 * [taylor]: Taking taylor expansion of (log n) in k
9.613 * [taylor]: Taking taylor expansion of n in k
9.613 * [backup-simplify]: Simplify n into n
9.613 * [backup-simplify]: Simplify (log n) into (log n)
9.613 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.613 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.613 * [taylor]: Taking taylor expansion of 2 in k
9.613 * [backup-simplify]: Simplify 2 into 2
9.613 * [taylor]: Taking taylor expansion of PI in k
9.613 * [backup-simplify]: Simplify PI into PI
9.613 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.614 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.614 * [backup-simplify]: Simplify (* 1/2 0) into 0
9.614 * [backup-simplify]: Simplify (- 0) into 0
9.615 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.615 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.616 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
9.617 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.617 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.617 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.617 * [taylor]: Taking taylor expansion of k in k
9.617 * [backup-simplify]: Simplify 0 into 0
9.617 * [backup-simplify]: Simplify 1 into 1
9.617 * [backup-simplify]: Simplify (/ 1 1) into 1
9.617 * [backup-simplify]: Simplify (sqrt 0) into 0
9.618 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.619 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
9.619 * [backup-simplify]: Simplify 0 into 0
9.620 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.620 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.621 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.621 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
9.622 * [backup-simplify]: Simplify (- 0) into 0
9.622 * [backup-simplify]: Simplify (+ 0 0) into 0
9.623 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.624 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
9.625 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.626 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
9.626 * [taylor]: Taking taylor expansion of 0 in k
9.626 * [backup-simplify]: Simplify 0 into 0
9.626 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
9.627 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.628 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.628 * [backup-simplify]: Simplify (+ 0 0) into 0
9.628 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
9.629 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.629 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.630 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
9.632 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.634 * [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)))))))
9.635 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.636 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.636 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.638 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.639 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
9.639 * [backup-simplify]: Simplify (- 0) into 0
9.639 * [backup-simplify]: Simplify (+ 0 0) into 0
9.640 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.641 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.643 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.643 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.643 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
9.644 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
9.644 * [taylor]: Taking taylor expansion of 0 in k
9.645 * [backup-simplify]: Simplify 0 into 0
9.645 * [backup-simplify]: Simplify 0 into 0
9.645 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
9.647 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.648 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
9.649 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.650 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.651 * [backup-simplify]: Simplify (+ 0 0) into 0
9.651 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
9.651 * [backup-simplify]: Simplify (- 0) into 0
9.652 * [backup-simplify]: Simplify (+ 0 0) into 0
9.653 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.655 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.660 * [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))))))))
9.663 * [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))))))))
9.664 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.665 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
9.671 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.672 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
9.672 * [backup-simplify]: Simplify (- 0) into 0
9.673 * [backup-simplify]: Simplify (+ 0 0) into 0
9.674 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.676 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
9.679 * [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
9.679 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.680 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
9.682 * [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
9.682 * [taylor]: Taking taylor expansion of 0 in k
9.682 * [backup-simplify]: Simplify 0 into 0
9.682 * [backup-simplify]: Simplify 0 into 0
9.682 * [backup-simplify]: Simplify 0 into 0
9.683 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.687 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.690 * [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
9.691 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.701 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.702 * [backup-simplify]: Simplify (+ 0 0) into 0
9.703 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
9.703 * [backup-simplify]: Simplify (- 0) into 0
9.704 * [backup-simplify]: Simplify (+ 0 0) into 0
9.706 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
9.713 * [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)))))))
9.730 * [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))))))))))))))
9.741 * [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))))))))))))))
9.761 * [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))))))))))))))))))))))
9.762 * [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)))))
9.762 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
9.762 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
9.762 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.762 * [taylor]: Taking taylor expansion of k in k
9.762 * [backup-simplify]: Simplify 0 into 0
9.762 * [backup-simplify]: Simplify 1 into 1
9.763 * [backup-simplify]: Simplify (sqrt 0) into 0
9.764 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.764 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
9.765 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
9.765 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
9.765 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
9.765 * [taylor]: Taking taylor expansion of 1/2 in k
9.765 * [backup-simplify]: Simplify 1/2 into 1/2
9.765 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.765 * [taylor]: Taking taylor expansion of 1/2 in k
9.765 * [backup-simplify]: Simplify 1/2 into 1/2
9.765 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.765 * [taylor]: Taking taylor expansion of k in k
9.765 * [backup-simplify]: Simplify 0 into 0
9.765 * [backup-simplify]: Simplify 1 into 1
9.765 * [backup-simplify]: Simplify (/ 1 1) into 1
9.765 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
9.765 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
9.765 * [taylor]: Taking taylor expansion of 2 in k
9.765 * [backup-simplify]: Simplify 2 into 2
9.766 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.766 * [taylor]: Taking taylor expansion of PI in k
9.766 * [backup-simplify]: Simplify PI into PI
9.766 * [taylor]: Taking taylor expansion of n in k
9.766 * [backup-simplify]: Simplify n into n
9.766 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.766 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
9.766 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
9.767 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.767 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.768 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.768 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
9.768 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
9.768 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
9.768 * [taylor]: Taking taylor expansion of (sqrt k) in n
9.768 * [taylor]: Taking taylor expansion of k in n
9.769 * [backup-simplify]: Simplify k into k
9.769 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
9.769 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
9.769 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
9.769 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.769 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.769 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
9.769 * [taylor]: Taking taylor expansion of 1/2 in n
9.769 * [backup-simplify]: Simplify 1/2 into 1/2
9.769 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.769 * [taylor]: Taking taylor expansion of 1/2 in n
9.769 * [backup-simplify]: Simplify 1/2 into 1/2
9.769 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.769 * [taylor]: Taking taylor expansion of k in n
9.769 * [backup-simplify]: Simplify k into k
9.769 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.769 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.769 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.769 * [taylor]: Taking taylor expansion of 2 in n
9.769 * [backup-simplify]: Simplify 2 into 2
9.769 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.769 * [taylor]: Taking taylor expansion of PI in n
9.769 * [backup-simplify]: Simplify PI into PI
9.769 * [taylor]: Taking taylor expansion of n in n
9.769 * [backup-simplify]: Simplify 0 into 0
9.769 * [backup-simplify]: Simplify 1 into 1
9.770 * [backup-simplify]: Simplify (/ PI 1) into PI
9.770 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.771 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.772 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.772 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
9.772 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
9.773 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.774 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
9.776 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.776 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
9.776 * [taylor]: Taking taylor expansion of (sqrt k) in n
9.776 * [taylor]: Taking taylor expansion of k in n
9.776 * [backup-simplify]: Simplify k into k
9.776 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
9.776 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
9.776 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
9.776 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.776 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.776 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
9.776 * [taylor]: Taking taylor expansion of 1/2 in n
9.776 * [backup-simplify]: Simplify 1/2 into 1/2
9.776 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.776 * [taylor]: Taking taylor expansion of 1/2 in n
9.776 * [backup-simplify]: Simplify 1/2 into 1/2
9.776 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.776 * [taylor]: Taking taylor expansion of k in n
9.776 * [backup-simplify]: Simplify k into k
9.776 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.776 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.776 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.776 * [taylor]: Taking taylor expansion of 2 in n
9.776 * [backup-simplify]: Simplify 2 into 2
9.776 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.776 * [taylor]: Taking taylor expansion of PI in n
9.776 * [backup-simplify]: Simplify PI into PI
9.776 * [taylor]: Taking taylor expansion of n in n
9.776 * [backup-simplify]: Simplify 0 into 0
9.776 * [backup-simplify]: Simplify 1 into 1
9.777 * [backup-simplify]: Simplify (/ PI 1) into PI
9.777 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.778 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.778 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.779 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
9.779 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
9.780 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.781 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
9.782 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.784 * [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))
9.784 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
9.784 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
9.784 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
9.784 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
9.784 * [taylor]: Taking taylor expansion of 1/2 in k
9.784 * [backup-simplify]: Simplify 1/2 into 1/2
9.784 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.784 * [taylor]: Taking taylor expansion of 1/2 in k
9.784 * [backup-simplify]: Simplify 1/2 into 1/2
9.784 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.784 * [taylor]: Taking taylor expansion of k in k
9.784 * [backup-simplify]: Simplify 0 into 0
9.784 * [backup-simplify]: Simplify 1 into 1
9.785 * [backup-simplify]: Simplify (/ 1 1) into 1
9.785 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
9.785 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.785 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.785 * [taylor]: Taking taylor expansion of 2 in k
9.785 * [backup-simplify]: Simplify 2 into 2
9.785 * [taylor]: Taking taylor expansion of PI in k
9.785 * [backup-simplify]: Simplify PI into PI
9.785 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.786 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.786 * [taylor]: Taking taylor expansion of (log n) in k
9.786 * [taylor]: Taking taylor expansion of n in k
9.786 * [backup-simplify]: Simplify n into n
9.786 * [backup-simplify]: Simplify (log n) into (log n)
9.787 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.787 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.788 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.788 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.789 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
9.790 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
9.791 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.791 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.791 * [taylor]: Taking taylor expansion of k in k
9.791 * [backup-simplify]: Simplify 0 into 0
9.791 * [backup-simplify]: Simplify 1 into 1
9.791 * [backup-simplify]: Simplify (sqrt 0) into 0
9.793 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.794 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
9.794 * [backup-simplify]: Simplify 0 into 0
9.795 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.796 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.798 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.798 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.799 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
9.799 * [backup-simplify]: Simplify (- 0) into 0
9.799 * [backup-simplify]: Simplify (+ 0 0) into 0
9.801 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.802 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
9.804 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.806 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
9.806 * [taylor]: Taking taylor expansion of 0 in k
9.806 * [backup-simplify]: Simplify 0 into 0
9.806 * [backup-simplify]: Simplify 0 into 0
9.808 * [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))))))
9.809 * [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))))))
9.810 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.811 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.815 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.816 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.817 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
9.817 * [backup-simplify]: Simplify (- 0) into 0
9.817 * [backup-simplify]: Simplify (+ 0 0) into 0
9.819 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.820 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
9.823 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.824 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
9.825 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
9.826 * [taylor]: Taking taylor expansion of 0 in k
9.826 * [backup-simplify]: Simplify 0 into 0
9.826 * [backup-simplify]: Simplify 0 into 0
9.826 * [backup-simplify]: Simplify 0 into 0
9.829 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.831 * [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))))))
9.832 * [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))))))
9.834 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.835 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.841 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.841 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.846 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
9.847 * [backup-simplify]: Simplify (- 0) into 0
9.847 * [backup-simplify]: Simplify (+ 0 0) into 0
9.849 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.851 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
9.854 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.855 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
9.857 * [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
9.857 * [taylor]: Taking taylor expansion of 0 in k
9.857 * [backup-simplify]: Simplify 0 into 0
9.857 * [backup-simplify]: Simplify 0 into 0
9.857 * [backup-simplify]: Simplify 0 into 0
9.857 * [backup-simplify]: Simplify 0 into 0
9.862 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.864 * [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))))))
9.865 * [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))))))
9.870 * [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))))))))
9.871 * [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)))
9.871 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
9.871 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
9.871 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
9.871 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
9.871 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
9.871 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
9.871 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.871 * [taylor]: Taking taylor expansion of 1/2 in k
9.871 * [backup-simplify]: Simplify 1/2 into 1/2
9.871 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.871 * [taylor]: Taking taylor expansion of k in k
9.871 * [backup-simplify]: Simplify 0 into 0
9.871 * [backup-simplify]: Simplify 1 into 1
9.871 * [backup-simplify]: Simplify (/ 1 1) into 1
9.872 * [taylor]: Taking taylor expansion of 1/2 in k
9.872 * [backup-simplify]: Simplify 1/2 into 1/2
9.872 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
9.872 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
9.872 * [taylor]: Taking taylor expansion of -2 in k
9.872 * [backup-simplify]: Simplify -2 into -2
9.872 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.872 * [taylor]: Taking taylor expansion of PI in k
9.872 * [backup-simplify]: Simplify PI into PI
9.872 * [taylor]: Taking taylor expansion of n in k
9.872 * [backup-simplify]: Simplify n into n
9.872 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.872 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
9.872 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
9.873 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.873 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.873 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
9.873 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
9.873 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.873 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.873 * [taylor]: Taking taylor expansion of -1 in k
9.874 * [backup-simplify]: Simplify -1 into -1
9.874 * [taylor]: Taking taylor expansion of k in k
9.874 * [backup-simplify]: Simplify 0 into 0
9.874 * [backup-simplify]: Simplify 1 into 1
9.874 * [backup-simplify]: Simplify (/ -1 1) into -1
9.874 * [backup-simplify]: Simplify (sqrt 0) into 0
9.876 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.876 * [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))))
9.876 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
9.876 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
9.877 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
9.877 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
9.877 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
9.877 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.877 * [taylor]: Taking taylor expansion of 1/2 in n
9.877 * [backup-simplify]: Simplify 1/2 into 1/2
9.877 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.877 * [taylor]: Taking taylor expansion of k in n
9.877 * [backup-simplify]: Simplify k into k
9.877 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.877 * [taylor]: Taking taylor expansion of 1/2 in n
9.877 * [backup-simplify]: Simplify 1/2 into 1/2
9.877 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.877 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.877 * [taylor]: Taking taylor expansion of -2 in n
9.877 * [backup-simplify]: Simplify -2 into -2
9.877 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.877 * [taylor]: Taking taylor expansion of PI in n
9.877 * [backup-simplify]: Simplify PI into PI
9.877 * [taylor]: Taking taylor expansion of n in n
9.877 * [backup-simplify]: Simplify 0 into 0
9.877 * [backup-simplify]: Simplify 1 into 1
9.878 * [backup-simplify]: Simplify (/ PI 1) into PI
9.878 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.879 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.880 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.880 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
9.881 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.882 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
9.884 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.884 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
9.884 * [taylor]: Taking taylor expansion of (/ -1 k) in n
9.884 * [taylor]: Taking taylor expansion of -1 in n
9.884 * [backup-simplify]: Simplify -1 into -1
9.884 * [taylor]: Taking taylor expansion of k in n
9.884 * [backup-simplify]: Simplify k into k
9.884 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
9.884 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
9.884 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
9.884 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
9.886 * [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)))
9.886 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
9.886 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
9.886 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
9.886 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
9.886 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
9.886 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.886 * [taylor]: Taking taylor expansion of 1/2 in n
9.886 * [backup-simplify]: Simplify 1/2 into 1/2
9.886 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.886 * [taylor]: Taking taylor expansion of k in n
9.886 * [backup-simplify]: Simplify k into k
9.886 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.886 * [taylor]: Taking taylor expansion of 1/2 in n
9.886 * [backup-simplify]: Simplify 1/2 into 1/2
9.886 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.886 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.886 * [taylor]: Taking taylor expansion of -2 in n
9.886 * [backup-simplify]: Simplify -2 into -2
9.886 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.886 * [taylor]: Taking taylor expansion of PI in n
9.886 * [backup-simplify]: Simplify PI into PI
9.886 * [taylor]: Taking taylor expansion of n in n
9.886 * [backup-simplify]: Simplify 0 into 0
9.886 * [backup-simplify]: Simplify 1 into 1
9.887 * [backup-simplify]: Simplify (/ PI 1) into PI
9.887 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.889 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.889 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.889 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
9.890 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.891 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
9.891 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.891 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
9.891 * [taylor]: Taking taylor expansion of (/ -1 k) in n
9.891 * [taylor]: Taking taylor expansion of -1 in n
9.891 * [backup-simplify]: Simplify -1 into -1
9.891 * [taylor]: Taking taylor expansion of k in n
9.892 * [backup-simplify]: Simplify k into k
9.892 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
9.892 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
9.892 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
9.892 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
9.892 * [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)))
9.893 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
9.893 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
9.893 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
9.893 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
9.893 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.893 * [taylor]: Taking taylor expansion of 1/2 in k
9.893 * [backup-simplify]: Simplify 1/2 into 1/2
9.893 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.893 * [taylor]: Taking taylor expansion of k in k
9.893 * [backup-simplify]: Simplify 0 into 0
9.893 * [backup-simplify]: Simplify 1 into 1
9.893 * [backup-simplify]: Simplify (/ 1 1) into 1
9.893 * [taylor]: Taking taylor expansion of 1/2 in k
9.893 * [backup-simplify]: Simplify 1/2 into 1/2
9.893 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
9.893 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
9.893 * [taylor]: Taking taylor expansion of (* -2 PI) in k
9.893 * [taylor]: Taking taylor expansion of -2 in k
9.893 * [backup-simplify]: Simplify -2 into -2
9.893 * [taylor]: Taking taylor expansion of PI in k
9.893 * [backup-simplify]: Simplify PI into PI
9.893 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.894 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.894 * [taylor]: Taking taylor expansion of (log n) in k
9.894 * [taylor]: Taking taylor expansion of n in k
9.894 * [backup-simplify]: Simplify n into n
9.894 * [backup-simplify]: Simplify (log n) into (log n)
9.894 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.895 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.895 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.895 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
9.896 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
9.897 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.897 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.897 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.897 * [taylor]: Taking taylor expansion of -1 in k
9.897 * [backup-simplify]: Simplify -1 into -1
9.897 * [taylor]: Taking taylor expansion of k in k
9.897 * [backup-simplify]: Simplify 0 into 0
9.897 * [backup-simplify]: Simplify 1 into 1
9.897 * [backup-simplify]: Simplify (/ -1 1) into -1
9.897 * [backup-simplify]: Simplify (sqrt 0) into 0
9.898 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.899 * [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)))))
9.900 * [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)))))
9.900 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.901 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.902 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
9.902 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.902 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
9.902 * [backup-simplify]: Simplify (+ 0 0) into 0
9.903 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.904 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
9.905 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.906 * [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
9.906 * [taylor]: Taking taylor expansion of 0 in k
9.906 * [backup-simplify]: Simplify 0 into 0
9.906 * [backup-simplify]: Simplify 0 into 0
9.907 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
9.908 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.910 * [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))))))
9.910 * [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))))))
9.911 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.912 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.914 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
9.914 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.914 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
9.915 * [backup-simplify]: Simplify (+ 0 0) into 0
9.916 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.917 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
9.918 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.918 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.919 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
9.919 * [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
9.920 * [taylor]: Taking taylor expansion of 0 in k
9.920 * [backup-simplify]: Simplify 0 into 0
9.920 * [backup-simplify]: Simplify 0 into 0
9.920 * [backup-simplify]: Simplify 0 into 0
9.920 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.923 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.925 * [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))))))
9.926 * [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))))))
9.929 * [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)))))))))))
9.929 * * * [progress]: simplifying candidates
9.929 * * * * [progress]: [ 1 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
9.929 * * * * [progress]: [ 2 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
9.929 * * * * [progress]: [ 3 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
9.929 * * * * [progress]: [ 4 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
9.929 * * * * [progress]: [ 5 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
9.929 * * * * [progress]: [ 6 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
9.929 * * * * [progress]: [ 7 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
9.929 * * * * [progress]: [ 8 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))>
9.930 * * * * [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)))>
9.930 * * * * [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)))>
9.930 * * * * [progress]: [ 11 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
9.930 * * * * [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)))>
9.930 * * * * [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)))>
9.930 * * * * [progress]: [ 14 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
9.930 * * * * [progress]: [ 15 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt k)))>
9.930 * * * * [progress]: [ 16 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt k)))>
9.930 * * * * [progress]: [ 17 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt k)))>
9.930 * * * * [progress]: [ 18 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
9.930 * * * * [progress]: [ 19 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
9.930 * * * * [progress]: [ 20 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
9.930 * * * * [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)))>
9.930 * * * * [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)))>
9.930 * * * * [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)))>
9.930 * * * * [progress]: [ 24 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
9.930 * * * * [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)))>
9.930 * * * * [progress]: [ 26 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
9.930 * * * * [progress]: [ 27 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
9.930 * * * * [progress]: [ 28 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
9.930 * * * * [progress]: [ 29 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
9.930 * * * * [progress]: [ 30 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.930 * * * * [progress]: [ 31 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.930 * * * * [progress]: [ 32 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.931 * * * * [progress]: [ 33 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.931 * * * * [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)))>
9.931 * * * * [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)))>
9.931 * * * * [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)))>
9.931 * * * * [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)))>
9.931 * * * * [progress]: [ 38 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.931 * * * * [progress]: [ 39 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
9.931 * * * * [progress]: [ 40 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
9.931 * * * * [progress]: [ 41 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
9.931 * * * * [progress]: [ 42 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
9.931 * * * * [progress]: [ 43 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
9.931 * * * * [progress]: [ 44 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.931 * * * * [progress]: [ 45 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))>
9.931 * * * * [progress]: [ 46 / 127 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) 1))>
9.931 * * * * [progress]: [ 47 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
9.931 * * * * [progress]: [ 48 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
9.931 * * * * [progress]: [ 49 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
9.931 * * * * [progress]: [ 50 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
9.931 * * * * [progress]: [ 51 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
9.931 * * * * [progress]: [ 52 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
9.931 * * * * [progress]: [ 53 / 127 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
9.931 * * * * [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)))))>
9.931 * * * * [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)))))>
9.931 * * * * [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)))))>
9.931 * * * * [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)))))>
9.931 * * * * [progress]: [ 58 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (- (sqrt k))))>
9.932 * * * * [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)))))>
9.932 * * * * [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)))))>
9.932 * * * * [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)))))>
9.932 * * * * [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))))>
9.932 * * * * [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)))))>
9.932 * * * * [progress]: [ 64 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
9.932 * * * * [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)))))>
9.932 * * * * [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)))))>
9.932 * * * * [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)))))>
9.932 * * * * [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))))>
9.932 * * * * [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)))))>
9.932 * * * * [progress]: [ 70 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
9.932 * * * * [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)))))>
9.932 * * * * [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)))))>
9.932 * * * * [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)))))>
9.932 * * * * [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))))>
9.932 * * * * [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)))))>
9.932 * * * * [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))))>
9.932 * * * * [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)))))>
9.932 * * * * [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)))))>
9.932 * * * * [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)))))>
9.932 * * * * [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))))>
9.932 * * * * [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)))))>
9.933 * * * * [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))))>
9.933 * * * * [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)))))>
9.933 * * * * [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)))))>
9.933 * * * * [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)))))>
9.933 * * * * [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))))>
9.933 * * * * [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)))))>
9.933 * * * * [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))))>
9.933 * * * * [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)))))>
9.933 * * * * [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)))))>
9.933 * * * * [progress]: [ 91 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
9.933 * * * * [progress]: [ 92 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
9.933 * * * * [progress]: [ 93 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
9.933 * * * * [progress]: [ 94 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
9.933 * * * * [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)))))>
9.933 * * * * [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)))))>
9.933 * * * * [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)))))>
9.933 * * * * [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))))>
9.933 * * * * [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)))))>
9.933 * * * * [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))))>
9.933 * * * * [progress]: [ 101 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
9.933 * * * * [progress]: [ 102 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
9.933 * * * * [progress]: [ 103 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
9.933 * * * * [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))))>
9.934 * * * * [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))))>
9.934 * * * * [progress]: [ 106 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
9.934 * * * * [progress]: [ 107 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k)))>
9.934 * * * * [progress]: [ 108 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
9.934 * * * * [progress]: [ 109 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
9.934 * * * * [progress]: [ 110 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
9.934 * * * * [progress]: [ 111 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
9.934 * * * * [progress]: [ 112 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
9.934 * * * * [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)))))))>
9.934 * * * * [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)))))))>
9.934 * * * * [progress]: [ 115 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
9.934 * * * * [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)))))>
9.934 * * * * [progress]: [ 117 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))>
9.934 * * * * [progress]: [ 118 / 127 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
9.934 * * * * [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)))>
9.934 * * * * [progress]: [ 120 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
9.934 * * * * [progress]: [ 121 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
9.934 * * * * [progress]: [ 122 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
9.934 * * * * [progress]: [ 123 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
9.934 * * * * [progress]: [ 124 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
9.934 * * * * [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)))))))))))))))))))))))>
9.934 * * * * [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)))))))))>
9.934 * * * * [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))))))))))))>
9.936 * [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)))))))))))
9.940 * * [simplify]: iteration 1: (267 enodes)
10.020 * * [simplify]: iteration 2: (645 enodes)
10.550 * * [simplify]: Extracting #0: cost 97 inf + 0
10.552 * * [simplify]: Extracting #1: cost 377 inf + 1
10.557 * * [simplify]: Extracting #2: cost 524 inf + 14272
10.566 * * [simplify]: Extracting #3: cost 450 inf + 67790
10.586 * * [simplify]: Extracting #4: cost 250 inf + 153269
10.628 * * [simplify]: Extracting #5: cost 139 inf + 201974
10.677 * * [simplify]: Extracting #6: cost 93 inf + 229429
10.720 * * [simplify]: Extracting #7: cost 31 inf + 262243
10.771 * * [simplify]: Extracting #8: cost 6 inf + 282585
10.846 * * [simplify]: Extracting #9: cost 0 inf + 289225
10.929 * * [simplify]: Extracting #10: cost 0 inf + 289105
10.994 * [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 8)) PI) (* PI PI))
  (* (* (* 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))
  (- (* (- 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))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (sqrt k)) 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)))) (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)))) (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)))) (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)))) (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)))) (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)))
  (+ (+ (* (* 1/4 (log (* PI 2))) (* (* (sqrt (* (* PI 2) n)) (log n)) (* k k))) (* (* 1/8 (* (* (log n) (log n)) (sqrt (* (* PI 2) n)))) (* k k))) (- (+ (* (* (* k k) (* (log (* PI 2)) (* (sqrt (* (* PI 2) n)) (log (* PI 2))))) 1/8) (sqrt (* (* PI 2) n))) (* 1/2 (* k (+ (* (sqrt (* (* PI 2) n)) (log n)) (* (sqrt (* (* PI 2) n)) (log (* PI 2))))))))
  (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)
  (+ (* (- (* (log (* PI 2)) +nan.0)) (* (* (sqrt (* (* PI 2) n)) (log n)) (* k k))) (- (* +nan.0 (* (* (sqrt (* (* PI 2) n)) (log (* PI 2))) (* k k))) (- (* (* (sqrt (* (* PI 2) n)) +nan.0) (* (* k (log n)) (* k (log n)))) (+ (- (* (* k (sqrt (* (* PI 2) n))) +nan.0) (* (sqrt (* (* PI 2) n)) +nan.0)) (+ (- (* (* (* k k) (* (log (* PI 2)) (* (sqrt (* (* PI 2) n)) (log (* PI 2))))) +nan.0) (* +nan.0 (* (* (sqrt (* (* PI 2) n)) (log n)) (* k k)))) (+ (- (* (* k k) (* (sqrt (* (* PI 2) n)) +nan.0)) (* +nan.0 (* k (* (sqrt (* (* PI 2) n)) (log (* PI 2)))))) (* (* (log n) k) (* (sqrt (* (* PI 2) n)) +nan.0))))))))
  (- (+ (- (* (/ (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) (* k (* k k))) +nan.0) (/ (* (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 (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) k)) (* +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))))))))
11.014 * * * [progress]: adding candidates to table
12.557 * * [progress]: iteration 2 / 4
12.557 * * * [progress]: picking best candidate
12.593 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
12.593 * * * [progress]: localizing error
12.621 * * * [progress]: generating rewritten candidates
12.621 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2)
12.637 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1)
12.657 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1)
12.670 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1)
12.686 * * * [progress]: generating series expansions
12.686 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2)
12.687 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))
12.687 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
12.687 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
12.687 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
12.687 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
12.687 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
12.687 * [taylor]: Taking taylor expansion of 1/2 in k
12.687 * [backup-simplify]: Simplify 1/2 into 1/2
12.687 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.687 * [taylor]: Taking taylor expansion of 1/2 in k
12.687 * [backup-simplify]: Simplify 1/2 into 1/2
12.687 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.687 * [taylor]: Taking taylor expansion of 1/2 in k
12.687 * [backup-simplify]: Simplify 1/2 into 1/2
12.687 * [taylor]: Taking taylor expansion of k in k
12.687 * [backup-simplify]: Simplify 0 into 0
12.687 * [backup-simplify]: Simplify 1 into 1
12.687 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.687 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.687 * [taylor]: Taking taylor expansion of 2 in k
12.687 * [backup-simplify]: Simplify 2 into 2
12.687 * [taylor]: Taking taylor expansion of (* n PI) in k
12.687 * [taylor]: Taking taylor expansion of n in k
12.687 * [backup-simplify]: Simplify n into n
12.687 * [taylor]: Taking taylor expansion of PI in k
12.687 * [backup-simplify]: Simplify PI into PI
12.687 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.687 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.687 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.688 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.688 * [backup-simplify]: Simplify (- 0) into 0
12.688 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.688 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
12.688 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
12.689 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
12.689 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
12.689 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
12.689 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
12.689 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
12.689 * [taylor]: Taking taylor expansion of 1/2 in n
12.689 * [backup-simplify]: Simplify 1/2 into 1/2
12.689 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.689 * [taylor]: Taking taylor expansion of 1/2 in n
12.689 * [backup-simplify]: Simplify 1/2 into 1/2
12.689 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.689 * [taylor]: Taking taylor expansion of 1/2 in n
12.689 * [backup-simplify]: Simplify 1/2 into 1/2
12.689 * [taylor]: Taking taylor expansion of k in n
12.689 * [backup-simplify]: Simplify k into k
12.689 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.689 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.689 * [taylor]: Taking taylor expansion of 2 in n
12.689 * [backup-simplify]: Simplify 2 into 2
12.689 * [taylor]: Taking taylor expansion of (* n PI) in n
12.689 * [taylor]: Taking taylor expansion of n in n
12.689 * [backup-simplify]: Simplify 0 into 0
12.689 * [backup-simplify]: Simplify 1 into 1
12.689 * [taylor]: Taking taylor expansion of PI in n
12.689 * [backup-simplify]: Simplify PI into PI
12.689 * [backup-simplify]: Simplify (* 0 PI) into 0
12.689 * [backup-simplify]: Simplify (* 2 0) into 0
12.690 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.691 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.692 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.692 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.692 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.692 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.692 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
12.693 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.694 * [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)))))
12.695 * [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))))))
12.695 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
12.695 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
12.695 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
12.695 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
12.695 * [taylor]: Taking taylor expansion of 1/2 in n
12.695 * [backup-simplify]: Simplify 1/2 into 1/2
12.695 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.695 * [taylor]: Taking taylor expansion of 1/2 in n
12.695 * [backup-simplify]: Simplify 1/2 into 1/2
12.695 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.695 * [taylor]: Taking taylor expansion of 1/2 in n
12.695 * [backup-simplify]: Simplify 1/2 into 1/2
12.695 * [taylor]: Taking taylor expansion of k in n
12.695 * [backup-simplify]: Simplify k into k
12.695 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.695 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.695 * [taylor]: Taking taylor expansion of 2 in n
12.695 * [backup-simplify]: Simplify 2 into 2
12.695 * [taylor]: Taking taylor expansion of (* n PI) in n
12.695 * [taylor]: Taking taylor expansion of n in n
12.695 * [backup-simplify]: Simplify 0 into 0
12.695 * [backup-simplify]: Simplify 1 into 1
12.695 * [taylor]: Taking taylor expansion of PI in n
12.695 * [backup-simplify]: Simplify PI into PI
12.695 * [backup-simplify]: Simplify (* 0 PI) into 0
12.696 * [backup-simplify]: Simplify (* 2 0) into 0
12.696 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.697 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.698 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.698 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.698 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.698 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.698 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
12.699 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.700 * [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)))))
12.701 * [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))))))
12.701 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
12.701 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
12.701 * [taylor]: Taking taylor expansion of 1/2 in k
12.701 * [backup-simplify]: Simplify 1/2 into 1/2
12.701 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
12.701 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.701 * [taylor]: Taking taylor expansion of 1/2 in k
12.701 * [backup-simplify]: Simplify 1/2 into 1/2
12.701 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.701 * [taylor]: Taking taylor expansion of 1/2 in k
12.701 * [backup-simplify]: Simplify 1/2 into 1/2
12.701 * [taylor]: Taking taylor expansion of k in k
12.701 * [backup-simplify]: Simplify 0 into 0
12.701 * [backup-simplify]: Simplify 1 into 1
12.701 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
12.701 * [taylor]: Taking taylor expansion of (log n) in k
12.701 * [taylor]: Taking taylor expansion of n in k
12.701 * [backup-simplify]: Simplify n into n
12.701 * [backup-simplify]: Simplify (log n) into (log n)
12.701 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.701 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.701 * [taylor]: Taking taylor expansion of 2 in k
12.701 * [backup-simplify]: Simplify 2 into 2
12.701 * [taylor]: Taking taylor expansion of PI in k
12.701 * [backup-simplify]: Simplify PI into PI
12.701 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.702 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.702 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.702 * [backup-simplify]: Simplify (- 0) into 0
12.703 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.703 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.704 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
12.705 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
12.705 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
12.706 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
12.707 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.707 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.708 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.708 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
12.709 * [backup-simplify]: Simplify (- 0) into 0
12.709 * [backup-simplify]: Simplify (+ 0 0) into 0
12.709 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
12.710 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.711 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
12.712 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.712 * [taylor]: Taking taylor expansion of 0 in k
12.712 * [backup-simplify]: Simplify 0 into 0
12.712 * [backup-simplify]: Simplify 0 into 0
12.713 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.713 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.714 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.714 * [backup-simplify]: Simplify (+ 0 0) into 0
12.715 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
12.715 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.716 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.717 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
12.719 * [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)))))
12.720 * [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)))))))
12.722 * [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)))))))
12.723 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.724 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.729 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
12.730 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
12.730 * [backup-simplify]: Simplify (- 0) into 0
12.731 * [backup-simplify]: Simplify (+ 0 0) into 0
12.731 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
12.732 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.733 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.735 * [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
12.735 * [taylor]: Taking taylor expansion of 0 in k
12.735 * [backup-simplify]: Simplify 0 into 0
12.735 * [backup-simplify]: Simplify 0 into 0
12.735 * [backup-simplify]: Simplify 0 into 0
12.736 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.736 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.738 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
12.739 * [backup-simplify]: Simplify (+ 0 0) into 0
12.739 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
12.739 * [backup-simplify]: Simplify (- 0) into 0
12.740 * [backup-simplify]: Simplify (+ 0 0) into 0
12.741 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.743 * [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
12.745 * [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)))))
12.748 * [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)))))
12.755 * [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)))))))
12.755 * [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)))))
12.755 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
12.755 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
12.755 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
12.755 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
12.755 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
12.755 * [taylor]: Taking taylor expansion of 1/2 in k
12.755 * [backup-simplify]: Simplify 1/2 into 1/2
12.755 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.755 * [taylor]: Taking taylor expansion of 1/2 in k
12.755 * [backup-simplify]: Simplify 1/2 into 1/2
12.755 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.755 * [taylor]: Taking taylor expansion of 1/2 in k
12.755 * [backup-simplify]: Simplify 1/2 into 1/2
12.755 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.755 * [taylor]: Taking taylor expansion of k in k
12.755 * [backup-simplify]: Simplify 0 into 0
12.755 * [backup-simplify]: Simplify 1 into 1
12.756 * [backup-simplify]: Simplify (/ 1 1) into 1
12.756 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.756 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.756 * [taylor]: Taking taylor expansion of 2 in k
12.756 * [backup-simplify]: Simplify 2 into 2
12.756 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.756 * [taylor]: Taking taylor expansion of PI in k
12.756 * [backup-simplify]: Simplify PI into PI
12.756 * [taylor]: Taking taylor expansion of n in k
12.756 * [backup-simplify]: Simplify n into n
12.756 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.756 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.756 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.756 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.756 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.757 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.757 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
12.757 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
12.757 * [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))))))
12.757 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
12.757 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
12.757 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
12.757 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
12.757 * [taylor]: Taking taylor expansion of 1/2 in n
12.757 * [backup-simplify]: Simplify 1/2 into 1/2
12.757 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.757 * [taylor]: Taking taylor expansion of 1/2 in n
12.757 * [backup-simplify]: Simplify 1/2 into 1/2
12.757 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.757 * [taylor]: Taking taylor expansion of 1/2 in n
12.757 * [backup-simplify]: Simplify 1/2 into 1/2
12.757 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.757 * [taylor]: Taking taylor expansion of k in n
12.757 * [backup-simplify]: Simplify k into k
12.758 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.758 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.758 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.758 * [taylor]: Taking taylor expansion of 2 in n
12.758 * [backup-simplify]: Simplify 2 into 2
12.758 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.758 * [taylor]: Taking taylor expansion of PI in n
12.758 * [backup-simplify]: Simplify PI into PI
12.758 * [taylor]: Taking taylor expansion of n in n
12.758 * [backup-simplify]: Simplify 0 into 0
12.758 * [backup-simplify]: Simplify 1 into 1
12.758 * [backup-simplify]: Simplify (/ PI 1) into PI
12.758 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.759 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.759 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.759 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.759 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.759 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
12.760 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.761 * [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))))
12.761 * [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)))))
12.761 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
12.761 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
12.761 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
12.761 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
12.761 * [taylor]: Taking taylor expansion of 1/2 in n
12.762 * [backup-simplify]: Simplify 1/2 into 1/2
12.762 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.762 * [taylor]: Taking taylor expansion of 1/2 in n
12.762 * [backup-simplify]: Simplify 1/2 into 1/2
12.762 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.762 * [taylor]: Taking taylor expansion of 1/2 in n
12.762 * [backup-simplify]: Simplify 1/2 into 1/2
12.762 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.762 * [taylor]: Taking taylor expansion of k in n
12.762 * [backup-simplify]: Simplify k into k
12.762 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.762 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.762 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.762 * [taylor]: Taking taylor expansion of 2 in n
12.762 * [backup-simplify]: Simplify 2 into 2
12.762 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.762 * [taylor]: Taking taylor expansion of PI in n
12.762 * [backup-simplify]: Simplify PI into PI
12.762 * [taylor]: Taking taylor expansion of n in n
12.762 * [backup-simplify]: Simplify 0 into 0
12.762 * [backup-simplify]: Simplify 1 into 1
12.762 * [backup-simplify]: Simplify (/ PI 1) into PI
12.762 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.763 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.763 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.763 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.763 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.763 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
12.764 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.765 * [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))))
12.766 * [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)))))
12.766 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
12.766 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
12.766 * [taylor]: Taking taylor expansion of 1/2 in k
12.766 * [backup-simplify]: Simplify 1/2 into 1/2
12.766 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
12.766 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.766 * [taylor]: Taking taylor expansion of 1/2 in k
12.766 * [backup-simplify]: Simplify 1/2 into 1/2
12.766 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.766 * [taylor]: Taking taylor expansion of 1/2 in k
12.766 * [backup-simplify]: Simplify 1/2 into 1/2
12.766 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.766 * [taylor]: Taking taylor expansion of k in k
12.766 * [backup-simplify]: Simplify 0 into 0
12.766 * [backup-simplify]: Simplify 1 into 1
12.766 * [backup-simplify]: Simplify (/ 1 1) into 1
12.766 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
12.766 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.766 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.766 * [taylor]: Taking taylor expansion of 2 in k
12.766 * [backup-simplify]: Simplify 2 into 2
12.766 * [taylor]: Taking taylor expansion of PI in k
12.766 * [backup-simplify]: Simplify PI into PI
12.767 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.767 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.767 * [taylor]: Taking taylor expansion of (log n) in k
12.767 * [taylor]: Taking taylor expansion of n in k
12.767 * [backup-simplify]: Simplify n into n
12.767 * [backup-simplify]: Simplify (log n) into (log n)
12.768 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.768 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.768 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.768 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.769 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
12.769 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
12.770 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
12.771 * [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)))))
12.771 * [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)))))
12.772 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.772 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.774 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.774 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.774 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.774 * [backup-simplify]: Simplify (- 0) into 0
12.774 * [backup-simplify]: Simplify (+ 0 0) into 0
12.775 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
12.776 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.776 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
12.778 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.778 * [taylor]: Taking taylor expansion of 0 in k
12.778 * [backup-simplify]: Simplify 0 into 0
12.778 * [backup-simplify]: Simplify 0 into 0
12.778 * [backup-simplify]: Simplify 0 into 0
12.778 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.779 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.781 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
12.781 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.781 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.782 * [backup-simplify]: Simplify (- 0) into 0
12.782 * [backup-simplify]: Simplify (+ 0 0) into 0
12.782 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
12.783 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.784 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
12.786 * [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
12.786 * [taylor]: Taking taylor expansion of 0 in k
12.786 * [backup-simplify]: Simplify 0 into 0
12.786 * [backup-simplify]: Simplify 0 into 0
12.786 * [backup-simplify]: Simplify 0 into 0
12.786 * [backup-simplify]: Simplify 0 into 0
12.786 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.787 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.790 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
12.790 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.791 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.791 * [backup-simplify]: Simplify (- 0) into 0
12.792 * [backup-simplify]: Simplify (+ 0 0) into 0
12.792 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
12.793 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.795 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
12.796 * [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
12.796 * [taylor]: Taking taylor expansion of 0 in k
12.796 * [backup-simplify]: Simplify 0 into 0
12.796 * [backup-simplify]: Simplify 0 into 0
12.797 * [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))))))
12.798 * [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)))
12.798 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
12.798 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
12.798 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
12.798 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
12.798 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
12.798 * [taylor]: Taking taylor expansion of 1/2 in k
12.798 * [backup-simplify]: Simplify 1/2 into 1/2
12.798 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.798 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.798 * [taylor]: Taking taylor expansion of 1/2 in k
12.798 * [backup-simplify]: Simplify 1/2 into 1/2
12.798 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.798 * [taylor]: Taking taylor expansion of k in k
12.798 * [backup-simplify]: Simplify 0 into 0
12.798 * [backup-simplify]: Simplify 1 into 1
12.798 * [backup-simplify]: Simplify (/ 1 1) into 1
12.798 * [taylor]: Taking taylor expansion of 1/2 in k
12.798 * [backup-simplify]: Simplify 1/2 into 1/2
12.798 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.798 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.798 * [taylor]: Taking taylor expansion of -2 in k
12.798 * [backup-simplify]: Simplify -2 into -2
12.798 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.798 * [taylor]: Taking taylor expansion of PI in k
12.798 * [backup-simplify]: Simplify PI into PI
12.798 * [taylor]: Taking taylor expansion of n in k
12.798 * [backup-simplify]: Simplify n into n
12.798 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.798 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.798 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.799 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.799 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.799 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
12.799 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
12.799 * [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))))
12.799 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
12.799 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
12.799 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
12.799 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.799 * [taylor]: Taking taylor expansion of 1/2 in n
12.799 * [backup-simplify]: Simplify 1/2 into 1/2
12.800 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.800 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.800 * [taylor]: Taking taylor expansion of 1/2 in n
12.800 * [backup-simplify]: Simplify 1/2 into 1/2
12.800 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.800 * [taylor]: Taking taylor expansion of k in n
12.800 * [backup-simplify]: Simplify k into k
12.800 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.800 * [taylor]: Taking taylor expansion of 1/2 in n
12.800 * [backup-simplify]: Simplify 1/2 into 1/2
12.800 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.800 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.800 * [taylor]: Taking taylor expansion of -2 in n
12.800 * [backup-simplify]: Simplify -2 into -2
12.800 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.800 * [taylor]: Taking taylor expansion of PI in n
12.800 * [backup-simplify]: Simplify PI into PI
12.800 * [taylor]: Taking taylor expansion of n in n
12.800 * [backup-simplify]: Simplify 0 into 0
12.800 * [backup-simplify]: Simplify 1 into 1
12.800 * [backup-simplify]: Simplify (/ PI 1) into PI
12.800 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.801 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.801 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.801 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.801 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
12.802 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.803 * [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))))
12.803 * [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)))))
12.803 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
12.804 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
12.804 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
12.804 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.804 * [taylor]: Taking taylor expansion of 1/2 in n
12.804 * [backup-simplify]: Simplify 1/2 into 1/2
12.804 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.804 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.804 * [taylor]: Taking taylor expansion of 1/2 in n
12.804 * [backup-simplify]: Simplify 1/2 into 1/2
12.804 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.804 * [taylor]: Taking taylor expansion of k in n
12.804 * [backup-simplify]: Simplify k into k
12.804 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.804 * [taylor]: Taking taylor expansion of 1/2 in n
12.804 * [backup-simplify]: Simplify 1/2 into 1/2
12.804 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.804 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.804 * [taylor]: Taking taylor expansion of -2 in n
12.804 * [backup-simplify]: Simplify -2 into -2
12.804 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.804 * [taylor]: Taking taylor expansion of PI in n
12.804 * [backup-simplify]: Simplify PI into PI
12.804 * [taylor]: Taking taylor expansion of n in n
12.804 * [backup-simplify]: Simplify 0 into 0
12.804 * [backup-simplify]: Simplify 1 into 1
12.804 * [backup-simplify]: Simplify (/ PI 1) into PI
12.804 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.805 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.805 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.805 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.805 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
12.806 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.807 * [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))))
12.808 * [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)))))
12.808 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
12.808 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
12.808 * [taylor]: Taking taylor expansion of 1/2 in k
12.808 * [backup-simplify]: Simplify 1/2 into 1/2
12.808 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
12.808 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.808 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.808 * [taylor]: Taking taylor expansion of 1/2 in k
12.808 * [backup-simplify]: Simplify 1/2 into 1/2
12.808 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.808 * [taylor]: Taking taylor expansion of k in k
12.808 * [backup-simplify]: Simplify 0 into 0
12.808 * [backup-simplify]: Simplify 1 into 1
12.808 * [backup-simplify]: Simplify (/ 1 1) into 1
12.808 * [taylor]: Taking taylor expansion of 1/2 in k
12.808 * [backup-simplify]: Simplify 1/2 into 1/2
12.808 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
12.808 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
12.808 * [taylor]: Taking taylor expansion of (* -2 PI) in k
12.808 * [taylor]: Taking taylor expansion of -2 in k
12.808 * [backup-simplify]: Simplify -2 into -2
12.808 * [taylor]: Taking taylor expansion of PI in k
12.808 * [backup-simplify]: Simplify PI into PI
12.809 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.809 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.809 * [taylor]: Taking taylor expansion of (log n) in k
12.809 * [taylor]: Taking taylor expansion of n in k
12.809 * [backup-simplify]: Simplify n into n
12.809 * [backup-simplify]: Simplify (log n) into (log n)
12.810 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.810 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.810 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.810 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
12.811 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
12.812 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
12.812 * [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)))))
12.813 * [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)))))
12.814 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.814 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.815 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
12.815 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.819 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.820 * [backup-simplify]: Simplify (+ 0 0) into 0
12.820 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
12.821 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.822 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
12.823 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.823 * [taylor]: Taking taylor expansion of 0 in k
12.823 * [backup-simplify]: Simplify 0 into 0
12.823 * [backup-simplify]: Simplify 0 into 0
12.823 * [backup-simplify]: Simplify 0 into 0
12.824 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.825 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.827 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
12.827 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.828 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.828 * [backup-simplify]: Simplify (+ 0 0) into 0
12.830 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
12.831 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.832 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
12.833 * [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
12.833 * [taylor]: Taking taylor expansion of 0 in k
12.833 * [backup-simplify]: Simplify 0 into 0
12.833 * [backup-simplify]: Simplify 0 into 0
12.834 * [backup-simplify]: Simplify 0 into 0
12.834 * [backup-simplify]: Simplify 0 into 0
12.834 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.835 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.838 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
12.839 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.839 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.840 * [backup-simplify]: Simplify (+ 0 0) into 0
12.840 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
12.841 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.842 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
12.844 * [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
12.844 * [taylor]: Taking taylor expansion of 0 in k
12.844 * [backup-simplify]: Simplify 0 into 0
12.844 * [backup-simplify]: Simplify 0 into 0
12.845 * [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))))))
12.845 * * * * [progress]: [ 2 / 4 ] generating series at (2 1)
12.846 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))
12.846 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
12.846 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
12.846 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
12.846 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
12.846 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
12.846 * [taylor]: Taking taylor expansion of 1/2 in k
12.846 * [backup-simplify]: Simplify 1/2 into 1/2
12.846 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.846 * [taylor]: Taking taylor expansion of 1/2 in k
12.846 * [backup-simplify]: Simplify 1/2 into 1/2
12.846 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.846 * [taylor]: Taking taylor expansion of 1/2 in k
12.846 * [backup-simplify]: Simplify 1/2 into 1/2
12.846 * [taylor]: Taking taylor expansion of k in k
12.846 * [backup-simplify]: Simplify 0 into 0
12.846 * [backup-simplify]: Simplify 1 into 1
12.846 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.846 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.846 * [taylor]: Taking taylor expansion of 2 in k
12.846 * [backup-simplify]: Simplify 2 into 2
12.846 * [taylor]: Taking taylor expansion of (* n PI) in k
12.846 * [taylor]: Taking taylor expansion of n in k
12.846 * [backup-simplify]: Simplify n into n
12.846 * [taylor]: Taking taylor expansion of PI in k
12.846 * [backup-simplify]: Simplify PI into PI
12.846 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.846 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.846 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.846 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.847 * [backup-simplify]: Simplify (- 0) into 0
12.847 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.847 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
12.847 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
12.847 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
12.847 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
12.847 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
12.847 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
12.847 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
12.847 * [taylor]: Taking taylor expansion of 1/2 in n
12.847 * [backup-simplify]: Simplify 1/2 into 1/2
12.848 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.848 * [taylor]: Taking taylor expansion of 1/2 in n
12.848 * [backup-simplify]: Simplify 1/2 into 1/2
12.848 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.848 * [taylor]: Taking taylor expansion of 1/2 in n
12.848 * [backup-simplify]: Simplify 1/2 into 1/2
12.848 * [taylor]: Taking taylor expansion of k in n
12.848 * [backup-simplify]: Simplify k into k
12.848 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.848 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.848 * [taylor]: Taking taylor expansion of 2 in n
12.848 * [backup-simplify]: Simplify 2 into 2
12.848 * [taylor]: Taking taylor expansion of (* n PI) in n
12.848 * [taylor]: Taking taylor expansion of n in n
12.848 * [backup-simplify]: Simplify 0 into 0
12.848 * [backup-simplify]: Simplify 1 into 1
12.848 * [taylor]: Taking taylor expansion of PI in n
12.848 * [backup-simplify]: Simplify PI into PI
12.848 * [backup-simplify]: Simplify (* 0 PI) into 0
12.848 * [backup-simplify]: Simplify (* 2 0) into 0
12.849 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.850 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.851 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.851 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.851 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.851 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.851 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
12.852 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.853 * [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)))))
12.854 * [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))))))
12.854 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
12.854 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
12.854 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
12.854 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
12.854 * [taylor]: Taking taylor expansion of 1/2 in n
12.854 * [backup-simplify]: Simplify 1/2 into 1/2
12.854 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.854 * [taylor]: Taking taylor expansion of 1/2 in n
12.854 * [backup-simplify]: Simplify 1/2 into 1/2
12.854 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.854 * [taylor]: Taking taylor expansion of 1/2 in n
12.854 * [backup-simplify]: Simplify 1/2 into 1/2
12.854 * [taylor]: Taking taylor expansion of k in n
12.854 * [backup-simplify]: Simplify k into k
12.854 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.854 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.854 * [taylor]: Taking taylor expansion of 2 in n
12.854 * [backup-simplify]: Simplify 2 into 2
12.854 * [taylor]: Taking taylor expansion of (* n PI) in n
12.854 * [taylor]: Taking taylor expansion of n in n
12.854 * [backup-simplify]: Simplify 0 into 0
12.854 * [backup-simplify]: Simplify 1 into 1
12.854 * [taylor]: Taking taylor expansion of PI in n
12.855 * [backup-simplify]: Simplify PI into PI
12.855 * [backup-simplify]: Simplify (* 0 PI) into 0
12.855 * [backup-simplify]: Simplify (* 2 0) into 0
12.857 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.858 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.860 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.860 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.860 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.860 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.860 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
12.861 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.863 * [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)))))
12.864 * [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))))))
12.864 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
12.864 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
12.864 * [taylor]: Taking taylor expansion of 1/2 in k
12.864 * [backup-simplify]: Simplify 1/2 into 1/2
12.864 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
12.864 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.864 * [taylor]: Taking taylor expansion of 1/2 in k
12.864 * [backup-simplify]: Simplify 1/2 into 1/2
12.864 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.864 * [taylor]: Taking taylor expansion of 1/2 in k
12.864 * [backup-simplify]: Simplify 1/2 into 1/2
12.864 * [taylor]: Taking taylor expansion of k in k
12.864 * [backup-simplify]: Simplify 0 into 0
12.864 * [backup-simplify]: Simplify 1 into 1
12.865 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
12.865 * [taylor]: Taking taylor expansion of (log n) in k
12.865 * [taylor]: Taking taylor expansion of n in k
12.865 * [backup-simplify]: Simplify n into n
12.865 * [backup-simplify]: Simplify (log n) into (log n)
12.865 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.865 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.865 * [taylor]: Taking taylor expansion of 2 in k
12.865 * [backup-simplify]: Simplify 2 into 2
12.865 * [taylor]: Taking taylor expansion of PI in k
12.865 * [backup-simplify]: Simplify PI into PI
12.865 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.866 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.867 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.867 * [backup-simplify]: Simplify (- 0) into 0
12.868 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.869 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.870 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
12.871 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
12.872 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
12.874 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
12.875 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.876 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.878 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.878 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
12.879 * [backup-simplify]: Simplify (- 0) into 0
12.879 * [backup-simplify]: Simplify (+ 0 0) into 0
12.880 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
12.881 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.882 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
12.885 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.885 * [taylor]: Taking taylor expansion of 0 in k
12.885 * [backup-simplify]: Simplify 0 into 0
12.885 * [backup-simplify]: Simplify 0 into 0
12.886 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.887 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.889 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.889 * [backup-simplify]: Simplify (+ 0 0) into 0
12.890 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
12.890 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.891 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.892 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
12.895 * [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)))))
12.898 * [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)))))))
12.901 * [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)))))))
12.902 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.903 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.907 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
12.908 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
12.908 * [backup-simplify]: Simplify (- 0) into 0
12.909 * [backup-simplify]: Simplify (+ 0 0) into 0
12.910 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
12.911 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.912 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.915 * [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
12.915 * [taylor]: Taking taylor expansion of 0 in k
12.915 * [backup-simplify]: Simplify 0 into 0
12.915 * [backup-simplify]: Simplify 0 into 0
12.915 * [backup-simplify]: Simplify 0 into 0
12.917 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.918 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.921 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
12.922 * [backup-simplify]: Simplify (+ 0 0) into 0
12.923 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
12.923 * [backup-simplify]: Simplify (- 0) into 0
12.923 * [backup-simplify]: Simplify (+ 0 0) into 0
12.925 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.928 * [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
12.932 * [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)))))
12.937 * [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)))))
12.951 * [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)))))))
12.952 * [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)))))
12.952 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
12.952 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
12.952 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
12.952 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
12.952 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
12.952 * [taylor]: Taking taylor expansion of 1/2 in k
12.952 * [backup-simplify]: Simplify 1/2 into 1/2
12.953 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.953 * [taylor]: Taking taylor expansion of 1/2 in k
12.953 * [backup-simplify]: Simplify 1/2 into 1/2
12.953 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.953 * [taylor]: Taking taylor expansion of 1/2 in k
12.953 * [backup-simplify]: Simplify 1/2 into 1/2
12.953 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.953 * [taylor]: Taking taylor expansion of k in k
12.953 * [backup-simplify]: Simplify 0 into 0
12.953 * [backup-simplify]: Simplify 1 into 1
12.953 * [backup-simplify]: Simplify (/ 1 1) into 1
12.953 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.953 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.953 * [taylor]: Taking taylor expansion of 2 in k
12.953 * [backup-simplify]: Simplify 2 into 2
12.953 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.953 * [taylor]: Taking taylor expansion of PI in k
12.953 * [backup-simplify]: Simplify PI into PI
12.953 * [taylor]: Taking taylor expansion of n in k
12.953 * [backup-simplify]: Simplify n into n
12.953 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.953 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.953 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.954 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.954 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.954 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.954 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
12.954 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
12.955 * [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))))))
12.955 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
12.955 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
12.955 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
12.955 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
12.955 * [taylor]: Taking taylor expansion of 1/2 in n
12.955 * [backup-simplify]: Simplify 1/2 into 1/2
12.955 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.955 * [taylor]: Taking taylor expansion of 1/2 in n
12.955 * [backup-simplify]: Simplify 1/2 into 1/2
12.955 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.955 * [taylor]: Taking taylor expansion of 1/2 in n
12.955 * [backup-simplify]: Simplify 1/2 into 1/2
12.955 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.955 * [taylor]: Taking taylor expansion of k in n
12.955 * [backup-simplify]: Simplify k into k
12.955 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.955 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.955 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.955 * [taylor]: Taking taylor expansion of 2 in n
12.955 * [backup-simplify]: Simplify 2 into 2
12.955 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.955 * [taylor]: Taking taylor expansion of PI in n
12.955 * [backup-simplify]: Simplify PI into PI
12.955 * [taylor]: Taking taylor expansion of n in n
12.955 * [backup-simplify]: Simplify 0 into 0
12.955 * [backup-simplify]: Simplify 1 into 1
12.955 * [backup-simplify]: Simplify (/ PI 1) into PI
12.956 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.956 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.956 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.956 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.956 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.956 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
12.957 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.958 * [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))))
12.959 * [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)))))
12.959 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
12.959 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
12.959 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
12.959 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
12.959 * [taylor]: Taking taylor expansion of 1/2 in n
12.959 * [backup-simplify]: Simplify 1/2 into 1/2
12.959 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.959 * [taylor]: Taking taylor expansion of 1/2 in n
12.959 * [backup-simplify]: Simplify 1/2 into 1/2
12.959 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.959 * [taylor]: Taking taylor expansion of 1/2 in n
12.959 * [backup-simplify]: Simplify 1/2 into 1/2
12.959 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.959 * [taylor]: Taking taylor expansion of k in n
12.959 * [backup-simplify]: Simplify k into k
12.959 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.959 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.959 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.959 * [taylor]: Taking taylor expansion of 2 in n
12.959 * [backup-simplify]: Simplify 2 into 2
12.959 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.959 * [taylor]: Taking taylor expansion of PI in n
12.959 * [backup-simplify]: Simplify PI into PI
12.959 * [taylor]: Taking taylor expansion of n in n
12.959 * [backup-simplify]: Simplify 0 into 0
12.959 * [backup-simplify]: Simplify 1 into 1
12.959 * [backup-simplify]: Simplify (/ PI 1) into PI
12.960 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.960 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.960 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.960 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.961 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.961 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
12.961 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.962 * [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))))
12.963 * [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)))))
12.963 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
12.963 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
12.963 * [taylor]: Taking taylor expansion of 1/2 in k
12.963 * [backup-simplify]: Simplify 1/2 into 1/2
12.963 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
12.963 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.963 * [taylor]: Taking taylor expansion of 1/2 in k
12.963 * [backup-simplify]: Simplify 1/2 into 1/2
12.963 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.963 * [taylor]: Taking taylor expansion of 1/2 in k
12.963 * [backup-simplify]: Simplify 1/2 into 1/2
12.963 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.963 * [taylor]: Taking taylor expansion of k in k
12.963 * [backup-simplify]: Simplify 0 into 0
12.963 * [backup-simplify]: Simplify 1 into 1
12.963 * [backup-simplify]: Simplify (/ 1 1) into 1
12.963 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
12.963 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.963 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.964 * [taylor]: Taking taylor expansion of 2 in k
12.964 * [backup-simplify]: Simplify 2 into 2
12.964 * [taylor]: Taking taylor expansion of PI in k
12.964 * [backup-simplify]: Simplify PI into PI
12.964 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.964 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.964 * [taylor]: Taking taylor expansion of (log n) in k
12.964 * [taylor]: Taking taylor expansion of n in k
12.965 * [backup-simplify]: Simplify n into n
12.965 * [backup-simplify]: Simplify (log n) into (log n)
12.965 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.965 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.966 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.966 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.966 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
12.967 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
12.968 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
12.968 * [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)))))
12.969 * [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)))))
12.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.970 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.971 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.971 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.972 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.972 * [backup-simplify]: Simplify (- 0) into 0
12.972 * [backup-simplify]: Simplify (+ 0 0) into 0
12.972 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
12.973 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.974 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
12.975 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.975 * [taylor]: Taking taylor expansion of 0 in k
12.975 * [backup-simplify]: Simplify 0 into 0
12.975 * [backup-simplify]: Simplify 0 into 0
12.975 * [backup-simplify]: Simplify 0 into 0
12.976 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.976 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.978 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
12.978 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.979 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.979 * [backup-simplify]: Simplify (- 0) into 0
12.979 * [backup-simplify]: Simplify (+ 0 0) into 0
12.980 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
12.981 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.982 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
12.985 * [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
12.985 * [taylor]: Taking taylor expansion of 0 in k
12.985 * [backup-simplify]: Simplify 0 into 0
12.985 * [backup-simplify]: Simplify 0 into 0
12.985 * [backup-simplify]: Simplify 0 into 0
12.985 * [backup-simplify]: Simplify 0 into 0
12.986 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.987 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.993 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
12.993 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.995 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.995 * [backup-simplify]: Simplify (- 0) into 0
12.995 * [backup-simplify]: Simplify (+ 0 0) into 0
12.997 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
12.997 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.999 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
13.000 * [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
13.000 * [taylor]: Taking taylor expansion of 0 in k
13.000 * [backup-simplify]: Simplify 0 into 0
13.000 * [backup-simplify]: Simplify 0 into 0
13.001 * [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))))))
13.001 * [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)))
13.001 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
13.001 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
13.001 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
13.001 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
13.001 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
13.001 * [taylor]: Taking taylor expansion of 1/2 in k
13.001 * [backup-simplify]: Simplify 1/2 into 1/2
13.001 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
13.002 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.002 * [taylor]: Taking taylor expansion of 1/2 in k
13.002 * [backup-simplify]: Simplify 1/2 into 1/2
13.002 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.002 * [taylor]: Taking taylor expansion of k in k
13.002 * [backup-simplify]: Simplify 0 into 0
13.002 * [backup-simplify]: Simplify 1 into 1
13.002 * [backup-simplify]: Simplify (/ 1 1) into 1
13.002 * [taylor]: Taking taylor expansion of 1/2 in k
13.002 * [backup-simplify]: Simplify 1/2 into 1/2
13.002 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.002 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.002 * [taylor]: Taking taylor expansion of -2 in k
13.002 * [backup-simplify]: Simplify -2 into -2
13.002 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.002 * [taylor]: Taking taylor expansion of PI in k
13.002 * [backup-simplify]: Simplify PI into PI
13.002 * [taylor]: Taking taylor expansion of n in k
13.002 * [backup-simplify]: Simplify n into n
13.002 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.002 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.002 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.002 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.003 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.003 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
13.003 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
13.003 * [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))))
13.003 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
13.003 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
13.003 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
13.003 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.003 * [taylor]: Taking taylor expansion of 1/2 in n
13.003 * [backup-simplify]: Simplify 1/2 into 1/2
13.003 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.003 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.003 * [taylor]: Taking taylor expansion of 1/2 in n
13.003 * [backup-simplify]: Simplify 1/2 into 1/2
13.003 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.003 * [taylor]: Taking taylor expansion of k in n
13.003 * [backup-simplify]: Simplify k into k
13.003 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.003 * [taylor]: Taking taylor expansion of 1/2 in n
13.003 * [backup-simplify]: Simplify 1/2 into 1/2
13.003 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.003 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.003 * [taylor]: Taking taylor expansion of -2 in n
13.003 * [backup-simplify]: Simplify -2 into -2
13.003 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.003 * [taylor]: Taking taylor expansion of PI in n
13.004 * [backup-simplify]: Simplify PI into PI
13.004 * [taylor]: Taking taylor expansion of n in n
13.004 * [backup-simplify]: Simplify 0 into 0
13.004 * [backup-simplify]: Simplify 1 into 1
13.004 * [backup-simplify]: Simplify (/ PI 1) into PI
13.004 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.005 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.005 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.005 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.005 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
13.006 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.007 * [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))))
13.007 * [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)))))
13.007 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
13.007 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
13.007 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
13.007 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.007 * [taylor]: Taking taylor expansion of 1/2 in n
13.008 * [backup-simplify]: Simplify 1/2 into 1/2
13.008 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.008 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.008 * [taylor]: Taking taylor expansion of 1/2 in n
13.008 * [backup-simplify]: Simplify 1/2 into 1/2
13.008 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.008 * [taylor]: Taking taylor expansion of k in n
13.008 * [backup-simplify]: Simplify k into k
13.008 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.008 * [taylor]: Taking taylor expansion of 1/2 in n
13.008 * [backup-simplify]: Simplify 1/2 into 1/2
13.008 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.008 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.008 * [taylor]: Taking taylor expansion of -2 in n
13.008 * [backup-simplify]: Simplify -2 into -2
13.008 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.008 * [taylor]: Taking taylor expansion of PI in n
13.008 * [backup-simplify]: Simplify PI into PI
13.008 * [taylor]: Taking taylor expansion of n in n
13.008 * [backup-simplify]: Simplify 0 into 0
13.008 * [backup-simplify]: Simplify 1 into 1
13.008 * [backup-simplify]: Simplify (/ PI 1) into PI
13.008 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.009 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.009 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.009 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.009 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
13.010 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.011 * [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))))
13.011 * [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)))))
13.012 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
13.012 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
13.012 * [taylor]: Taking taylor expansion of 1/2 in k
13.012 * [backup-simplify]: Simplify 1/2 into 1/2
13.012 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
13.012 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
13.012 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.012 * [taylor]: Taking taylor expansion of 1/2 in k
13.012 * [backup-simplify]: Simplify 1/2 into 1/2
13.012 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.012 * [taylor]: Taking taylor expansion of k in k
13.012 * [backup-simplify]: Simplify 0 into 0
13.012 * [backup-simplify]: Simplify 1 into 1
13.012 * [backup-simplify]: Simplify (/ 1 1) into 1
13.012 * [taylor]: Taking taylor expansion of 1/2 in k
13.012 * [backup-simplify]: Simplify 1/2 into 1/2
13.012 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
13.012 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
13.012 * [taylor]: Taking taylor expansion of (* -2 PI) in k
13.012 * [taylor]: Taking taylor expansion of -2 in k
13.012 * [backup-simplify]: Simplify -2 into -2
13.012 * [taylor]: Taking taylor expansion of PI in k
13.012 * [backup-simplify]: Simplify PI into PI
13.012 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.013 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.013 * [taylor]: Taking taylor expansion of (log n) in k
13.013 * [taylor]: Taking taylor expansion of n in k
13.013 * [backup-simplify]: Simplify n into n
13.013 * [backup-simplify]: Simplify (log n) into (log n)
13.013 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.014 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.014 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.014 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
13.015 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
13.016 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
13.016 * [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)))))
13.017 * [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)))))
13.018 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.018 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.020 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
13.020 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.020 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
13.021 * [backup-simplify]: Simplify (+ 0 0) into 0
13.021 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
13.022 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.023 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
13.024 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.024 * [taylor]: Taking taylor expansion of 0 in k
13.024 * [backup-simplify]: Simplify 0 into 0
13.024 * [backup-simplify]: Simplify 0 into 0
13.024 * [backup-simplify]: Simplify 0 into 0
13.025 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.026 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
13.029 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
13.029 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.030 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
13.030 * [backup-simplify]: Simplify (+ 0 0) into 0
13.031 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
13.033 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.034 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
13.036 * [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
13.036 * [taylor]: Taking taylor expansion of 0 in k
13.036 * [backup-simplify]: Simplify 0 into 0
13.036 * [backup-simplify]: Simplify 0 into 0
13.036 * [backup-simplify]: Simplify 0 into 0
13.036 * [backup-simplify]: Simplify 0 into 0
13.037 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.038 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.044 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
13.044 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.045 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
13.045 * [backup-simplify]: Simplify (+ 0 0) into 0
13.047 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
13.048 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.049 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
13.059 * [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
13.059 * [taylor]: Taking taylor expansion of 0 in k
13.059 * [backup-simplify]: Simplify 0 into 0
13.059 * [backup-simplify]: Simplify 0 into 0
13.061 * [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))))))
13.061 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1)
13.062 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
13.062 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
13.062 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.062 * [taylor]: Taking taylor expansion of 2 in n
13.062 * [backup-simplify]: Simplify 2 into 2
13.062 * [taylor]: Taking taylor expansion of (* n PI) in n
13.062 * [taylor]: Taking taylor expansion of n in n
13.062 * [backup-simplify]: Simplify 0 into 0
13.062 * [backup-simplify]: Simplify 1 into 1
13.062 * [taylor]: Taking taylor expansion of PI in n
13.062 * [backup-simplify]: Simplify PI into PI
13.062 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.062 * [taylor]: Taking taylor expansion of 2 in n
13.062 * [backup-simplify]: Simplify 2 into 2
13.062 * [taylor]: Taking taylor expansion of (* n PI) in n
13.062 * [taylor]: Taking taylor expansion of n in n
13.062 * [backup-simplify]: Simplify 0 into 0
13.062 * [backup-simplify]: Simplify 1 into 1
13.062 * [taylor]: Taking taylor expansion of PI in n
13.062 * [backup-simplify]: Simplify PI into PI
13.063 * [backup-simplify]: Simplify (* 0 PI) into 0
13.063 * [backup-simplify]: Simplify (* 2 0) into 0
13.063 * [backup-simplify]: Simplify 0 into 0
13.065 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.066 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.067 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.068 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.069 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.069 * [backup-simplify]: Simplify 0 into 0
13.070 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.071 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.071 * [backup-simplify]: Simplify 0 into 0
13.073 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.074 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.074 * [backup-simplify]: Simplify 0 into 0
13.076 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.077 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
13.077 * [backup-simplify]: Simplify 0 into 0
13.079 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.081 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
13.081 * [backup-simplify]: Simplify 0 into 0
13.083 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
13.085 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
13.085 * [backup-simplify]: Simplify 0 into 0
13.086 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
13.086 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
13.086 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
13.086 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.086 * [taylor]: Taking taylor expansion of 2 in n
13.086 * [backup-simplify]: Simplify 2 into 2
13.086 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.086 * [taylor]: Taking taylor expansion of PI in n
13.087 * [backup-simplify]: Simplify PI into PI
13.087 * [taylor]: Taking taylor expansion of n in n
13.087 * [backup-simplify]: Simplify 0 into 0
13.087 * [backup-simplify]: Simplify 1 into 1
13.087 * [backup-simplify]: Simplify (/ PI 1) into PI
13.087 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.087 * [taylor]: Taking taylor expansion of 2 in n
13.087 * [backup-simplify]: Simplify 2 into 2
13.087 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.087 * [taylor]: Taking taylor expansion of PI in n
13.087 * [backup-simplify]: Simplify PI into PI
13.087 * [taylor]: Taking taylor expansion of n in n
13.087 * [backup-simplify]: Simplify 0 into 0
13.087 * [backup-simplify]: Simplify 1 into 1
13.088 * [backup-simplify]: Simplify (/ PI 1) into PI
13.088 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.089 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.089 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.090 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.090 * [backup-simplify]: Simplify 0 into 0
13.091 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.091 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.091 * [backup-simplify]: Simplify 0 into 0
13.092 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.092 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.092 * [backup-simplify]: Simplify 0 into 0
13.093 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.094 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.094 * [backup-simplify]: Simplify 0 into 0
13.095 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.095 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.095 * [backup-simplify]: Simplify 0 into 0
13.096 * [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
13.097 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.097 * [backup-simplify]: Simplify 0 into 0
13.098 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
13.098 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
13.098 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
13.098 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.098 * [taylor]: Taking taylor expansion of -2 in n
13.098 * [backup-simplify]: Simplify -2 into -2
13.098 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.098 * [taylor]: Taking taylor expansion of PI in n
13.098 * [backup-simplify]: Simplify PI into PI
13.098 * [taylor]: Taking taylor expansion of n in n
13.098 * [backup-simplify]: Simplify 0 into 0
13.098 * [backup-simplify]: Simplify 1 into 1
13.099 * [backup-simplify]: Simplify (/ PI 1) into PI
13.099 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.099 * [taylor]: Taking taylor expansion of -2 in n
13.099 * [backup-simplify]: Simplify -2 into -2
13.099 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.099 * [taylor]: Taking taylor expansion of PI in n
13.099 * [backup-simplify]: Simplify PI into PI
13.099 * [taylor]: Taking taylor expansion of n in n
13.099 * [backup-simplify]: Simplify 0 into 0
13.099 * [backup-simplify]: Simplify 1 into 1
13.099 * [backup-simplify]: Simplify (/ PI 1) into PI
13.100 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.100 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.100 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.101 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.101 * [backup-simplify]: Simplify 0 into 0
13.102 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.102 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
13.102 * [backup-simplify]: Simplify 0 into 0
13.103 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.103 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.104 * [backup-simplify]: Simplify 0 into 0
13.104 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.105 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.105 * [backup-simplify]: Simplify 0 into 0
13.106 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.106 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.106 * [backup-simplify]: Simplify 0 into 0
13.107 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.108 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.108 * [backup-simplify]: Simplify 0 into 0
13.108 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
13.109 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1)
13.109 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
13.109 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
13.109 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.109 * [taylor]: Taking taylor expansion of 2 in n
13.109 * [backup-simplify]: Simplify 2 into 2
13.109 * [taylor]: Taking taylor expansion of (* n PI) in n
13.109 * [taylor]: Taking taylor expansion of n in n
13.109 * [backup-simplify]: Simplify 0 into 0
13.109 * [backup-simplify]: Simplify 1 into 1
13.109 * [taylor]: Taking taylor expansion of PI in n
13.109 * [backup-simplify]: Simplify PI into PI
13.109 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.109 * [taylor]: Taking taylor expansion of 2 in n
13.109 * [backup-simplify]: Simplify 2 into 2
13.109 * [taylor]: Taking taylor expansion of (* n PI) in n
13.109 * [taylor]: Taking taylor expansion of n in n
13.109 * [backup-simplify]: Simplify 0 into 0
13.109 * [backup-simplify]: Simplify 1 into 1
13.109 * [taylor]: Taking taylor expansion of PI in n
13.109 * [backup-simplify]: Simplify PI into PI
13.110 * [backup-simplify]: Simplify (* 0 PI) into 0
13.110 * [backup-simplify]: Simplify (* 2 0) into 0
13.110 * [backup-simplify]: Simplify 0 into 0
13.111 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.112 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.112 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.113 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.113 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.113 * [backup-simplify]: Simplify 0 into 0
13.114 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.115 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.115 * [backup-simplify]: Simplify 0 into 0
13.116 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.117 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.117 * [backup-simplify]: Simplify 0 into 0
13.118 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.119 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
13.119 * [backup-simplify]: Simplify 0 into 0
13.120 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.121 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
13.121 * [backup-simplify]: Simplify 0 into 0
13.122 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
13.123 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
13.123 * [backup-simplify]: Simplify 0 into 0
13.124 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
13.124 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
13.124 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
13.124 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.124 * [taylor]: Taking taylor expansion of 2 in n
13.124 * [backup-simplify]: Simplify 2 into 2
13.124 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.124 * [taylor]: Taking taylor expansion of PI in n
13.124 * [backup-simplify]: Simplify PI into PI
13.124 * [taylor]: Taking taylor expansion of n in n
13.124 * [backup-simplify]: Simplify 0 into 0
13.124 * [backup-simplify]: Simplify 1 into 1
13.125 * [backup-simplify]: Simplify (/ PI 1) into PI
13.125 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.125 * [taylor]: Taking taylor expansion of 2 in n
13.125 * [backup-simplify]: Simplify 2 into 2
13.125 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.125 * [taylor]: Taking taylor expansion of PI in n
13.125 * [backup-simplify]: Simplify PI into PI
13.125 * [taylor]: Taking taylor expansion of n in n
13.125 * [backup-simplify]: Simplify 0 into 0
13.125 * [backup-simplify]: Simplify 1 into 1
13.125 * [backup-simplify]: Simplify (/ PI 1) into PI
13.125 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.126 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.126 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.127 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.127 * [backup-simplify]: Simplify 0 into 0
13.127 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.128 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.128 * [backup-simplify]: Simplify 0 into 0
13.129 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.129 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.129 * [backup-simplify]: Simplify 0 into 0
13.130 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.131 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.131 * [backup-simplify]: Simplify 0 into 0
13.132 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.132 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.132 * [backup-simplify]: Simplify 0 into 0
13.133 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.134 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.134 * [backup-simplify]: Simplify 0 into 0
13.134 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
13.135 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
13.135 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
13.135 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.135 * [taylor]: Taking taylor expansion of -2 in n
13.135 * [backup-simplify]: Simplify -2 into -2
13.135 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.135 * [taylor]: Taking taylor expansion of PI in n
13.135 * [backup-simplify]: Simplify PI into PI
13.135 * [taylor]: Taking taylor expansion of n in n
13.135 * [backup-simplify]: Simplify 0 into 0
13.135 * [backup-simplify]: Simplify 1 into 1
13.135 * [backup-simplify]: Simplify (/ PI 1) into PI
13.135 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.135 * [taylor]: Taking taylor expansion of -2 in n
13.135 * [backup-simplify]: Simplify -2 into -2
13.135 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.135 * [taylor]: Taking taylor expansion of PI in n
13.135 * [backup-simplify]: Simplify PI into PI
13.135 * [taylor]: Taking taylor expansion of n in n
13.135 * [backup-simplify]: Simplify 0 into 0
13.136 * [backup-simplify]: Simplify 1 into 1
13.136 * [backup-simplify]: Simplify (/ PI 1) into PI
13.136 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.137 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.137 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.137 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.138 * [backup-simplify]: Simplify 0 into 0
13.138 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.139 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
13.139 * [backup-simplify]: Simplify 0 into 0
13.139 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.140 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.140 * [backup-simplify]: Simplify 0 into 0
13.141 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.142 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.142 * [backup-simplify]: Simplify 0 into 0
13.142 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.143 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.143 * [backup-simplify]: Simplify 0 into 0
13.144 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.145 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.145 * [backup-simplify]: Simplify 0 into 0
13.145 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
13.145 * * * [progress]: simplifying candidates
13.145 * * * * [progress]: [ 1 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2))))))>
13.145 * * * * [progress]: [ 2 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))))))>
13.145 * * * * [progress]: [ 3 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))))))>
13.145 * * * * [progress]: [ 4 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))))))>
13.145 * * * * [progress]: [ 5 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))))))>
13.145 * * * * [progress]: [ 6 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))))))>
13.146 * * * * [progress]: [ 7 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))))))>
13.146 * * * * [progress]: [ 8 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (/ (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2))))))>
13.146 * * * * [progress]: [ 9 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (cbrt (/ (- 1/2 (/ k 2)) 2))))))>
13.146 * * * * [progress]: [ 10 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2))))))>
13.146 * * * * [progress]: [ 11 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (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))))))>
13.146 * * * * [progress]: [ 12 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2))))))>
13.146 * * * * [progress]: [ 13 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (/ (cbrt (- 1/2 (/ k 2))) 2)))))>
13.146 * * * * [progress]: [ 14 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2))))))>
13.146 * * * * [progress]: [ 15 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))))))>
13.146 * * * * [progress]: [ 16 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2)))))>
13.146 * * * * [progress]: [ 17 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))))))>
13.146 * * * * [progress]: [ 18 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))))))>
13.146 * * * * [progress]: [ 19 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)))))>
13.146 * * * * [progress]: [ 20 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2))))))>
13.146 * * * * [progress]: [ 21 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))))))>
13.146 * * * * [progress]: [ 22 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (/ (- (sqrt 1/2) (sqrt (/ k 2))) 2)))))>
13.146 * * * * [progress]: [ 23 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (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))))))>
13.146 * * * * [progress]: [ 24 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))))))>
13.146 * * * * [progress]: [ 25 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 2)))))>
13.146 * * * * [progress]: [ 26 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))))))>
13.147 * * * * [progress]: [ 27 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))))))>
13.147 * * * * [progress]: [ 28 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)))))>
13.147 * * * * [progress]: [ 29 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)))))>
13.147 * * * * [progress]: [ 30 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
13.147 * * * * [progress]: [ 31 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))))))>
13.147 * * * * [progress]: [ 32 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1))))>
13.147 * * * * [progress]: [ 33 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (exp (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))))>
13.147 * * * * [progress]: [ 34 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (log (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))))>
13.147 * * * * [progress]: [ 35 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (* (* (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)))))))>
13.147 * * * * [progress]: [ 36 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (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)))))))>
13.147 * * * * [progress]: [ 37 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))))>
13.147 * * * * [progress]: [ 38 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (* 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.147 * * * * [progress]: [ 39 / 130 ] 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)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2))))))>
13.147 * * * * [progress]: [ 40 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))))>
13.147 * * * * [progress]: [ 41 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.147 * * * * [progress]: [ 42 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.147 * * * * [progress]: [ 43 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.147 * * * * [progress]: [ 44 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.147 * * * * [progress]: [ 45 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.147 * * * * [progress]: [ 46 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.147 * * * * [progress]: [ 47 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 48 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 49 / 130 ] 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))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 50 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 51 / 130 ] 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))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 52 / 130 ] 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))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 53 / 130 ] 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)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 54 / 130 ] 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))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 55 / 130 ] 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))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 56 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 57 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 58 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 59 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 60 / 130 ] 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))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 61 / 130 ] 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))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 62 / 130 ] 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)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 63 / 130 ] 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))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 64 / 130 ] 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))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 65 / 130 ] 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)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 66 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 67 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.148 * * * * [progress]: [ 68 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 69 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 70 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 71 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 72 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 73 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 74 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 75 / 130 ] 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)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 76 / 130 ] 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)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 77 / 130 ] 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 k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 78 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 79 / 130 ] 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))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 80 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 81 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 82 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 83 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 84 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 85 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 86 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (exp (log (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 87 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (log (exp (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 88 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 89 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 90 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 91 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)))))>
13.149 * * * * [progress]: [ 92 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 93 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 94 / 130 ] 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)))))>
13.150 * * * * [progress]: [ 95 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 96 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 97 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 98 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 99 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (* 2 PI) n) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 100 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 101 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 102 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 103 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 104 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 105 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 106 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 107 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 108 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 109 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 110 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 111 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 112 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 113 / 130 ] 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)))))>
13.150 * * * * [progress]: [ 114 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.150 * * * * [progress]: [ 115 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.151 * * * * [progress]: [ 116 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.151 * * * * [progress]: [ 117 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.151 * * * * [progress]: [ 118 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.151 * * * * [progress]: [ 119 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))))))>
13.151 * * * * [progress]: [ 120 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))>
13.151 * * * * [progress]: [ 121 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))>
13.151 * * * * [progress]: [ 122 / 130 ] 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))))))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.151 * * * * [progress]: [ 123 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.151 * * * * [progress]: [ 124 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.151 * * * * [progress]: [ 125 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.151 * * * * [progress]: [ 126 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.151 * * * * [progress]: [ 127 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.151 * * * * [progress]: [ 128 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.151 * * * * [progress]: [ 129 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.151 * * * * [progress]: [ 130 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.152 * [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)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))
  (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
13.156 * * [simplify]: iteration 1: (161 enodes)
13.217 * * [simplify]: iteration 2: (448 enodes)
13.676 * * [simplify]: iteration 3: (1358 enodes)
14.861 * * [simplify]: Extracting #0: cost 44 inf + 0
14.863 * * [simplify]: Extracting #1: cost 469 inf + 0
14.872 * * [simplify]: Extracting #2: cost 1013 inf + 7693
14.901 * * [simplify]: Extracting #3: cost 1142 inf + 41471
14.966 * * [simplify]: Extracting #4: cost 680 inf + 200624
15.076 * * [simplify]: Extracting #5: cost 267 inf + 387889
15.201 * * [simplify]: Extracting #6: cost 86 inf + 458870
15.343 * * [simplify]: Extracting #7: cost 5 inf + 490985
15.502 * * [simplify]: Extracting #8: cost 0 inf + 491024
15.657 * * [simplify]: Extracting #9: cost 0 inf + 490884
15.790 * [simplify]: Simplified to:
  (* (- 1/4 (/ k 4)) (log (* n (* PI 2))))
  (* (- 1/4 (/ k 4)) (log (* n (* PI 2))))
  (* (- 1/4 (/ k 4)) (log (* n (* PI 2))))
  (* (- 1/4 (/ k 4)) (log (* n (* PI 2))))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (exp (* (log (* n (* PI 2))) 1/4))
  (pow (* n (* PI 2)) (/ k 4))
  (pow (* n (* PI 2)) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4)))))
  (pow (* n (* PI 2)) (sqrt (- 1/4 (/ k 4))))
  (pow (* n (* PI 2)) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))))
  (pow (* n (* PI 2)) (/ (cbrt (- 1/2 (/ k 2))) (/ (sqrt 2) (cbrt (- 1/2 (/ k 2))))))
  (pow (* n (* PI 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* PI 2)) (/ (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* n (* PI 2)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* n (* PI 2)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* PI 2)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* n (* PI 2)) (/ 1 (sqrt 2)))
  (* n (* PI 2))
  (pow (* n (* PI 2)) (/ (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* n (* PI 2)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* n (* PI 2)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* PI 2)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* PI 2)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2)))
  (pow (* n (* PI 2)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* PI 2)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* n (* PI 2)) (/ 1 (sqrt 2)))
  (* n (* PI 2))
  (* n (* PI 2))
  (pow (* n (* PI 2)) (- 1/2 (/ k 2)))
  (pow n (- 1/4 (/ k 4)))
  (pow (* PI 2) (- 1/4 (/ k 4)))
  (* (- 1/4 (/ k 4)) (log (* n (* PI 2))))
  (exp (pow (* n (* PI 2)) (- 1/4 (/ k 4))))
  (* (cbrt (pow (* n (* PI 2)) (- 1/4 (/ k 4)))) (cbrt (pow (* n (* PI 2)) (- 1/4 (/ k 4)))))
  (cbrt (pow (* n (* PI 2)) (- 1/4 (/ k 4))))
  (* (* (pow (* n (* PI 2)) (- 1/4 (/ k 4))) (pow (* n (* PI 2)) (- 1/4 (/ k 4)))) (pow (* n (* PI 2)) (- 1/4 (/ k 4))))
  (fabs (pow (* n (* PI 2)) (- 1/8 (/ k 8))))
  (fabs (pow (* n (* PI 2)) (- 1/8 (/ k 8))))
  (pow (* n (* PI 2)) (- 1/8 (/ k 8)))
  (pow (* n (* PI 2)) (- 1/8 (/ k 8)))
  (real->posit16 (pow (* n (* PI 2)) (- 1/4 (/ k 4))))
  (* (- 1/4 (/ k 4)) (log (* n (* PI 2))))
  (* (- 1/4 (/ k 4)) (log (* n (* PI 2))))
  (* (- 1/4 (/ k 4)) (log (* n (* PI 2))))
  (* (- 1/4 (/ k 4)) (log (* n (* PI 2))))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (exp (* (log (* n (* PI 2))) 1/4))
  (pow (* n (* PI 2)) (/ k 4))
  (pow (* n (* PI 2)) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4)))))
  (pow (* n (* PI 2)) (sqrt (- 1/4 (/ k 4))))
  (pow (* n (* PI 2)) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))))
  (pow (* n (* PI 2)) (/ (cbrt (- 1/2 (/ k 2))) (/ (sqrt 2) (cbrt (- 1/2 (/ k 2))))))
  (pow (* n (* PI 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* PI 2)) (/ (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* n (* PI 2)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* n (* PI 2)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* PI 2)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* n (* PI 2)) (/ 1 (sqrt 2)))
  (* n (* PI 2))
  (pow (* n (* PI 2)) (/ (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* n (* PI 2)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* n (* PI 2)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* PI 2)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* PI 2)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2)))
  (pow (* n (* PI 2)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* PI 2)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* n (* PI 2)) (/ 1 (sqrt 2)))
  (* n (* PI 2))
  (* n (* PI 2))
  (pow (* n (* PI 2)) (- 1/2 (/ k 2)))
  (pow n (- 1/4 (/ k 4)))
  (pow (* PI 2) (- 1/4 (/ k 4)))
  (* (- 1/4 (/ k 4)) (log (* n (* PI 2))))
  (exp (pow (* n (* PI 2)) (- 1/4 (/ k 4))))
  (* (cbrt (pow (* n (* PI 2)) (- 1/4 (/ k 4)))) (cbrt (pow (* n (* PI 2)) (- 1/4 (/ k 4)))))
  (cbrt (pow (* n (* PI 2)) (- 1/4 (/ k 4))))
  (* (* (pow (* n (* PI 2)) (- 1/4 (/ k 4))) (pow (* n (* PI 2)) (- 1/4 (/ k 4)))) (pow (* n (* PI 2)) (- 1/4 (/ k 4))))
  (fabs (pow (* n (* PI 2)) (- 1/8 (/ k 8))))
  (fabs (pow (* n (* PI 2)) (- 1/8 (/ k 8))))
  (pow (* n (* PI 2)) (- 1/8 (/ k 8)))
  (pow (* n (* PI 2)) (- 1/8 (/ k 8)))
  (real->posit16 (pow (* n (* PI 2)) (- 1/4 (/ k 4))))
  (* n (* PI 2))
  (* n (* PI 2))
  (log (* n (* PI 2)))
  (log (* n (* PI 2)))
  (log (* n (* PI 2)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2))))
  (cbrt (* n (* PI 2)))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (sqrt (* n (* PI 2)))
  (sqrt (* n (* PI 2)))
  (* n 2)
  (* (* (cbrt n) PI) 2)
  (* 2 (* PI (sqrt n)))
  (* n (* PI 2))
  (real->posit16 (* n (* PI 2)))
  (* n (* PI 2))
  (* n (* PI 2))
  (log (* n (* PI 2)))
  (log (* n (* PI 2)))
  (log (* n (* PI 2)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2))))
  (cbrt (* n (* PI 2)))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (sqrt (* n (* PI 2)))
  (sqrt (* n (* PI 2)))
  (* n 2)
  (* (* (cbrt n) PI) 2)
  (* 2 (* PI (sqrt n)))
  (* n (* PI 2))
  (real->posit16 (* n (* PI 2)))
  (+ (* (* (exp (* (log (* n (* PI 2))) 1/4)) (+ (* (* k (log n)) (* k (log n))) (* (* k (log (* PI 2))) (* k (log (* PI 2)))))) 1/32) (+ (exp (* (log (* n (* PI 2))) 1/4)) (- (* (* (* (log (* PI 2)) (* k (* (log n) k))) (exp (* (log (* n (* PI 2))) 1/4))) 1/16) (* (* 1/4 k) (* (exp (* (log (* n (* PI 2))) 1/4)) (+ (log n) (log (* PI 2))))))))
  (exp (* (* (- 1/2 (* k 1/2)) 1/2) (log (* n (* PI 2)))))
  (exp (* (* (- 1/2 (* k 1/2)) 1/2) (- (log (* -2 PI)) (log (/ -1 n)))))
  (+ (* (* (exp (* (log (* n (* PI 2))) 1/4)) (+ (* (* k (log n)) (* k (log n))) (* (* k (log (* PI 2))) (* k (log (* PI 2)))))) 1/32) (+ (exp (* (log (* n (* PI 2))) 1/4)) (- (* (* (* (log (* PI 2)) (* k (* (log n) k))) (exp (* (log (* n (* PI 2))) 1/4))) 1/16) (* (* 1/4 k) (* (exp (* (log (* n (* PI 2))) 1/4)) (+ (log n) (log (* PI 2))))))))
  (exp (* (* (- 1/2 (* k 1/2)) 1/2) (log (* n (* PI 2)))))
  (exp (* (* (- 1/2 (* k 1/2)) 1/2) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* n (* PI 2))
  (* n (* PI 2))
  (* n (* PI 2))
  (* n (* PI 2))
  (* n (* PI 2))
  (* n (* PI 2))
15.811 * * * [progress]: adding candidates to table
17.541 * * [progress]: iteration 3 / 4
17.541 * * * [progress]: picking best candidate
17.599 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
17.599 * * * [progress]: localizing error
17.663 * * * [progress]: generating rewritten candidates
17.664 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1)
17.694 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1)
17.719 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1 1)
17.732 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1)
17.750 * * * [progress]: generating series expansions
17.750 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1)
17.751 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
17.751 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
17.751 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
17.751 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
17.751 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
17.751 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
17.751 * [taylor]: Taking taylor expansion of 1/2 in k
17.751 * [backup-simplify]: Simplify 1/2 into 1/2
17.751 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
17.751 * [taylor]: Taking taylor expansion of 1/2 in k
17.751 * [backup-simplify]: Simplify 1/2 into 1/2
17.751 * [taylor]: Taking taylor expansion of k in k
17.751 * [backup-simplify]: Simplify 0 into 0
17.751 * [backup-simplify]: Simplify 1 into 1
17.751 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
17.751 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
17.751 * [taylor]: Taking taylor expansion of 2 in k
17.751 * [backup-simplify]: Simplify 2 into 2
17.751 * [taylor]: Taking taylor expansion of (* n PI) in k
17.751 * [taylor]: Taking taylor expansion of n in k
17.751 * [backup-simplify]: Simplify n into n
17.751 * [taylor]: Taking taylor expansion of PI in k
17.751 * [backup-simplify]: Simplify PI into PI
17.751 * [backup-simplify]: Simplify (* n PI) into (* n PI)
17.751 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
17.751 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
17.751 * [backup-simplify]: Simplify (* 1/2 0) into 0
17.752 * [backup-simplify]: Simplify (- 0) into 0
17.752 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.752 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
17.752 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
17.752 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
17.752 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
17.752 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
17.752 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
17.752 * [taylor]: Taking taylor expansion of 1/2 in n
17.752 * [backup-simplify]: Simplify 1/2 into 1/2
17.752 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
17.752 * [taylor]: Taking taylor expansion of 1/2 in n
17.752 * [backup-simplify]: Simplify 1/2 into 1/2
17.752 * [taylor]: Taking taylor expansion of k in n
17.752 * [backup-simplify]: Simplify k into k
17.752 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
17.752 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.752 * [taylor]: Taking taylor expansion of 2 in n
17.752 * [backup-simplify]: Simplify 2 into 2
17.752 * [taylor]: Taking taylor expansion of (* n PI) in n
17.752 * [taylor]: Taking taylor expansion of n in n
17.752 * [backup-simplify]: Simplify 0 into 0
17.752 * [backup-simplify]: Simplify 1 into 1
17.752 * [taylor]: Taking taylor expansion of PI in n
17.752 * [backup-simplify]: Simplify PI into PI
17.753 * [backup-simplify]: Simplify (* 0 PI) into 0
17.753 * [backup-simplify]: Simplify (* 2 0) into 0
17.754 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.755 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.755 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.756 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
17.756 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
17.756 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
17.756 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.757 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
17.758 * [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)))))
17.758 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
17.758 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
17.758 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
17.758 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
17.758 * [taylor]: Taking taylor expansion of 1/2 in n
17.758 * [backup-simplify]: Simplify 1/2 into 1/2
17.758 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
17.758 * [taylor]: Taking taylor expansion of 1/2 in n
17.758 * [backup-simplify]: Simplify 1/2 into 1/2
17.758 * [taylor]: Taking taylor expansion of k in n
17.758 * [backup-simplify]: Simplify k into k
17.758 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
17.758 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.758 * [taylor]: Taking taylor expansion of 2 in n
17.758 * [backup-simplify]: Simplify 2 into 2
17.758 * [taylor]: Taking taylor expansion of (* n PI) in n
17.758 * [taylor]: Taking taylor expansion of n in n
17.758 * [backup-simplify]: Simplify 0 into 0
17.758 * [backup-simplify]: Simplify 1 into 1
17.758 * [taylor]: Taking taylor expansion of PI in n
17.758 * [backup-simplify]: Simplify PI into PI
17.758 * [backup-simplify]: Simplify (* 0 PI) into 0
17.759 * [backup-simplify]: Simplify (* 2 0) into 0
17.760 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.760 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.761 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.761 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
17.761 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
17.761 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
17.762 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.763 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
17.763 * [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)))))
17.763 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
17.763 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
17.764 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
17.764 * [taylor]: Taking taylor expansion of 1/2 in k
17.764 * [backup-simplify]: Simplify 1/2 into 1/2
17.764 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
17.764 * [taylor]: Taking taylor expansion of 1/2 in k
17.764 * [backup-simplify]: Simplify 1/2 into 1/2
17.764 * [taylor]: Taking taylor expansion of k in k
17.764 * [backup-simplify]: Simplify 0 into 0
17.764 * [backup-simplify]: Simplify 1 into 1
17.764 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
17.764 * [taylor]: Taking taylor expansion of (log n) in k
17.764 * [taylor]: Taking taylor expansion of n in k
17.764 * [backup-simplify]: Simplify n into n
17.764 * [backup-simplify]: Simplify (log n) into (log n)
17.764 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
17.764 * [taylor]: Taking taylor expansion of (* 2 PI) in k
17.764 * [taylor]: Taking taylor expansion of 2 in k
17.764 * [backup-simplify]: Simplify 2 into 2
17.764 * [taylor]: Taking taylor expansion of PI in k
17.764 * [backup-simplify]: Simplify PI into PI
17.764 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.765 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.765 * [backup-simplify]: Simplify (* 1/2 0) into 0
17.765 * [backup-simplify]: Simplify (- 0) into 0
17.765 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.766 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.767 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
17.767 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
17.768 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
17.769 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
17.769 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
17.770 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.770 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
17.771 * [backup-simplify]: Simplify (- 0) into 0
17.771 * [backup-simplify]: Simplify (+ 0 0) into 0
17.772 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.772 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
17.773 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
17.773 * [taylor]: Taking taylor expansion of 0 in k
17.774 * [backup-simplify]: Simplify 0 into 0
17.774 * [backup-simplify]: Simplify 0 into 0
17.774 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
17.774 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.775 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.776 * [backup-simplify]: Simplify (+ 0 0) into 0
17.776 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
17.776 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.777 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.777 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
17.779 * [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)))))))
17.781 * [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)))))))
17.782 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
17.783 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
17.784 * [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
17.785 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
17.785 * [backup-simplify]: Simplify (- 0) into 0
17.785 * [backup-simplify]: Simplify (+ 0 0) into 0
17.786 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.787 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
17.789 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.789 * [taylor]: Taking taylor expansion of 0 in k
17.789 * [backup-simplify]: Simplify 0 into 0
17.789 * [backup-simplify]: Simplify 0 into 0
17.789 * [backup-simplify]: Simplify 0 into 0
17.790 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
17.790 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.792 * [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
17.792 * [backup-simplify]: Simplify (+ 0 0) into 0
17.793 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
17.793 * [backup-simplify]: Simplify (- 0) into 0
17.794 * [backup-simplify]: Simplify (+ 0 0) into 0
17.795 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
17.799 * [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)))))
17.804 * [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)))))
17.813 * [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)))))
17.814 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
17.814 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
17.814 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
17.814 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
17.814 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
17.814 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
17.814 * [taylor]: Taking taylor expansion of 1/2 in k
17.814 * [backup-simplify]: Simplify 1/2 into 1/2
17.814 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.814 * [taylor]: Taking taylor expansion of 1/2 in k
17.814 * [backup-simplify]: Simplify 1/2 into 1/2
17.814 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.814 * [taylor]: Taking taylor expansion of k in k
17.814 * [backup-simplify]: Simplify 0 into 0
17.814 * [backup-simplify]: Simplify 1 into 1
17.815 * [backup-simplify]: Simplify (/ 1 1) into 1
17.815 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
17.815 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
17.815 * [taylor]: Taking taylor expansion of 2 in k
17.815 * [backup-simplify]: Simplify 2 into 2
17.815 * [taylor]: Taking taylor expansion of (/ PI n) in k
17.815 * [taylor]: Taking taylor expansion of PI in k
17.815 * [backup-simplify]: Simplify PI into PI
17.815 * [taylor]: Taking taylor expansion of n in k
17.815 * [backup-simplify]: Simplify n into n
17.815 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
17.815 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
17.815 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
17.816 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.816 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.816 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.816 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
17.817 * [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))))
17.817 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
17.817 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
17.817 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
17.817 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
17.817 * [taylor]: Taking taylor expansion of 1/2 in n
17.817 * [backup-simplify]: Simplify 1/2 into 1/2
17.817 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.817 * [taylor]: Taking taylor expansion of 1/2 in n
17.817 * [backup-simplify]: Simplify 1/2 into 1/2
17.817 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.817 * [taylor]: Taking taylor expansion of k in n
17.817 * [backup-simplify]: Simplify k into k
17.817 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.817 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
17.817 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.817 * [taylor]: Taking taylor expansion of 2 in n
17.817 * [backup-simplify]: Simplify 2 into 2
17.817 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.817 * [taylor]: Taking taylor expansion of PI in n
17.817 * [backup-simplify]: Simplify PI into PI
17.817 * [taylor]: Taking taylor expansion of n in n
17.817 * [backup-simplify]: Simplify 0 into 0
17.817 * [backup-simplify]: Simplify 1 into 1
17.818 * [backup-simplify]: Simplify (/ PI 1) into PI
17.818 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.819 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.819 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.819 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
17.819 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
17.821 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.822 * [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)))
17.823 * [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))))
17.823 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
17.823 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
17.823 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
17.823 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
17.823 * [taylor]: Taking taylor expansion of 1/2 in n
17.823 * [backup-simplify]: Simplify 1/2 into 1/2
17.823 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.823 * [taylor]: Taking taylor expansion of 1/2 in n
17.823 * [backup-simplify]: Simplify 1/2 into 1/2
17.823 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.823 * [taylor]: Taking taylor expansion of k in n
17.823 * [backup-simplify]: Simplify k into k
17.823 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.823 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
17.823 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.824 * [taylor]: Taking taylor expansion of 2 in n
17.824 * [backup-simplify]: Simplify 2 into 2
17.824 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.824 * [taylor]: Taking taylor expansion of PI in n
17.824 * [backup-simplify]: Simplify PI into PI
17.824 * [taylor]: Taking taylor expansion of n in n
17.824 * [backup-simplify]: Simplify 0 into 0
17.824 * [backup-simplify]: Simplify 1 into 1
17.824 * [backup-simplify]: Simplify (/ PI 1) into PI
17.825 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.826 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.826 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.826 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
17.826 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
17.827 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.828 * [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)))
17.829 * [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))))
17.829 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
17.829 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
17.829 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
17.829 * [taylor]: Taking taylor expansion of 1/2 in k
17.829 * [backup-simplify]: Simplify 1/2 into 1/2
17.829 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.830 * [taylor]: Taking taylor expansion of 1/2 in k
17.830 * [backup-simplify]: Simplify 1/2 into 1/2
17.830 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.830 * [taylor]: Taking taylor expansion of k in k
17.830 * [backup-simplify]: Simplify 0 into 0
17.830 * [backup-simplify]: Simplify 1 into 1
17.830 * [backup-simplify]: Simplify (/ 1 1) into 1
17.830 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
17.830 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
17.830 * [taylor]: Taking taylor expansion of (* 2 PI) in k
17.830 * [taylor]: Taking taylor expansion of 2 in k
17.830 * [backup-simplify]: Simplify 2 into 2
17.830 * [taylor]: Taking taylor expansion of PI in k
17.830 * [backup-simplify]: Simplify PI into PI
17.831 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.832 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.832 * [taylor]: Taking taylor expansion of (log n) in k
17.832 * [taylor]: Taking taylor expansion of n in k
17.832 * [backup-simplify]: Simplify n into n
17.832 * [backup-simplify]: Simplify (log n) into (log n)
17.832 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.833 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.833 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.833 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.834 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
17.835 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
17.836 * [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))))
17.838 * [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))))
17.839 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.839 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.841 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.841 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.842 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
17.848 * [backup-simplify]: Simplify (- 0) into 0
17.849 * [backup-simplify]: Simplify (+ 0 0) into 0
17.850 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.851 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
17.854 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
17.854 * [taylor]: Taking taylor expansion of 0 in k
17.854 * [backup-simplify]: Simplify 0 into 0
17.854 * [backup-simplify]: Simplify 0 into 0
17.854 * [backup-simplify]: Simplify 0 into 0
17.855 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.856 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.860 * [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
17.860 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.861 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
17.861 * [backup-simplify]: Simplify (- 0) into 0
17.862 * [backup-simplify]: Simplify (+ 0 0) into 0
17.863 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.864 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
17.867 * [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
17.867 * [taylor]: Taking taylor expansion of 0 in k
17.867 * [backup-simplify]: Simplify 0 into 0
17.867 * [backup-simplify]: Simplify 0 into 0
17.867 * [backup-simplify]: Simplify 0 into 0
17.867 * [backup-simplify]: Simplify 0 into 0
17.868 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.869 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.875 * [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
17.875 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.876 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
17.877 * [backup-simplify]: Simplify (- 0) into 0
17.877 * [backup-simplify]: Simplify (+ 0 0) into 0
17.878 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.881 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
17.884 * [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
17.884 * [taylor]: Taking taylor expansion of 0 in k
17.884 * [backup-simplify]: Simplify 0 into 0
17.884 * [backup-simplify]: Simplify 0 into 0
17.885 * [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)))))
17.886 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
17.886 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
17.886 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
17.886 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
17.886 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
17.886 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
17.886 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.886 * [taylor]: Taking taylor expansion of 1/2 in k
17.886 * [backup-simplify]: Simplify 1/2 into 1/2
17.886 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.886 * [taylor]: Taking taylor expansion of k in k
17.886 * [backup-simplify]: Simplify 0 into 0
17.886 * [backup-simplify]: Simplify 1 into 1
17.886 * [backup-simplify]: Simplify (/ 1 1) into 1
17.887 * [taylor]: Taking taylor expansion of 1/2 in k
17.887 * [backup-simplify]: Simplify 1/2 into 1/2
17.887 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
17.887 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
17.887 * [taylor]: Taking taylor expansion of -2 in k
17.887 * [backup-simplify]: Simplify -2 into -2
17.887 * [taylor]: Taking taylor expansion of (/ PI n) in k
17.887 * [taylor]: Taking taylor expansion of PI in k
17.887 * [backup-simplify]: Simplify PI into PI
17.887 * [taylor]: Taking taylor expansion of n in k
17.887 * [backup-simplify]: Simplify n into n
17.887 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
17.887 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
17.887 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
17.887 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.888 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.888 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
17.888 * [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)))
17.888 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
17.888 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
17.888 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
17.888 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
17.888 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.888 * [taylor]: Taking taylor expansion of 1/2 in n
17.889 * [backup-simplify]: Simplify 1/2 into 1/2
17.889 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.889 * [taylor]: Taking taylor expansion of k in n
17.889 * [backup-simplify]: Simplify k into k
17.889 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.889 * [taylor]: Taking taylor expansion of 1/2 in n
17.889 * [backup-simplify]: Simplify 1/2 into 1/2
17.889 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
17.889 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.889 * [taylor]: Taking taylor expansion of -2 in n
17.889 * [backup-simplify]: Simplify -2 into -2
17.889 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.889 * [taylor]: Taking taylor expansion of PI in n
17.889 * [backup-simplify]: Simplify PI into PI
17.889 * [taylor]: Taking taylor expansion of n in n
17.889 * [backup-simplify]: Simplify 0 into 0
17.889 * [backup-simplify]: Simplify 1 into 1
17.889 * [backup-simplify]: Simplify (/ PI 1) into PI
17.890 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.891 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.891 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.891 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
17.892 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.893 * [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)))
17.894 * [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))))
17.895 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
17.895 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
17.895 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
17.895 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
17.895 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.895 * [taylor]: Taking taylor expansion of 1/2 in n
17.895 * [backup-simplify]: Simplify 1/2 into 1/2
17.895 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.895 * [taylor]: Taking taylor expansion of k in n
17.895 * [backup-simplify]: Simplify k into k
17.895 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.895 * [taylor]: Taking taylor expansion of 1/2 in n
17.895 * [backup-simplify]: Simplify 1/2 into 1/2
17.895 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
17.895 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.895 * [taylor]: Taking taylor expansion of -2 in n
17.895 * [backup-simplify]: Simplify -2 into -2
17.895 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.895 * [taylor]: Taking taylor expansion of PI in n
17.895 * [backup-simplify]: Simplify PI into PI
17.895 * [taylor]: Taking taylor expansion of n in n
17.895 * [backup-simplify]: Simplify 0 into 0
17.895 * [backup-simplify]: Simplify 1 into 1
17.896 * [backup-simplify]: Simplify (/ PI 1) into PI
17.896 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.897 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.897 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.897 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
17.899 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.900 * [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)))
17.901 * [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))))
17.901 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
17.901 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
17.901 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
17.901 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.901 * [taylor]: Taking taylor expansion of 1/2 in k
17.901 * [backup-simplify]: Simplify 1/2 into 1/2
17.901 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.901 * [taylor]: Taking taylor expansion of k in k
17.901 * [backup-simplify]: Simplify 0 into 0
17.901 * [backup-simplify]: Simplify 1 into 1
17.902 * [backup-simplify]: Simplify (/ 1 1) into 1
17.902 * [taylor]: Taking taylor expansion of 1/2 in k
17.902 * [backup-simplify]: Simplify 1/2 into 1/2
17.902 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
17.902 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
17.902 * [taylor]: Taking taylor expansion of (* -2 PI) in k
17.902 * [taylor]: Taking taylor expansion of -2 in k
17.902 * [backup-simplify]: Simplify -2 into -2
17.902 * [taylor]: Taking taylor expansion of PI in k
17.902 * [backup-simplify]: Simplify PI into PI
17.902 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.903 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.903 * [taylor]: Taking taylor expansion of (log n) in k
17.903 * [taylor]: Taking taylor expansion of n in k
17.903 * [backup-simplify]: Simplify n into n
17.903 * [backup-simplify]: Simplify (log n) into (log n)
17.904 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.904 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.904 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.905 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
17.906 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
17.907 * [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))))
17.908 * [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))))
17.909 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.910 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
17.912 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
17.912 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.912 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
17.913 * [backup-simplify]: Simplify (+ 0 0) into 0
17.914 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.915 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
17.917 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
17.917 * [taylor]: Taking taylor expansion of 0 in k
17.917 * [backup-simplify]: Simplify 0 into 0
17.917 * [backup-simplify]: Simplify 0 into 0
17.917 * [backup-simplify]: Simplify 0 into 0
17.918 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.919 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
17.923 * [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
17.923 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.924 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
17.925 * [backup-simplify]: Simplify (+ 0 0) into 0
17.926 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.927 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
17.930 * [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
17.930 * [taylor]: Taking taylor expansion of 0 in k
17.930 * [backup-simplify]: Simplify 0 into 0
17.930 * [backup-simplify]: Simplify 0 into 0
17.930 * [backup-simplify]: Simplify 0 into 0
17.930 * [backup-simplify]: Simplify 0 into 0
17.931 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.933 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.939 * [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
17.939 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.940 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
17.941 * [backup-simplify]: Simplify (+ 0 0) into 0
17.942 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.944 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
17.946 * [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
17.946 * [taylor]: Taking taylor expansion of 0 in k
17.946 * [backup-simplify]: Simplify 0 into 0
17.946 * [backup-simplify]: Simplify 0 into 0
17.948 * [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)))))
17.948 * * * * [progress]: [ 2 / 4 ] generating series at (2 1)
17.948 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))
17.948 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
17.948 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
17.948 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
17.948 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
17.948 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
17.948 * [taylor]: Taking taylor expansion of 1/2 in k
17.948 * [backup-simplify]: Simplify 1/2 into 1/2
17.949 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
17.949 * [taylor]: Taking taylor expansion of 1/2 in k
17.949 * [backup-simplify]: Simplify 1/2 into 1/2
17.949 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
17.949 * [taylor]: Taking taylor expansion of 1/2 in k
17.949 * [backup-simplify]: Simplify 1/2 into 1/2
17.949 * [taylor]: Taking taylor expansion of k in k
17.949 * [backup-simplify]: Simplify 0 into 0
17.949 * [backup-simplify]: Simplify 1 into 1
17.949 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
17.949 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
17.949 * [taylor]: Taking taylor expansion of 2 in k
17.949 * [backup-simplify]: Simplify 2 into 2
17.949 * [taylor]: Taking taylor expansion of (* n PI) in k
17.949 * [taylor]: Taking taylor expansion of n in k
17.949 * [backup-simplify]: Simplify n into n
17.949 * [taylor]: Taking taylor expansion of PI in k
17.949 * [backup-simplify]: Simplify PI into PI
17.949 * [backup-simplify]: Simplify (* n PI) into (* n PI)
17.949 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
17.949 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
17.950 * [backup-simplify]: Simplify (* 1/2 0) into 0
17.950 * [backup-simplify]: Simplify (- 0) into 0
17.951 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.951 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
17.951 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
17.951 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
17.951 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
17.951 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
17.951 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
17.951 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
17.951 * [taylor]: Taking taylor expansion of 1/2 in n
17.951 * [backup-simplify]: Simplify 1/2 into 1/2
17.951 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
17.951 * [taylor]: Taking taylor expansion of 1/2 in n
17.951 * [backup-simplify]: Simplify 1/2 into 1/2
17.951 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
17.952 * [taylor]: Taking taylor expansion of 1/2 in n
17.952 * [backup-simplify]: Simplify 1/2 into 1/2
17.952 * [taylor]: Taking taylor expansion of k in n
17.952 * [backup-simplify]: Simplify k into k
17.952 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
17.952 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.952 * [taylor]: Taking taylor expansion of 2 in n
17.952 * [backup-simplify]: Simplify 2 into 2
17.952 * [taylor]: Taking taylor expansion of (* n PI) in n
17.952 * [taylor]: Taking taylor expansion of n in n
17.952 * [backup-simplify]: Simplify 0 into 0
17.952 * [backup-simplify]: Simplify 1 into 1
17.952 * [taylor]: Taking taylor expansion of PI in n
17.952 * [backup-simplify]: Simplify PI into PI
17.952 * [backup-simplify]: Simplify (* 0 PI) into 0
17.953 * [backup-simplify]: Simplify (* 2 0) into 0
17.954 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.956 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.957 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.957 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
17.957 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
17.958 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
17.958 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
17.959 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.960 * [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)))))
17.962 * [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))))))
17.962 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
17.962 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
17.962 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
17.962 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
17.962 * [taylor]: Taking taylor expansion of 1/2 in n
17.962 * [backup-simplify]: Simplify 1/2 into 1/2
17.962 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
17.962 * [taylor]: Taking taylor expansion of 1/2 in n
17.962 * [backup-simplify]: Simplify 1/2 into 1/2
17.962 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
17.962 * [taylor]: Taking taylor expansion of 1/2 in n
17.962 * [backup-simplify]: Simplify 1/2 into 1/2
17.962 * [taylor]: Taking taylor expansion of k in n
17.962 * [backup-simplify]: Simplify k into k
17.962 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
17.962 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.962 * [taylor]: Taking taylor expansion of 2 in n
17.962 * [backup-simplify]: Simplify 2 into 2
17.962 * [taylor]: Taking taylor expansion of (* n PI) in n
17.962 * [taylor]: Taking taylor expansion of n in n
17.962 * [backup-simplify]: Simplify 0 into 0
17.962 * [backup-simplify]: Simplify 1 into 1
17.962 * [taylor]: Taking taylor expansion of PI in n
17.962 * [backup-simplify]: Simplify PI into PI
17.963 * [backup-simplify]: Simplify (* 0 PI) into 0
17.963 * [backup-simplify]: Simplify (* 2 0) into 0
17.965 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.967 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.968 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.968 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
17.968 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
17.968 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
17.968 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
17.970 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.971 * [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)))))
17.972 * [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))))))
17.973 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
17.973 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
17.973 * [taylor]: Taking taylor expansion of 1/2 in k
17.973 * [backup-simplify]: Simplify 1/2 into 1/2
17.973 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
17.973 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
17.973 * [taylor]: Taking taylor expansion of 1/2 in k
17.973 * [backup-simplify]: Simplify 1/2 into 1/2
17.973 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
17.973 * [taylor]: Taking taylor expansion of 1/2 in k
17.973 * [backup-simplify]: Simplify 1/2 into 1/2
17.973 * [taylor]: Taking taylor expansion of k in k
17.973 * [backup-simplify]: Simplify 0 into 0
17.973 * [backup-simplify]: Simplify 1 into 1
17.973 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
17.973 * [taylor]: Taking taylor expansion of (log n) in k
17.973 * [taylor]: Taking taylor expansion of n in k
17.973 * [backup-simplify]: Simplify n into n
17.973 * [backup-simplify]: Simplify (log n) into (log n)
17.973 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
17.973 * [taylor]: Taking taylor expansion of (* 2 PI) in k
17.973 * [taylor]: Taking taylor expansion of 2 in k
17.973 * [backup-simplify]: Simplify 2 into 2
17.973 * [taylor]: Taking taylor expansion of PI in k
17.973 * [backup-simplify]: Simplify PI into PI
17.974 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.975 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.975 * [backup-simplify]: Simplify (* 1/2 0) into 0
17.976 * [backup-simplify]: Simplify (- 0) into 0
17.976 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.977 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.978 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
17.979 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
17.980 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
17.981 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
17.982 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
17.983 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
17.985 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.986 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
17.986 * [backup-simplify]: Simplify (- 0) into 0
17.986 * [backup-simplify]: Simplify (+ 0 0) into 0
17.987 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
17.988 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.989 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
17.991 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
17.991 * [taylor]: Taking taylor expansion of 0 in k
17.991 * [backup-simplify]: Simplify 0 into 0
17.991 * [backup-simplify]: Simplify 0 into 0
17.996 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
17.997 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.998 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.998 * [backup-simplify]: Simplify (+ 0 0) into 0
17.999 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
17.999 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.999 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
18.000 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
18.002 * [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)))))
18.004 * [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)))))))
18.006 * [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)))))))
18.006 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
18.007 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
18.009 * [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
18.009 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
18.010 * [backup-simplify]: Simplify (- 0) into 0
18.010 * [backup-simplify]: Simplify (+ 0 0) into 0
18.010 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
18.011 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
18.012 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
18.014 * [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
18.014 * [taylor]: Taking taylor expansion of 0 in k
18.014 * [backup-simplify]: Simplify 0 into 0
18.014 * [backup-simplify]: Simplify 0 into 0
18.014 * [backup-simplify]: Simplify 0 into 0
18.015 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
18.015 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
18.017 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
18.017 * [backup-simplify]: Simplify (+ 0 0) into 0
18.018 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
18.018 * [backup-simplify]: Simplify (- 0) into 0
18.018 * [backup-simplify]: Simplify (+ 0 0) into 0
18.020 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
18.023 * [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
18.027 * [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)))))
18.032 * [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)))))
18.041 * [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)))))))
18.042 * [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)))))
18.042 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
18.042 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
18.042 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
18.042 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
18.042 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
18.042 * [taylor]: Taking taylor expansion of 1/2 in k
18.042 * [backup-simplify]: Simplify 1/2 into 1/2
18.042 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
18.042 * [taylor]: Taking taylor expansion of 1/2 in k
18.042 * [backup-simplify]: Simplify 1/2 into 1/2
18.043 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
18.043 * [taylor]: Taking taylor expansion of 1/2 in k
18.043 * [backup-simplify]: Simplify 1/2 into 1/2
18.043 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.043 * [taylor]: Taking taylor expansion of k in k
18.043 * [backup-simplify]: Simplify 0 into 0
18.043 * [backup-simplify]: Simplify 1 into 1
18.043 * [backup-simplify]: Simplify (/ 1 1) into 1
18.043 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
18.043 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
18.043 * [taylor]: Taking taylor expansion of 2 in k
18.043 * [backup-simplify]: Simplify 2 into 2
18.043 * [taylor]: Taking taylor expansion of (/ PI n) in k
18.043 * [taylor]: Taking taylor expansion of PI in k
18.043 * [backup-simplify]: Simplify PI into PI
18.043 * [taylor]: Taking taylor expansion of n in k
18.043 * [backup-simplify]: Simplify n into n
18.043 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
18.043 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
18.044 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
18.044 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
18.044 * [backup-simplify]: Simplify (- 1/2) into -1/2
18.045 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
18.045 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
18.045 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
18.046 * [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))))))
18.046 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
18.046 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
18.046 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
18.046 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
18.046 * [taylor]: Taking taylor expansion of 1/2 in n
18.046 * [backup-simplify]: Simplify 1/2 into 1/2
18.046 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
18.046 * [taylor]: Taking taylor expansion of 1/2 in n
18.046 * [backup-simplify]: Simplify 1/2 into 1/2
18.046 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
18.046 * [taylor]: Taking taylor expansion of 1/2 in n
18.046 * [backup-simplify]: Simplify 1/2 into 1/2
18.046 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.046 * [taylor]: Taking taylor expansion of k in n
18.046 * [backup-simplify]: Simplify k into k
18.046 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.046 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
18.046 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
18.046 * [taylor]: Taking taylor expansion of 2 in n
18.046 * [backup-simplify]: Simplify 2 into 2
18.046 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.046 * [taylor]: Taking taylor expansion of PI in n
18.046 * [backup-simplify]: Simplify PI into PI
18.046 * [taylor]: Taking taylor expansion of n in n
18.046 * [backup-simplify]: Simplify 0 into 0
18.046 * [backup-simplify]: Simplify 1 into 1
18.047 * [backup-simplify]: Simplify (/ PI 1) into PI
18.048 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.048 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
18.049 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
18.049 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
18.049 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
18.049 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
18.050 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
18.051 * [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))))
18.052 * [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)))))
18.052 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
18.052 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
18.052 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
18.052 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
18.052 * [taylor]: Taking taylor expansion of 1/2 in n
18.052 * [backup-simplify]: Simplify 1/2 into 1/2
18.052 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
18.052 * [taylor]: Taking taylor expansion of 1/2 in n
18.052 * [backup-simplify]: Simplify 1/2 into 1/2
18.053 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
18.053 * [taylor]: Taking taylor expansion of 1/2 in n
18.053 * [backup-simplify]: Simplify 1/2 into 1/2
18.053 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.053 * [taylor]: Taking taylor expansion of k in n
18.053 * [backup-simplify]: Simplify k into k
18.053 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.053 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
18.053 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
18.053 * [taylor]: Taking taylor expansion of 2 in n
18.053 * [backup-simplify]: Simplify 2 into 2
18.053 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.053 * [taylor]: Taking taylor expansion of PI in n
18.053 * [backup-simplify]: Simplify PI into PI
18.053 * [taylor]: Taking taylor expansion of n in n
18.053 * [backup-simplify]: Simplify 0 into 0
18.053 * [backup-simplify]: Simplify 1 into 1
18.054 * [backup-simplify]: Simplify (/ PI 1) into PI
18.054 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.055 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
18.055 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
18.055 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
18.055 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
18.055 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
18.057 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
18.058 * [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))))
18.059 * [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)))))
18.059 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
18.059 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
18.059 * [taylor]: Taking taylor expansion of 1/2 in k
18.059 * [backup-simplify]: Simplify 1/2 into 1/2
18.059 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
18.059 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
18.059 * [taylor]: Taking taylor expansion of 1/2 in k
18.059 * [backup-simplify]: Simplify 1/2 into 1/2
18.059 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
18.059 * [taylor]: Taking taylor expansion of 1/2 in k
18.059 * [backup-simplify]: Simplify 1/2 into 1/2
18.059 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.059 * [taylor]: Taking taylor expansion of k in k
18.059 * [backup-simplify]: Simplify 0 into 0
18.059 * [backup-simplify]: Simplify 1 into 1
18.060 * [backup-simplify]: Simplify (/ 1 1) into 1
18.060 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
18.060 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
18.060 * [taylor]: Taking taylor expansion of (* 2 PI) in k
18.060 * [taylor]: Taking taylor expansion of 2 in k
18.060 * [backup-simplify]: Simplify 2 into 2
18.060 * [taylor]: Taking taylor expansion of PI in k
18.060 * [backup-simplify]: Simplify PI into PI
18.060 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.061 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
18.061 * [taylor]: Taking taylor expansion of (log n) in k
18.061 * [taylor]: Taking taylor expansion of n in k
18.062 * [backup-simplify]: Simplify n into n
18.062 * [backup-simplify]: Simplify (log n) into (log n)
18.062 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
18.062 * [backup-simplify]: Simplify (- 1/2) into -1/2
18.063 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
18.063 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
18.064 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
18.065 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
18.066 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
18.067 * [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)))))
18.069 * [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)))))
18.070 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.071 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
18.072 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
18.073 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
18.073 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
18.074 * [backup-simplify]: Simplify (- 0) into 0
18.074 * [backup-simplify]: Simplify (+ 0 0) into 0
18.074 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
18.076 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
18.077 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
18.079 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
18.079 * [taylor]: Taking taylor expansion of 0 in k
18.079 * [backup-simplify]: Simplify 0 into 0
18.079 * [backup-simplify]: Simplify 0 into 0
18.079 * [backup-simplify]: Simplify 0 into 0
18.080 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.082 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
18.085 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
18.085 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.086 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
18.086 * [backup-simplify]: Simplify (- 0) into 0
18.087 * [backup-simplify]: Simplify (+ 0 0) into 0
18.088 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
18.089 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
18.091 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
18.093 * [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
18.093 * [taylor]: Taking taylor expansion of 0 in k
18.093 * [backup-simplify]: Simplify 0 into 0
18.093 * [backup-simplify]: Simplify 0 into 0
18.093 * [backup-simplify]: Simplify 0 into 0
18.093 * [backup-simplify]: Simplify 0 into 0
18.095 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.096 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.102 * [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
18.102 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.104 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
18.104 * [backup-simplify]: Simplify (- 0) into 0
18.104 * [backup-simplify]: Simplify (+ 0 0) into 0
18.107 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
18.109 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
18.110 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
18.113 * [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
18.113 * [taylor]: Taking taylor expansion of 0 in k
18.113 * [backup-simplify]: Simplify 0 into 0
18.113 * [backup-simplify]: Simplify 0 into 0
18.114 * [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))))))
18.115 * [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)))
18.115 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
18.115 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
18.115 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
18.115 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
18.115 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
18.115 * [taylor]: Taking taylor expansion of 1/2 in k
18.115 * [backup-simplify]: Simplify 1/2 into 1/2
18.115 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
18.115 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
18.115 * [taylor]: Taking taylor expansion of 1/2 in k
18.116 * [backup-simplify]: Simplify 1/2 into 1/2
18.116 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.116 * [taylor]: Taking taylor expansion of k in k
18.116 * [backup-simplify]: Simplify 0 into 0
18.116 * [backup-simplify]: Simplify 1 into 1
18.116 * [backup-simplify]: Simplify (/ 1 1) into 1
18.116 * [taylor]: Taking taylor expansion of 1/2 in k
18.116 * [backup-simplify]: Simplify 1/2 into 1/2
18.116 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
18.116 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
18.116 * [taylor]: Taking taylor expansion of -2 in k
18.116 * [backup-simplify]: Simplify -2 into -2
18.116 * [taylor]: Taking taylor expansion of (/ PI n) in k
18.116 * [taylor]: Taking taylor expansion of PI in k
18.116 * [backup-simplify]: Simplify PI into PI
18.116 * [taylor]: Taking taylor expansion of n in k
18.116 * [backup-simplify]: Simplify n into n
18.116 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
18.116 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
18.117 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
18.117 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
18.117 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
18.118 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
18.118 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
18.118 * [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))))
18.118 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
18.118 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
18.118 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
18.118 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
18.118 * [taylor]: Taking taylor expansion of 1/2 in n
18.118 * [backup-simplify]: Simplify 1/2 into 1/2
18.118 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
18.118 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
18.118 * [taylor]: Taking taylor expansion of 1/2 in n
18.118 * [backup-simplify]: Simplify 1/2 into 1/2
18.118 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.118 * [taylor]: Taking taylor expansion of k in n
18.119 * [backup-simplify]: Simplify k into k
18.119 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.119 * [taylor]: Taking taylor expansion of 1/2 in n
18.119 * [backup-simplify]: Simplify 1/2 into 1/2
18.119 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
18.119 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
18.119 * [taylor]: Taking taylor expansion of -2 in n
18.119 * [backup-simplify]: Simplify -2 into -2
18.119 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.119 * [taylor]: Taking taylor expansion of PI in n
18.119 * [backup-simplify]: Simplify PI into PI
18.119 * [taylor]: Taking taylor expansion of n in n
18.119 * [backup-simplify]: Simplify 0 into 0
18.119 * [backup-simplify]: Simplify 1 into 1
18.119 * [backup-simplify]: Simplify (/ PI 1) into PI
18.120 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
18.121 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
18.121 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
18.121 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
18.121 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
18.123 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
18.130 * [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))))
18.132 * [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)))))
18.132 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
18.132 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
18.132 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
18.132 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
18.132 * [taylor]: Taking taylor expansion of 1/2 in n
18.132 * [backup-simplify]: Simplify 1/2 into 1/2
18.132 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
18.132 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
18.132 * [taylor]: Taking taylor expansion of 1/2 in n
18.132 * [backup-simplify]: Simplify 1/2 into 1/2
18.132 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.132 * [taylor]: Taking taylor expansion of k in n
18.132 * [backup-simplify]: Simplify k into k
18.132 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.132 * [taylor]: Taking taylor expansion of 1/2 in n
18.132 * [backup-simplify]: Simplify 1/2 into 1/2
18.132 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
18.132 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
18.132 * [taylor]: Taking taylor expansion of -2 in n
18.132 * [backup-simplify]: Simplify -2 into -2
18.132 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.132 * [taylor]: Taking taylor expansion of PI in n
18.132 * [backup-simplify]: Simplify PI into PI
18.132 * [taylor]: Taking taylor expansion of n in n
18.132 * [backup-simplify]: Simplify 0 into 0
18.132 * [backup-simplify]: Simplify 1 into 1
18.133 * [backup-simplify]: Simplify (/ PI 1) into PI
18.133 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
18.134 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
18.134 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
18.135 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
18.135 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
18.136 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
18.138 * [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))))
18.139 * [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)))))
18.139 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
18.139 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
18.139 * [taylor]: Taking taylor expansion of 1/2 in k
18.139 * [backup-simplify]: Simplify 1/2 into 1/2
18.139 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
18.139 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
18.139 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
18.139 * [taylor]: Taking taylor expansion of 1/2 in k
18.139 * [backup-simplify]: Simplify 1/2 into 1/2
18.140 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.140 * [taylor]: Taking taylor expansion of k in k
18.140 * [backup-simplify]: Simplify 0 into 0
18.140 * [backup-simplify]: Simplify 1 into 1
18.140 * [backup-simplify]: Simplify (/ 1 1) into 1
18.140 * [taylor]: Taking taylor expansion of 1/2 in k
18.140 * [backup-simplify]: Simplify 1/2 into 1/2
18.140 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
18.140 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
18.141 * [taylor]: Taking taylor expansion of (* -2 PI) in k
18.141 * [taylor]: Taking taylor expansion of -2 in k
18.141 * [backup-simplify]: Simplify -2 into -2
18.141 * [taylor]: Taking taylor expansion of PI in k
18.141 * [backup-simplify]: Simplify PI into PI
18.141 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
18.142 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
18.142 * [taylor]: Taking taylor expansion of (log n) in k
18.142 * [taylor]: Taking taylor expansion of n in k
18.142 * [backup-simplify]: Simplify n into n
18.142 * [backup-simplify]: Simplify (log n) into (log n)
18.143 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
18.143 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
18.143 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
18.144 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
18.145 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
18.146 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
18.146 * [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)))))
18.147 * [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)))))
18.148 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.148 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
18.149 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
18.149 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
18.150 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
18.150 * [backup-simplify]: Simplify (+ 0 0) into 0
18.150 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
18.151 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
18.152 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
18.153 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
18.153 * [taylor]: Taking taylor expansion of 0 in k
18.153 * [backup-simplify]: Simplify 0 into 0
18.153 * [backup-simplify]: Simplify 0 into 0
18.153 * [backup-simplify]: Simplify 0 into 0
18.153 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.154 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
18.156 * [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
18.156 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.156 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
18.157 * [backup-simplify]: Simplify (+ 0 0) into 0
18.157 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
18.158 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
18.159 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
18.160 * [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
18.160 * [taylor]: Taking taylor expansion of 0 in k
18.160 * [backup-simplify]: Simplify 0 into 0
18.161 * [backup-simplify]: Simplify 0 into 0
18.161 * [backup-simplify]: Simplify 0 into 0
18.161 * [backup-simplify]: Simplify 0 into 0
18.161 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.162 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.165 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
18.165 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.166 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
18.166 * [backup-simplify]: Simplify (+ 0 0) into 0
18.167 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
18.168 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
18.169 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
18.170 * [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
18.170 * [taylor]: Taking taylor expansion of 0 in k
18.170 * [backup-simplify]: Simplify 0 into 0
18.170 * [backup-simplify]: Simplify 0 into 0
18.171 * [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))))))
18.171 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1 1)
18.172 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
18.172 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
18.172 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
18.172 * [taylor]: Taking taylor expansion of 2 in n
18.172 * [backup-simplify]: Simplify 2 into 2
18.172 * [taylor]: Taking taylor expansion of (* n PI) in n
18.172 * [taylor]: Taking taylor expansion of n in n
18.172 * [backup-simplify]: Simplify 0 into 0
18.172 * [backup-simplify]: Simplify 1 into 1
18.172 * [taylor]: Taking taylor expansion of PI in n
18.172 * [backup-simplify]: Simplify PI into PI
18.172 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
18.172 * [taylor]: Taking taylor expansion of 2 in n
18.172 * [backup-simplify]: Simplify 2 into 2
18.172 * [taylor]: Taking taylor expansion of (* n PI) in n
18.172 * [taylor]: Taking taylor expansion of n in n
18.172 * [backup-simplify]: Simplify 0 into 0
18.172 * [backup-simplify]: Simplify 1 into 1
18.172 * [taylor]: Taking taylor expansion of PI in n
18.172 * [backup-simplify]: Simplify PI into PI
18.172 * [backup-simplify]: Simplify (* 0 PI) into 0
18.172 * [backup-simplify]: Simplify (* 2 0) into 0
18.172 * [backup-simplify]: Simplify 0 into 0
18.173 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
18.174 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
18.175 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.175 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
18.176 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
18.176 * [backup-simplify]: Simplify 0 into 0
18.176 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
18.177 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
18.177 * [backup-simplify]: Simplify 0 into 0
18.178 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.179 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
18.179 * [backup-simplify]: Simplify 0 into 0
18.179 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.180 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
18.180 * [backup-simplify]: Simplify 0 into 0
18.181 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.182 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
18.182 * [backup-simplify]: Simplify 0 into 0
18.183 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
18.184 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
18.184 * [backup-simplify]: Simplify 0 into 0
18.184 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
18.185 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
18.185 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
18.185 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
18.185 * [taylor]: Taking taylor expansion of 2 in n
18.185 * [backup-simplify]: Simplify 2 into 2
18.185 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.185 * [taylor]: Taking taylor expansion of PI in n
18.185 * [backup-simplify]: Simplify PI into PI
18.185 * [taylor]: Taking taylor expansion of n in n
18.185 * [backup-simplify]: Simplify 0 into 0
18.185 * [backup-simplify]: Simplify 1 into 1
18.185 * [backup-simplify]: Simplify (/ PI 1) into PI
18.185 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
18.185 * [taylor]: Taking taylor expansion of 2 in n
18.185 * [backup-simplify]: Simplify 2 into 2
18.185 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.185 * [taylor]: Taking taylor expansion of PI in n
18.186 * [backup-simplify]: Simplify PI into PI
18.186 * [taylor]: Taking taylor expansion of n in n
18.186 * [backup-simplify]: Simplify 0 into 0
18.186 * [backup-simplify]: Simplify 1 into 1
18.186 * [backup-simplify]: Simplify (/ PI 1) into PI
18.186 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.186 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.187 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.187 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
18.187 * [backup-simplify]: Simplify 0 into 0
18.188 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.189 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
18.189 * [backup-simplify]: Simplify 0 into 0
18.189 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.190 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.190 * [backup-simplify]: Simplify 0 into 0
18.190 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.191 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.191 * [backup-simplify]: Simplify 0 into 0
18.192 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.193 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.193 * [backup-simplify]: Simplify 0 into 0
18.193 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.194 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.194 * [backup-simplify]: Simplify 0 into 0
18.195 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
18.195 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
18.195 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
18.195 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
18.195 * [taylor]: Taking taylor expansion of -2 in n
18.195 * [backup-simplify]: Simplify -2 into -2
18.195 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.195 * [taylor]: Taking taylor expansion of PI in n
18.195 * [backup-simplify]: Simplify PI into PI
18.195 * [taylor]: Taking taylor expansion of n in n
18.195 * [backup-simplify]: Simplify 0 into 0
18.195 * [backup-simplify]: Simplify 1 into 1
18.195 * [backup-simplify]: Simplify (/ PI 1) into PI
18.195 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
18.195 * [taylor]: Taking taylor expansion of -2 in n
18.195 * [backup-simplify]: Simplify -2 into -2
18.195 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.195 * [taylor]: Taking taylor expansion of PI in n
18.195 * [backup-simplify]: Simplify PI into PI
18.196 * [taylor]: Taking taylor expansion of n in n
18.196 * [backup-simplify]: Simplify 0 into 0
18.196 * [backup-simplify]: Simplify 1 into 1
18.196 * [backup-simplify]: Simplify (/ PI 1) into PI
18.196 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
18.196 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
18.197 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.197 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
18.197 * [backup-simplify]: Simplify 0 into 0
18.198 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.199 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
18.199 * [backup-simplify]: Simplify 0 into 0
18.199 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.200 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.200 * [backup-simplify]: Simplify 0 into 0
18.200 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.201 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.201 * [backup-simplify]: Simplify 0 into 0
18.202 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.203 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.203 * [backup-simplify]: Simplify 0 into 0
18.203 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.204 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.204 * [backup-simplify]: Simplify 0 into 0
18.205 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
18.205 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1)
18.205 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
18.205 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
18.205 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
18.205 * [taylor]: Taking taylor expansion of 2 in n
18.205 * [backup-simplify]: Simplify 2 into 2
18.205 * [taylor]: Taking taylor expansion of (* n PI) in n
18.205 * [taylor]: Taking taylor expansion of n in n
18.205 * [backup-simplify]: Simplify 0 into 0
18.205 * [backup-simplify]: Simplify 1 into 1
18.205 * [taylor]: Taking taylor expansion of PI in n
18.205 * [backup-simplify]: Simplify PI into PI
18.205 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
18.205 * [taylor]: Taking taylor expansion of 2 in n
18.205 * [backup-simplify]: Simplify 2 into 2
18.205 * [taylor]: Taking taylor expansion of (* n PI) in n
18.205 * [taylor]: Taking taylor expansion of n in n
18.205 * [backup-simplify]: Simplify 0 into 0
18.205 * [backup-simplify]: Simplify 1 into 1
18.205 * [taylor]: Taking taylor expansion of PI in n
18.205 * [backup-simplify]: Simplify PI into PI
18.206 * [backup-simplify]: Simplify (* 0 PI) into 0
18.206 * [backup-simplify]: Simplify (* 2 0) into 0
18.206 * [backup-simplify]: Simplify 0 into 0
18.207 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
18.208 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
18.208 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.209 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
18.209 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
18.209 * [backup-simplify]: Simplify 0 into 0
18.210 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
18.210 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
18.210 * [backup-simplify]: Simplify 0 into 0
18.211 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.212 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
18.212 * [backup-simplify]: Simplify 0 into 0
18.213 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.214 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
18.214 * [backup-simplify]: Simplify 0 into 0
18.215 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.215 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
18.215 * [backup-simplify]: Simplify 0 into 0
18.216 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
18.217 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
18.217 * [backup-simplify]: Simplify 0 into 0
18.218 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
18.218 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
18.218 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
18.218 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
18.218 * [taylor]: Taking taylor expansion of 2 in n
18.218 * [backup-simplify]: Simplify 2 into 2
18.218 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.218 * [taylor]: Taking taylor expansion of PI in n
18.218 * [backup-simplify]: Simplify PI into PI
18.218 * [taylor]: Taking taylor expansion of n in n
18.218 * [backup-simplify]: Simplify 0 into 0
18.218 * [backup-simplify]: Simplify 1 into 1
18.223 * [backup-simplify]: Simplify (/ PI 1) into PI
18.223 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
18.223 * [taylor]: Taking taylor expansion of 2 in n
18.223 * [backup-simplify]: Simplify 2 into 2
18.223 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.223 * [taylor]: Taking taylor expansion of PI in n
18.223 * [backup-simplify]: Simplify PI into PI
18.223 * [taylor]: Taking taylor expansion of n in n
18.223 * [backup-simplify]: Simplify 0 into 0
18.223 * [backup-simplify]: Simplify 1 into 1
18.224 * [backup-simplify]: Simplify (/ PI 1) into PI
18.224 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.224 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.225 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.225 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
18.225 * [backup-simplify]: Simplify 0 into 0
18.226 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.227 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
18.227 * [backup-simplify]: Simplify 0 into 0
18.227 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.228 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.228 * [backup-simplify]: Simplify 0 into 0
18.229 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.230 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.230 * [backup-simplify]: Simplify 0 into 0
18.230 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.231 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.231 * [backup-simplify]: Simplify 0 into 0
18.232 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.233 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.233 * [backup-simplify]: Simplify 0 into 0
18.233 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
18.233 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
18.233 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
18.233 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
18.233 * [taylor]: Taking taylor expansion of -2 in n
18.233 * [backup-simplify]: Simplify -2 into -2
18.234 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.234 * [taylor]: Taking taylor expansion of PI in n
18.234 * [backup-simplify]: Simplify PI into PI
18.234 * [taylor]: Taking taylor expansion of n in n
18.234 * [backup-simplify]: Simplify 0 into 0
18.234 * [backup-simplify]: Simplify 1 into 1
18.234 * [backup-simplify]: Simplify (/ PI 1) into PI
18.234 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
18.234 * [taylor]: Taking taylor expansion of -2 in n
18.234 * [backup-simplify]: Simplify -2 into -2
18.234 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.234 * [taylor]: Taking taylor expansion of PI in n
18.234 * [backup-simplify]: Simplify PI into PI
18.234 * [taylor]: Taking taylor expansion of n in n
18.234 * [backup-simplify]: Simplify 0 into 0
18.234 * [backup-simplify]: Simplify 1 into 1
18.234 * [backup-simplify]: Simplify (/ PI 1) into PI
18.235 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
18.235 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
18.235 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.236 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
18.236 * [backup-simplify]: Simplify 0 into 0
18.237 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.237 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
18.238 * [backup-simplify]: Simplify 0 into 0
18.238 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.239 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.239 * [backup-simplify]: Simplify 0 into 0
18.240 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.240 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.240 * [backup-simplify]: Simplify 0 into 0
18.241 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.242 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.242 * [backup-simplify]: Simplify 0 into 0
18.243 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.244 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.244 * [backup-simplify]: Simplify 0 into 0
18.244 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
18.244 * * * [progress]: simplifying candidates
18.244 * * * * [progress]: [ 1 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))) (/ 1 2)))))>
18.244 * * * * [progress]: [ 2 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))) (/ 1 2)))))>
18.244 * * * * [progress]: [ 3 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (/ 1 2)))))>
18.244 * * * * [progress]: [ 4 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (/ 1 2)))))>
18.244 * * * * [progress]: [ 5 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 6 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 7 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 8 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 9 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 10 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 11 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 12 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 13 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 14 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 15 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 16 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 17 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 18 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (/ 1 2)))))>
18.245 * * * * [progress]: [ 19 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 20 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 21 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (* (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))))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 22 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (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))))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 23 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 24 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ 1 2)))))>
18.245 * * * * [progress]: [ 25 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 26 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 27 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 28 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 29 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 30 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 31 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 32 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 33 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 34 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 35 / 116 ] 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))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 36 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 37 / 116 ] 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))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 38 / 116 ] 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))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 39 / 116 ] 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)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.246 * * * * [progress]: [ 40 / 116 ] 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))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 41 / 116 ] 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))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 42 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 43 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 44 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 45 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 46 / 116 ] 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))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 47 / 116 ] 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))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 48 / 116 ] 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)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 49 / 116 ] 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))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 50 / 116 ] 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))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 51 / 116 ] 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)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 52 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 53 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 54 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 55 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 56 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 57 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 58 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 59 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 60 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.247 * * * * [progress]: [ 61 / 116 ] 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)))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 62 / 116 ] 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)))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 63 / 116 ] 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 k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 64 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 65 / 116 ] 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))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 66 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 67 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 68 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 69 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 70 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 71 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 72 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 73 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 74 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 75 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 76 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 77 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 78 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 79 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 80 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 81 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 82 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 83 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.248 * * * * [progress]: [ 84 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 85 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 86 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 87 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 88 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 89 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 90 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 91 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 92 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 93 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 94 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 95 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 96 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 97 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 98 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 99 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 100 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 101 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 102 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.249 * * * * [progress]: [ 103 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 104 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 105 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 106 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 107 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 108 / 116 ] 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))))))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 109 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 110 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 111 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 112 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 113 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 114 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 115 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.250 * * * * [progress]: [ 116 / 116 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))>
18.251 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 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)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
18.253 * * [simplify]: iteration 1: (206 enodes)
18.362 * * [simplify]: iteration 2: (603 enodes)
19.062 * * [simplify]: iteration 3: (1913 enodes)
21.750 * * [simplify]: Extracting #0: cost 60 inf + 0
21.754 * * [simplify]: Extracting #1: cost 631 inf + 0
21.761 * * [simplify]: Extracting #2: cost 1451 inf + 6565
21.778 * * [simplify]: Extracting #3: cost 1643 inf + 61002
21.855 * * [simplify]: Extracting #4: cost 855 inf + 333695
22.063 * * [simplify]: Extracting #5: cost 221 inf + 639743
22.290 * * [simplify]: Extracting #6: cost 66 inf + 704537
22.529 * * [simplify]: Extracting #7: cost 5 inf + 731268
22.769 * * [simplify]: Extracting #8: cost 0 inf + 734210
22.984 * [simplify]: Simplified to:
  (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
  (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
  (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
  (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (/ k 2))
  (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2))))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* PI (* n 2)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* PI (* n 2))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (- (/ k 2)))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
  (exp (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (pow (* PI (* n 2)) (- 1/4 (/ k 4)))
  (pow (* PI (* n 2)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (* (log (* PI (* n 2))) (- 1/4 (/ k 4)))
  (* (log (* PI (* n 2))) (- 1/4 (/ k 4)))
  (* (log (* PI (* n 2))) (- 1/4 (/ k 4)))
  (* (log (* PI (* n 2))) (- 1/4 (/ k 4)))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (exp (* 1/4 (log (* PI (* n 2)))))
  (pow (* PI (* n 2)) (/ k 4))
  (pow (* PI (* n 2)) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4)))))
  (pow (* PI (* n 2)) (sqrt (- 1/4 (/ k 4))))
  (pow (* PI (* n 2)) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (cbrt (- 1/2 (/ k 2))) (/ (sqrt 2) (cbrt (- 1/2 (/ k 2))))))
  (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* PI (* n 2)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2))))
  (pow (* PI (* n 2)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* PI (* n 2)) (/ 1 (sqrt 2)))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* PI (* n 2)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* PI (* n 2)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* PI (* n 2)) (/ (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)) (sqrt 2)))
  (pow (* PI (* n 2)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (pow (* PI (* n 2)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* PI (* n 2)) (/ 1 (sqrt 2)))
  (* PI (* n 2))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (- 1/2 (/ k 2)))
  (pow n (- 1/4 (/ k 4)))
  (pow (* PI 2) (- 1/4 (/ k 4)))
  (* (log (* PI (* n 2))) (- 1/4 (/ k 4)))
  (exp (pow (* PI (* n 2)) (- 1/4 (/ k 4))))
  (* (cbrt (pow (* PI (* n 2)) (- 1/4 (/ k 4)))) (cbrt (pow (* PI (* n 2)) (- 1/4 (/ k 4)))))
  (cbrt (pow (* PI (* n 2)) (- 1/4 (/ k 4))))
  (* (* (* (pow (* PI (* n 2)) (- 1/8 (/ k 8))) (pow (* PI (* n 2)) (- 1/8 (/ k 8)))) (* (pow (* PI (* n 2)) (- 1/8 (/ k 8))) (pow (* PI (* n 2)) (- 1/8 (/ k 8))))) (* (pow (* PI (* n 2)) (- 1/8 (/ k 8))) (pow (* PI (* n 2)) (- 1/8 (/ k 8)))))
  (fabs (pow (* PI (* n 2)) (- 1/8 (/ k 8))))
  (fabs (pow (* PI (* n 2)) (- 1/8 (/ k 8))))
  (pow (* PI (* n 2)) (- 1/8 (/ k 8)))
  (pow (* PI (* n 2)) (- 1/8 (/ k 8)))
  (real->posit16 (pow (* PI (* n 2)) (- 1/4 (/ k 4))))
  (* PI (* n 2))
  (* PI (* n 2))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (exp (+ (* PI n) (* PI n)))
  (* (* (* (* PI n) (* PI n)) 8) (* PI n))
  (* (* (* (* PI n) (* PI n)) 8) (* PI n))
  (* (cbrt (* PI (* n 2))) (cbrt (* PI (* n 2))))
  (cbrt (* PI (* n 2)))
  (* (* (* (* PI n) (* PI n)) 8) (* PI n))
  (sqrt (* PI (* n 2)))
  (sqrt (* PI (* n 2)))
  (* n 2)
  (* (cbrt n) (* PI 2))
  (* (sqrt n) (* PI 2))
  (* PI (* n 2))
  (real->posit16 (* PI (* n 2)))
  (* PI (* n 2))
  (* PI (* n 2))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (exp (+ (* PI n) (* PI n)))
  (* (* (* (* PI n) (* PI n)) 8) (* PI n))
  (* (* (* (* PI n) (* PI n)) 8) (* PI n))
  (* (cbrt (* PI (* n 2))) (cbrt (* PI (* n 2))))
  (cbrt (* PI (* n 2)))
  (* (* (* (* PI n) (* PI n)) 8) (* PI n))
  (sqrt (* PI (* n 2)))
  (sqrt (* PI (* n 2)))
  (* n 2)
  (* (cbrt n) (* PI 2))
  (* (sqrt n) (* PI 2))
  (* PI (* n 2))
  (real->posit16 (* PI (* n 2)))
  (+ (* (* (* k (sqrt (* PI (* n 2)))) (log (* PI (* n 2)))) -1/2) (+ (+ (* (* 1/4 (sqrt (* PI (* n 2)))) (* (* (log n) (* k k)) (log (* PI 2)))) (* (* 1/8 (* k k)) (+ (* (* (log (* PI 2)) (sqrt (* PI (* n 2)))) (log (* PI 2))) (* (log n) (* (sqrt (* PI (* n 2))) (log n)))))) (sqrt (* PI (* n 2)))))
  (exp (* (- 1/2 (* k 1/2)) (log (* PI (* n 2)))))
  (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2))))
  (+ (+ (* (* 1/32 (* k k)) (* (exp (* 1/4 (log (* PI (* n 2))))) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2)))))) (exp (* 1/4 (log (* PI (* n 2)))))) (- (* (* (* (log n) (* k k)) (log (* PI 2))) (* (exp (* 1/4 (log (* PI (* n 2))))) 1/16)) (* (* k 1/4) (* (exp (* 1/4 (log (* PI (* n 2))))) (+ (log n) (log (* PI 2)))))))
  (exp (* (- 1/2 (* k 1/2)) (log (sqrt (* PI (* n 2))))))
  (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (+ 1/4 (* (- k) 1/4))))
  (* PI (* n 2))
  (* PI (* n 2))
  (* PI (* n 2))
  (* PI (* n 2))
  (* PI (* n 2))
  (* PI (* n 2))
23.004 * * * [progress]: adding candidates to table
24.780 * * [progress]: iteration 4 / 4
24.780 * * * [progress]: picking best candidate
24.824 * * * * [pick]: Picked  #<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))))>
24.824 * * * [progress]: localizing error
24.867 * * * [progress]: generating rewritten candidates
24.867 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1)
24.890 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1)
24.910 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 1)
24.924 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1 1)
24.946 * * * [progress]: generating series expansions
24.946 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1)
24.947 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
24.947 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
24.947 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
24.947 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
24.947 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
24.947 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
24.947 * [taylor]: Taking taylor expansion of 1/2 in k
24.947 * [backup-simplify]: Simplify 1/2 into 1/2
24.947 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
24.947 * [taylor]: Taking taylor expansion of 1/2 in k
24.947 * [backup-simplify]: Simplify 1/2 into 1/2
24.947 * [taylor]: Taking taylor expansion of k in k
24.947 * [backup-simplify]: Simplify 0 into 0
24.947 * [backup-simplify]: Simplify 1 into 1
24.947 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
24.947 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
24.947 * [taylor]: Taking taylor expansion of 2 in k
24.947 * [backup-simplify]: Simplify 2 into 2
24.947 * [taylor]: Taking taylor expansion of (* n PI) in k
24.947 * [taylor]: Taking taylor expansion of n in k
24.947 * [backup-simplify]: Simplify n into n
24.947 * [taylor]: Taking taylor expansion of PI in k
24.947 * [backup-simplify]: Simplify PI into PI
24.947 * [backup-simplify]: Simplify (* n PI) into (* n PI)
24.947 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
24.947 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
24.948 * [backup-simplify]: Simplify (* 1/2 0) into 0
24.948 * [backup-simplify]: Simplify (- 0) into 0
24.948 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
24.948 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
24.948 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
24.948 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
24.948 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
24.948 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
24.948 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
24.949 * [taylor]: Taking taylor expansion of 1/2 in n
24.949 * [backup-simplify]: Simplify 1/2 into 1/2
24.949 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
24.949 * [taylor]: Taking taylor expansion of 1/2 in n
24.949 * [backup-simplify]: Simplify 1/2 into 1/2
24.949 * [taylor]: Taking taylor expansion of k in n
24.949 * [backup-simplify]: Simplify k into k
24.949 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
24.949 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
24.949 * [taylor]: Taking taylor expansion of 2 in n
24.949 * [backup-simplify]: Simplify 2 into 2
24.949 * [taylor]: Taking taylor expansion of (* n PI) in n
24.949 * [taylor]: Taking taylor expansion of n in n
24.949 * [backup-simplify]: Simplify 0 into 0
24.949 * [backup-simplify]: Simplify 1 into 1
24.949 * [taylor]: Taking taylor expansion of PI in n
24.949 * [backup-simplify]: Simplify PI into PI
24.949 * [backup-simplify]: Simplify (* 0 PI) into 0
24.950 * [backup-simplify]: Simplify (* 2 0) into 0
24.951 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
24.952 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
24.952 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
24.952 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
24.952 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
24.952 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
24.953 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
24.954 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
24.955 * [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)))))
24.955 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
24.955 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
24.955 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
24.955 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
24.955 * [taylor]: Taking taylor expansion of 1/2 in n
24.955 * [backup-simplify]: Simplify 1/2 into 1/2
24.955 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
24.955 * [taylor]: Taking taylor expansion of 1/2 in n
24.955 * [backup-simplify]: Simplify 1/2 into 1/2
24.955 * [taylor]: Taking taylor expansion of k in n
24.955 * [backup-simplify]: Simplify k into k
24.955 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
24.955 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
24.955 * [taylor]: Taking taylor expansion of 2 in n
24.955 * [backup-simplify]: Simplify 2 into 2
24.955 * [taylor]: Taking taylor expansion of (* n PI) in n
24.955 * [taylor]: Taking taylor expansion of n in n
24.955 * [backup-simplify]: Simplify 0 into 0
24.955 * [backup-simplify]: Simplify 1 into 1
24.955 * [taylor]: Taking taylor expansion of PI in n
24.955 * [backup-simplify]: Simplify PI into PI
24.955 * [backup-simplify]: Simplify (* 0 PI) into 0
24.956 * [backup-simplify]: Simplify (* 2 0) into 0
24.957 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
24.958 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
24.958 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
24.958 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
24.958 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
24.959 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
24.959 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
24.960 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
24.961 * [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)))))
24.961 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
24.961 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
24.961 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
24.961 * [taylor]: Taking taylor expansion of 1/2 in k
24.961 * [backup-simplify]: Simplify 1/2 into 1/2
24.961 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
24.961 * [taylor]: Taking taylor expansion of 1/2 in k
24.961 * [backup-simplify]: Simplify 1/2 into 1/2
24.961 * [taylor]: Taking taylor expansion of k in k
24.961 * [backup-simplify]: Simplify 0 into 0
24.961 * [backup-simplify]: Simplify 1 into 1
24.961 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
24.961 * [taylor]: Taking taylor expansion of (log n) in k
24.961 * [taylor]: Taking taylor expansion of n in k
24.961 * [backup-simplify]: Simplify n into n
24.961 * [backup-simplify]: Simplify (log n) into (log n)
24.961 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
24.961 * [taylor]: Taking taylor expansion of (* 2 PI) in k
24.961 * [taylor]: Taking taylor expansion of 2 in k
24.961 * [backup-simplify]: Simplify 2 into 2
24.961 * [taylor]: Taking taylor expansion of PI in k
24.961 * [backup-simplify]: Simplify PI into PI
24.962 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
24.962 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
24.963 * [backup-simplify]: Simplify (* 1/2 0) into 0
24.963 * [backup-simplify]: Simplify (- 0) into 0
24.963 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
24.964 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
24.969 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
24.970 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
24.971 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
24.972 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
24.973 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
24.975 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
24.976 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
24.976 * [backup-simplify]: Simplify (- 0) into 0
24.977 * [backup-simplify]: Simplify (+ 0 0) into 0
24.978 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
24.979 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
24.982 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
24.982 * [taylor]: Taking taylor expansion of 0 in k
24.982 * [backup-simplify]: Simplify 0 into 0
24.982 * [backup-simplify]: Simplify 0 into 0
24.983 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
24.983 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
24.985 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
24.986 * [backup-simplify]: Simplify (+ 0 0) into 0
24.986 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
24.987 * [backup-simplify]: Simplify (- 1/2) into -1/2
24.987 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
24.989 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
24.992 * [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)))))))
24.995 * [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)))))))
24.996 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
24.997 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
24.999 * [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
25.000 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
25.000 * [backup-simplify]: Simplify (- 0) into 0
25.000 * [backup-simplify]: Simplify (+ 0 0) into 0
25.001 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
25.002 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
25.003 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.003 * [taylor]: Taking taylor expansion of 0 in k
25.003 * [backup-simplify]: Simplify 0 into 0
25.004 * [backup-simplify]: Simplify 0 into 0
25.004 * [backup-simplify]: Simplify 0 into 0
25.005 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
25.005 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
25.007 * [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
25.007 * [backup-simplify]: Simplify (+ 0 0) into 0
25.008 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
25.008 * [backup-simplify]: Simplify (- 0) into 0
25.008 * [backup-simplify]: Simplify (+ 0 0) into 0
25.010 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
25.012 * [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)))))
25.015 * [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)))))
25.021 * [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)))))
25.021 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
25.021 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
25.021 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
25.021 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
25.021 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
25.021 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
25.021 * [taylor]: Taking taylor expansion of 1/2 in k
25.021 * [backup-simplify]: Simplify 1/2 into 1/2
25.021 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
25.021 * [taylor]: Taking taylor expansion of 1/2 in k
25.021 * [backup-simplify]: Simplify 1/2 into 1/2
25.021 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.021 * [taylor]: Taking taylor expansion of k in k
25.021 * [backup-simplify]: Simplify 0 into 0
25.022 * [backup-simplify]: Simplify 1 into 1
25.022 * [backup-simplify]: Simplify (/ 1 1) into 1
25.022 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
25.022 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
25.022 * [taylor]: Taking taylor expansion of 2 in k
25.022 * [backup-simplify]: Simplify 2 into 2
25.022 * [taylor]: Taking taylor expansion of (/ PI n) in k
25.022 * [taylor]: Taking taylor expansion of PI in k
25.022 * [backup-simplify]: Simplify PI into PI
25.022 * [taylor]: Taking taylor expansion of n in k
25.022 * [backup-simplify]: Simplify n into n
25.022 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
25.022 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
25.022 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
25.022 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
25.023 * [backup-simplify]: Simplify (- 1/2) into -1/2
25.023 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
25.023 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
25.023 * [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))))
25.023 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
25.023 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
25.023 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
25.023 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
25.023 * [taylor]: Taking taylor expansion of 1/2 in n
25.023 * [backup-simplify]: Simplify 1/2 into 1/2
25.023 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
25.023 * [taylor]: Taking taylor expansion of 1/2 in n
25.023 * [backup-simplify]: Simplify 1/2 into 1/2
25.023 * [taylor]: Taking taylor expansion of (/ 1 k) in n
25.023 * [taylor]: Taking taylor expansion of k in n
25.023 * [backup-simplify]: Simplify k into k
25.023 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
25.023 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
25.023 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
25.023 * [taylor]: Taking taylor expansion of 2 in n
25.023 * [backup-simplify]: Simplify 2 into 2
25.023 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.023 * [taylor]: Taking taylor expansion of PI in n
25.023 * [backup-simplify]: Simplify PI into PI
25.023 * [taylor]: Taking taylor expansion of n in n
25.023 * [backup-simplify]: Simplify 0 into 0
25.023 * [backup-simplify]: Simplify 1 into 1
25.024 * [backup-simplify]: Simplify (/ PI 1) into PI
25.024 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.025 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.025 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
25.025 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
25.025 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
25.026 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.027 * [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)))
25.027 * [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))))
25.027 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
25.027 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
25.027 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
25.028 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
25.028 * [taylor]: Taking taylor expansion of 1/2 in n
25.028 * [backup-simplify]: Simplify 1/2 into 1/2
25.028 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
25.028 * [taylor]: Taking taylor expansion of 1/2 in n
25.028 * [backup-simplify]: Simplify 1/2 into 1/2
25.028 * [taylor]: Taking taylor expansion of (/ 1 k) in n
25.028 * [taylor]: Taking taylor expansion of k in n
25.028 * [backup-simplify]: Simplify k into k
25.028 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
25.028 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
25.028 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
25.028 * [taylor]: Taking taylor expansion of 2 in n
25.028 * [backup-simplify]: Simplify 2 into 2
25.028 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.028 * [taylor]: Taking taylor expansion of PI in n
25.028 * [backup-simplify]: Simplify PI into PI
25.028 * [taylor]: Taking taylor expansion of n in n
25.028 * [backup-simplify]: Simplify 0 into 0
25.028 * [backup-simplify]: Simplify 1 into 1
25.028 * [backup-simplify]: Simplify (/ PI 1) into PI
25.028 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.029 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.029 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
25.029 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
25.029 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
25.030 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.031 * [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)))
25.032 * [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))))
25.032 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
25.032 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
25.032 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
25.032 * [taylor]: Taking taylor expansion of 1/2 in k
25.032 * [backup-simplify]: Simplify 1/2 into 1/2
25.032 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
25.032 * [taylor]: Taking taylor expansion of 1/2 in k
25.032 * [backup-simplify]: Simplify 1/2 into 1/2
25.032 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.032 * [taylor]: Taking taylor expansion of k in k
25.032 * [backup-simplify]: Simplify 0 into 0
25.032 * [backup-simplify]: Simplify 1 into 1
25.032 * [backup-simplify]: Simplify (/ 1 1) into 1
25.032 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
25.032 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
25.032 * [taylor]: Taking taylor expansion of (* 2 PI) in k
25.032 * [taylor]: Taking taylor expansion of 2 in k
25.032 * [backup-simplify]: Simplify 2 into 2
25.032 * [taylor]: Taking taylor expansion of PI in k
25.032 * [backup-simplify]: Simplify PI into PI
25.033 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.033 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.033 * [taylor]: Taking taylor expansion of (log n) in k
25.033 * [taylor]: Taking taylor expansion of n in k
25.033 * [backup-simplify]: Simplify n into n
25.033 * [backup-simplify]: Simplify (log n) into (log n)
25.034 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
25.034 * [backup-simplify]: Simplify (- 1/2) into -1/2
25.034 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
25.034 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
25.035 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
25.035 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
25.036 * [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))))
25.037 * [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))))
25.037 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
25.038 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
25.039 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
25.039 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
25.039 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
25.039 * [backup-simplify]: Simplify (- 0) into 0
25.040 * [backup-simplify]: Simplify (+ 0 0) into 0
25.041 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.041 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
25.043 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
25.043 * [taylor]: Taking taylor expansion of 0 in k
25.043 * [backup-simplify]: Simplify 0 into 0
25.043 * [backup-simplify]: Simplify 0 into 0
25.043 * [backup-simplify]: Simplify 0 into 0
25.043 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.044 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
25.046 * [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
25.046 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
25.046 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
25.047 * [backup-simplify]: Simplify (- 0) into 0
25.047 * [backup-simplify]: Simplify (+ 0 0) into 0
25.048 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.049 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
25.050 * [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
25.050 * [taylor]: Taking taylor expansion of 0 in k
25.050 * [backup-simplify]: Simplify 0 into 0
25.050 * [backup-simplify]: Simplify 0 into 0
25.050 * [backup-simplify]: Simplify 0 into 0
25.050 * [backup-simplify]: Simplify 0 into 0
25.051 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.052 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
25.055 * [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
25.055 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
25.056 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
25.056 * [backup-simplify]: Simplify (- 0) into 0
25.056 * [backup-simplify]: Simplify (+ 0 0) into 0
25.057 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.058 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
25.060 * [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
25.060 * [taylor]: Taking taylor expansion of 0 in k
25.060 * [backup-simplify]: Simplify 0 into 0
25.060 * [backup-simplify]: Simplify 0 into 0
25.061 * [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)))))
25.061 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
25.061 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
25.061 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
25.061 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
25.061 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
25.061 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
25.061 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
25.061 * [taylor]: Taking taylor expansion of 1/2 in k
25.061 * [backup-simplify]: Simplify 1/2 into 1/2
25.061 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.061 * [taylor]: Taking taylor expansion of k in k
25.061 * [backup-simplify]: Simplify 0 into 0
25.061 * [backup-simplify]: Simplify 1 into 1
25.062 * [backup-simplify]: Simplify (/ 1 1) into 1
25.062 * [taylor]: Taking taylor expansion of 1/2 in k
25.062 * [backup-simplify]: Simplify 1/2 into 1/2
25.062 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
25.062 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
25.062 * [taylor]: Taking taylor expansion of -2 in k
25.062 * [backup-simplify]: Simplify -2 into -2
25.062 * [taylor]: Taking taylor expansion of (/ PI n) in k
25.062 * [taylor]: Taking taylor expansion of PI in k
25.062 * [backup-simplify]: Simplify PI into PI
25.062 * [taylor]: Taking taylor expansion of n in k
25.062 * [backup-simplify]: Simplify n into n
25.062 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
25.062 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
25.062 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
25.062 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
25.063 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
25.063 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
25.063 * [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)))
25.063 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
25.063 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
25.063 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
25.063 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
25.063 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
25.063 * [taylor]: Taking taylor expansion of 1/2 in n
25.063 * [backup-simplify]: Simplify 1/2 into 1/2
25.063 * [taylor]: Taking taylor expansion of (/ 1 k) in n
25.063 * [taylor]: Taking taylor expansion of k in n
25.063 * [backup-simplify]: Simplify k into k
25.063 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
25.063 * [taylor]: Taking taylor expansion of 1/2 in n
25.063 * [backup-simplify]: Simplify 1/2 into 1/2
25.063 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
25.063 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
25.063 * [taylor]: Taking taylor expansion of -2 in n
25.063 * [backup-simplify]: Simplify -2 into -2
25.063 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.063 * [taylor]: Taking taylor expansion of PI in n
25.063 * [backup-simplify]: Simplify PI into PI
25.063 * [taylor]: Taking taylor expansion of n in n
25.063 * [backup-simplify]: Simplify 0 into 0
25.063 * [backup-simplify]: Simplify 1 into 1
25.063 * [backup-simplify]: Simplify (/ PI 1) into PI
25.064 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.064 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
25.064 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
25.064 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
25.065 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.066 * [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)))
25.071 * [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))))
25.072 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
25.072 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
25.072 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
25.072 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
25.072 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
25.072 * [taylor]: Taking taylor expansion of 1/2 in n
25.072 * [backup-simplify]: Simplify 1/2 into 1/2
25.072 * [taylor]: Taking taylor expansion of (/ 1 k) in n
25.072 * [taylor]: Taking taylor expansion of k in n
25.072 * [backup-simplify]: Simplify k into k
25.072 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
25.072 * [taylor]: Taking taylor expansion of 1/2 in n
25.072 * [backup-simplify]: Simplify 1/2 into 1/2
25.072 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
25.072 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
25.072 * [taylor]: Taking taylor expansion of -2 in n
25.072 * [backup-simplify]: Simplify -2 into -2
25.072 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.072 * [taylor]: Taking taylor expansion of PI in n
25.072 * [backup-simplify]: Simplify PI into PI
25.072 * [taylor]: Taking taylor expansion of n in n
25.072 * [backup-simplify]: Simplify 0 into 0
25.072 * [backup-simplify]: Simplify 1 into 1
25.073 * [backup-simplify]: Simplify (/ PI 1) into PI
25.073 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.074 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
25.075 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
25.075 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
25.076 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.078 * [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)))
25.079 * [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))))
25.079 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
25.079 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
25.079 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
25.079 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
25.079 * [taylor]: Taking taylor expansion of 1/2 in k
25.079 * [backup-simplify]: Simplify 1/2 into 1/2
25.079 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.079 * [taylor]: Taking taylor expansion of k in k
25.079 * [backup-simplify]: Simplify 0 into 0
25.079 * [backup-simplify]: Simplify 1 into 1
25.080 * [backup-simplify]: Simplify (/ 1 1) into 1
25.080 * [taylor]: Taking taylor expansion of 1/2 in k
25.080 * [backup-simplify]: Simplify 1/2 into 1/2
25.080 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
25.080 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
25.080 * [taylor]: Taking taylor expansion of (* -2 PI) in k
25.080 * [taylor]: Taking taylor expansion of -2 in k
25.080 * [backup-simplify]: Simplify -2 into -2
25.080 * [taylor]: Taking taylor expansion of PI in k
25.080 * [backup-simplify]: Simplify PI into PI
25.080 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.081 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
25.082 * [taylor]: Taking taylor expansion of (log n) in k
25.082 * [taylor]: Taking taylor expansion of n in k
25.082 * [backup-simplify]: Simplify n into n
25.082 * [backup-simplify]: Simplify (log n) into (log n)
25.082 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
25.083 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
25.083 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
25.084 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
25.085 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
25.086 * [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))))
25.087 * [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))))
25.088 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
25.089 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
25.091 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
25.091 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
25.092 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
25.092 * [backup-simplify]: Simplify (+ 0 0) into 0
25.093 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.095 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
25.097 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
25.097 * [taylor]: Taking taylor expansion of 0 in k
25.097 * [backup-simplify]: Simplify 0 into 0
25.097 * [backup-simplify]: Simplify 0 into 0
25.097 * [backup-simplify]: Simplify 0 into 0
25.098 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.099 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
25.102 * [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
25.103 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
25.104 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
25.104 * [backup-simplify]: Simplify (+ 0 0) into 0
25.106 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.107 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
25.110 * [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
25.110 * [taylor]: Taking taylor expansion of 0 in k
25.110 * [backup-simplify]: Simplify 0 into 0
25.110 * [backup-simplify]: Simplify 0 into 0
25.110 * [backup-simplify]: Simplify 0 into 0
25.110 * [backup-simplify]: Simplify 0 into 0
25.111 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.112 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
25.119 * [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
25.119 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
25.120 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
25.121 * [backup-simplify]: Simplify (+ 0 0) into 0
25.122 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.124 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
25.127 * [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
25.127 * [taylor]: Taking taylor expansion of 0 in k
25.127 * [backup-simplify]: Simplify 0 into 0
25.127 * [backup-simplify]: Simplify 0 into 0
25.129 * [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)))))
25.129 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1)
25.129 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
25.129 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
25.130 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
25.130 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
25.130 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
25.130 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
25.130 * [taylor]: Taking taylor expansion of 1/2 in k
25.130 * [backup-simplify]: Simplify 1/2 into 1/2
25.130 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
25.130 * [taylor]: Taking taylor expansion of 1/2 in k
25.130 * [backup-simplify]: Simplify 1/2 into 1/2
25.130 * [taylor]: Taking taylor expansion of k in k
25.130 * [backup-simplify]: Simplify 0 into 0
25.130 * [backup-simplify]: Simplify 1 into 1
25.130 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
25.130 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
25.130 * [taylor]: Taking taylor expansion of 2 in k
25.130 * [backup-simplify]: Simplify 2 into 2
25.130 * [taylor]: Taking taylor expansion of (* n PI) in k
25.130 * [taylor]: Taking taylor expansion of n in k
25.130 * [backup-simplify]: Simplify n into n
25.130 * [taylor]: Taking taylor expansion of PI in k
25.130 * [backup-simplify]: Simplify PI into PI
25.130 * [backup-simplify]: Simplify (* n PI) into (* n PI)
25.130 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
25.130 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
25.131 * [backup-simplify]: Simplify (* 1/2 0) into 0
25.131 * [backup-simplify]: Simplify (- 0) into 0
25.132 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
25.132 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
25.132 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
25.132 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
25.132 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
25.132 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
25.132 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
25.132 * [taylor]: Taking taylor expansion of 1/2 in n
25.132 * [backup-simplify]: Simplify 1/2 into 1/2
25.132 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
25.132 * [taylor]: Taking taylor expansion of 1/2 in n
25.132 * [backup-simplify]: Simplify 1/2 into 1/2
25.132 * [taylor]: Taking taylor expansion of k in n
25.132 * [backup-simplify]: Simplify k into k
25.132 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
25.132 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
25.132 * [taylor]: Taking taylor expansion of 2 in n
25.132 * [backup-simplify]: Simplify 2 into 2
25.132 * [taylor]: Taking taylor expansion of (* n PI) in n
25.132 * [taylor]: Taking taylor expansion of n in n
25.132 * [backup-simplify]: Simplify 0 into 0
25.132 * [backup-simplify]: Simplify 1 into 1
25.132 * [taylor]: Taking taylor expansion of PI in n
25.132 * [backup-simplify]: Simplify PI into PI
25.133 * [backup-simplify]: Simplify (* 0 PI) into 0
25.133 * [backup-simplify]: Simplify (* 2 0) into 0
25.135 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
25.136 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
25.137 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.137 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
25.137 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
25.137 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
25.138 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
25.139 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
25.140 * [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)))))
25.140 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
25.140 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
25.140 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
25.140 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
25.140 * [taylor]: Taking taylor expansion of 1/2 in n
25.140 * [backup-simplify]: Simplify 1/2 into 1/2
25.140 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
25.140 * [taylor]: Taking taylor expansion of 1/2 in n
25.140 * [backup-simplify]: Simplify 1/2 into 1/2
25.140 * [taylor]: Taking taylor expansion of k in n
25.140 * [backup-simplify]: Simplify k into k
25.140 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
25.140 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
25.140 * [taylor]: Taking taylor expansion of 2 in n
25.140 * [backup-simplify]: Simplify 2 into 2
25.140 * [taylor]: Taking taylor expansion of (* n PI) in n
25.140 * [taylor]: Taking taylor expansion of n in n
25.140 * [backup-simplify]: Simplify 0 into 0
25.140 * [backup-simplify]: Simplify 1 into 1
25.140 * [taylor]: Taking taylor expansion of PI in n
25.140 * [backup-simplify]: Simplify PI into PI
25.141 * [backup-simplify]: Simplify (* 0 PI) into 0
25.141 * [backup-simplify]: Simplify (* 2 0) into 0
25.142 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
25.143 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
25.143 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.143 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
25.143 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
25.143 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
25.144 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
25.145 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
25.146 * [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)))))
25.146 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
25.146 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
25.146 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
25.146 * [taylor]: Taking taylor expansion of 1/2 in k
25.146 * [backup-simplify]: Simplify 1/2 into 1/2
25.146 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
25.146 * [taylor]: Taking taylor expansion of 1/2 in k
25.146 * [backup-simplify]: Simplify 1/2 into 1/2
25.146 * [taylor]: Taking taylor expansion of k in k
25.146 * [backup-simplify]: Simplify 0 into 0
25.146 * [backup-simplify]: Simplify 1 into 1
25.146 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
25.146 * [taylor]: Taking taylor expansion of (log n) in k
25.146 * [taylor]: Taking taylor expansion of n in k
25.146 * [backup-simplify]: Simplify n into n
25.146 * [backup-simplify]: Simplify (log n) into (log n)
25.146 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
25.146 * [taylor]: Taking taylor expansion of (* 2 PI) in k
25.146 * [taylor]: Taking taylor expansion of 2 in k
25.146 * [backup-simplify]: Simplify 2 into 2
25.146 * [taylor]: Taking taylor expansion of PI in k
25.146 * [backup-simplify]: Simplify PI into PI
25.147 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.147 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.148 * [backup-simplify]: Simplify (* 1/2 0) into 0
25.148 * [backup-simplify]: Simplify (- 0) into 0
25.148 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
25.149 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
25.150 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
25.150 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
25.151 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
25.151 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
25.152 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
25.153 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
25.153 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
25.154 * [backup-simplify]: Simplify (- 0) into 0
25.154 * [backup-simplify]: Simplify (+ 0 0) into 0
25.155 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
25.155 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
25.157 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
25.157 * [taylor]: Taking taylor expansion of 0 in k
25.157 * [backup-simplify]: Simplify 0 into 0
25.157 * [backup-simplify]: Simplify 0 into 0
25.157 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
25.158 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
25.159 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
25.159 * [backup-simplify]: Simplify (+ 0 0) into 0
25.159 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
25.160 * [backup-simplify]: Simplify (- 1/2) into -1/2
25.160 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
25.161 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
25.163 * [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)))))))
25.164 * [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)))))))
25.165 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
25.166 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
25.168 * [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
25.168 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
25.169 * [backup-simplify]: Simplify (- 0) into 0
25.169 * [backup-simplify]: Simplify (+ 0 0) into 0
25.170 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
25.171 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
25.172 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.172 * [taylor]: Taking taylor expansion of 0 in k
25.172 * [backup-simplify]: Simplify 0 into 0
25.172 * [backup-simplify]: Simplify 0 into 0
25.172 * [backup-simplify]: Simplify 0 into 0
25.173 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
25.174 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
25.176 * [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
25.176 * [backup-simplify]: Simplify (+ 0 0) into 0
25.177 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
25.177 * [backup-simplify]: Simplify (- 0) into 0
25.177 * [backup-simplify]: Simplify (+ 0 0) into 0
25.179 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
25.181 * [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)))))
25.184 * [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)))))
25.193 * [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)))))
25.194 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
25.194 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
25.194 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
25.194 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
25.194 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
25.194 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
25.194 * [taylor]: Taking taylor expansion of 1/2 in k
25.194 * [backup-simplify]: Simplify 1/2 into 1/2
25.194 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
25.194 * [taylor]: Taking taylor expansion of 1/2 in k
25.194 * [backup-simplify]: Simplify 1/2 into 1/2
25.194 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.194 * [taylor]: Taking taylor expansion of k in k
25.194 * [backup-simplify]: Simplify 0 into 0
25.194 * [backup-simplify]: Simplify 1 into 1
25.194 * [backup-simplify]: Simplify (/ 1 1) into 1
25.194 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
25.194 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
25.194 * [taylor]: Taking taylor expansion of 2 in k
25.194 * [backup-simplify]: Simplify 2 into 2
25.194 * [taylor]: Taking taylor expansion of (/ PI n) in k
25.194 * [taylor]: Taking taylor expansion of PI in k
25.194 * [backup-simplify]: Simplify PI into PI
25.194 * [taylor]: Taking taylor expansion of n in k
25.194 * [backup-simplify]: Simplify n into n
25.194 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
25.195 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
25.195 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
25.195 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
25.195 * [backup-simplify]: Simplify (- 1/2) into -1/2
25.195 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
25.195 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
25.196 * [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))))
25.196 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
25.196 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
25.196 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
25.196 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
25.196 * [taylor]: Taking taylor expansion of 1/2 in n
25.196 * [backup-simplify]: Simplify 1/2 into 1/2
25.196 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
25.196 * [taylor]: Taking taylor expansion of 1/2 in n
25.196 * [backup-simplify]: Simplify 1/2 into 1/2
25.196 * [taylor]: Taking taylor expansion of (/ 1 k) in n
25.196 * [taylor]: Taking taylor expansion of k in n
25.196 * [backup-simplify]: Simplify k into k
25.196 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
25.196 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
25.196 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
25.196 * [taylor]: Taking taylor expansion of 2 in n
25.196 * [backup-simplify]: Simplify 2 into 2
25.196 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.196 * [taylor]: Taking taylor expansion of PI in n
25.196 * [backup-simplify]: Simplify PI into PI
25.196 * [taylor]: Taking taylor expansion of n in n
25.196 * [backup-simplify]: Simplify 0 into 0
25.196 * [backup-simplify]: Simplify 1 into 1
25.196 * [backup-simplify]: Simplify (/ PI 1) into PI
25.197 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.197 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.197 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
25.197 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
25.197 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
25.198 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.199 * [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)))
25.200 * [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))))
25.200 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
25.200 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
25.200 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
25.200 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
25.200 * [taylor]: Taking taylor expansion of 1/2 in n
25.200 * [backup-simplify]: Simplify 1/2 into 1/2
25.200 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
25.200 * [taylor]: Taking taylor expansion of 1/2 in n
25.200 * [backup-simplify]: Simplify 1/2 into 1/2
25.200 * [taylor]: Taking taylor expansion of (/ 1 k) in n
25.200 * [taylor]: Taking taylor expansion of k in n
25.200 * [backup-simplify]: Simplify k into k
25.200 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
25.200 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
25.200 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
25.200 * [taylor]: Taking taylor expansion of 2 in n
25.200 * [backup-simplify]: Simplify 2 into 2
25.200 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.200 * [taylor]: Taking taylor expansion of PI in n
25.200 * [backup-simplify]: Simplify PI into PI
25.200 * [taylor]: Taking taylor expansion of n in n
25.200 * [backup-simplify]: Simplify 0 into 0
25.200 * [backup-simplify]: Simplify 1 into 1
25.201 * [backup-simplify]: Simplify (/ PI 1) into PI
25.201 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.201 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.202 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
25.202 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
25.202 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
25.203 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.203 * [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)))
25.204 * [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))))
25.204 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
25.204 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
25.204 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
25.204 * [taylor]: Taking taylor expansion of 1/2 in k
25.204 * [backup-simplify]: Simplify 1/2 into 1/2
25.204 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
25.204 * [taylor]: Taking taylor expansion of 1/2 in k
25.204 * [backup-simplify]: Simplify 1/2 into 1/2
25.204 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.204 * [taylor]: Taking taylor expansion of k in k
25.204 * [backup-simplify]: Simplify 0 into 0
25.204 * [backup-simplify]: Simplify 1 into 1
25.204 * [backup-simplify]: Simplify (/ 1 1) into 1
25.205 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
25.205 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
25.205 * [taylor]: Taking taylor expansion of (* 2 PI) in k
25.205 * [taylor]: Taking taylor expansion of 2 in k
25.205 * [backup-simplify]: Simplify 2 into 2
25.205 * [taylor]: Taking taylor expansion of PI in k
25.205 * [backup-simplify]: Simplify PI into PI
25.205 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.206 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.206 * [taylor]: Taking taylor expansion of (log n) in k
25.206 * [taylor]: Taking taylor expansion of n in k
25.206 * [backup-simplify]: Simplify n into n
25.206 * [backup-simplify]: Simplify (log n) into (log n)
25.206 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
25.206 * [backup-simplify]: Simplify (- 1/2) into -1/2
25.206 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
25.207 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
25.207 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
25.208 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
25.209 * [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))))
25.209 * [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))))
25.210 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
25.210 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
25.211 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
25.211 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
25.212 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
25.212 * [backup-simplify]: Simplify (- 0) into 0
25.212 * [backup-simplify]: Simplify (+ 0 0) into 0
25.213 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.214 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
25.215 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
25.215 * [taylor]: Taking taylor expansion of 0 in k
25.215 * [backup-simplify]: Simplify 0 into 0
25.215 * [backup-simplify]: Simplify 0 into 0
25.215 * [backup-simplify]: Simplify 0 into 0
25.216 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.216 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
25.218 * [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
25.218 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
25.219 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
25.219 * [backup-simplify]: Simplify (- 0) into 0
25.219 * [backup-simplify]: Simplify (+ 0 0) into 0
25.220 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.221 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
25.223 * [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
25.223 * [taylor]: Taking taylor expansion of 0 in k
25.223 * [backup-simplify]: Simplify 0 into 0
25.223 * [backup-simplify]: Simplify 0 into 0
25.223 * [backup-simplify]: Simplify 0 into 0
25.223 * [backup-simplify]: Simplify 0 into 0
25.223 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.224 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
25.227 * [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
25.227 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
25.229 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
25.229 * [backup-simplify]: Simplify (- 0) into 0
25.229 * [backup-simplify]: Simplify (+ 0 0) into 0
25.230 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.231 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
25.233 * [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
25.233 * [taylor]: Taking taylor expansion of 0 in k
25.233 * [backup-simplify]: Simplify 0 into 0
25.233 * [backup-simplify]: Simplify 0 into 0
25.234 * [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)))))
25.234 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
25.234 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
25.234 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
25.234 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
25.234 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
25.234 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
25.235 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
25.235 * [taylor]: Taking taylor expansion of 1/2 in k
25.235 * [backup-simplify]: Simplify 1/2 into 1/2
25.235 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.235 * [taylor]: Taking taylor expansion of k in k
25.235 * [backup-simplify]: Simplify 0 into 0
25.235 * [backup-simplify]: Simplify 1 into 1
25.235 * [backup-simplify]: Simplify (/ 1 1) into 1
25.235 * [taylor]: Taking taylor expansion of 1/2 in k
25.235 * [backup-simplify]: Simplify 1/2 into 1/2
25.235 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
25.235 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
25.235 * [taylor]: Taking taylor expansion of -2 in k
25.235 * [backup-simplify]: Simplify -2 into -2
25.235 * [taylor]: Taking taylor expansion of (/ PI n) in k
25.235 * [taylor]: Taking taylor expansion of PI in k
25.235 * [backup-simplify]: Simplify PI into PI
25.235 * [taylor]: Taking taylor expansion of n in k
25.235 * [backup-simplify]: Simplify n into n
25.235 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
25.235 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
25.235 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
25.236 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
25.236 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
25.236 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
25.236 * [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)))
25.236 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
25.236 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
25.236 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
25.236 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
25.236 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
25.236 * [taylor]: Taking taylor expansion of 1/2 in n
25.236 * [backup-simplify]: Simplify 1/2 into 1/2
25.236 * [taylor]: Taking taylor expansion of (/ 1 k) in n
25.236 * [taylor]: Taking taylor expansion of k in n
25.236 * [backup-simplify]: Simplify k into k
25.236 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
25.236 * [taylor]: Taking taylor expansion of 1/2 in n
25.236 * [backup-simplify]: Simplify 1/2 into 1/2
25.236 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
25.236 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
25.236 * [taylor]: Taking taylor expansion of -2 in n
25.236 * [backup-simplify]: Simplify -2 into -2
25.236 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.236 * [taylor]: Taking taylor expansion of PI in n
25.236 * [backup-simplify]: Simplify PI into PI
25.236 * [taylor]: Taking taylor expansion of n in n
25.236 * [backup-simplify]: Simplify 0 into 0
25.236 * [backup-simplify]: Simplify 1 into 1
25.237 * [backup-simplify]: Simplify (/ PI 1) into PI
25.237 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.238 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
25.238 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
25.238 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
25.239 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.239 * [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)))
25.240 * [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))))
25.240 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
25.240 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
25.240 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
25.240 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
25.240 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
25.240 * [taylor]: Taking taylor expansion of 1/2 in n
25.240 * [backup-simplify]: Simplify 1/2 into 1/2
25.240 * [taylor]: Taking taylor expansion of (/ 1 k) in n
25.240 * [taylor]: Taking taylor expansion of k in n
25.240 * [backup-simplify]: Simplify k into k
25.240 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
25.240 * [taylor]: Taking taylor expansion of 1/2 in n
25.240 * [backup-simplify]: Simplify 1/2 into 1/2
25.240 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
25.240 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
25.240 * [taylor]: Taking taylor expansion of -2 in n
25.241 * [backup-simplify]: Simplify -2 into -2
25.241 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.241 * [taylor]: Taking taylor expansion of PI in n
25.241 * [backup-simplify]: Simplify PI into PI
25.241 * [taylor]: Taking taylor expansion of n in n
25.241 * [backup-simplify]: Simplify 0 into 0
25.241 * [backup-simplify]: Simplify 1 into 1
25.241 * [backup-simplify]: Simplify (/ PI 1) into PI
25.242 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.243 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
25.243 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
25.243 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
25.248 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.249 * [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)))
25.251 * [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))))
25.251 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
25.251 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
25.251 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
25.251 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
25.251 * [taylor]: Taking taylor expansion of 1/2 in k
25.251 * [backup-simplify]: Simplify 1/2 into 1/2
25.251 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.251 * [taylor]: Taking taylor expansion of k in k
25.251 * [backup-simplify]: Simplify 0 into 0
25.251 * [backup-simplify]: Simplify 1 into 1
25.251 * [backup-simplify]: Simplify (/ 1 1) into 1
25.252 * [taylor]: Taking taylor expansion of 1/2 in k
25.252 * [backup-simplify]: Simplify 1/2 into 1/2
25.252 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
25.252 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
25.252 * [taylor]: Taking taylor expansion of (* -2 PI) in k
25.252 * [taylor]: Taking taylor expansion of -2 in k
25.252 * [backup-simplify]: Simplify -2 into -2
25.252 * [taylor]: Taking taylor expansion of PI in k
25.252 * [backup-simplify]: Simplify PI into PI
25.252 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.253 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
25.253 * [taylor]: Taking taylor expansion of (log n) in k
25.253 * [taylor]: Taking taylor expansion of n in k
25.253 * [backup-simplify]: Simplify n into n
25.254 * [backup-simplify]: Simplify (log n) into (log n)
25.254 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
25.254 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
25.255 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
25.256 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
25.257 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
25.258 * [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))))
25.260 * [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))))
25.261 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
25.261 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
25.262 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
25.262 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
25.263 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
25.263 * [backup-simplify]: Simplify (+ 0 0) into 0
25.264 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.265 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
25.266 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
25.266 * [taylor]: Taking taylor expansion of 0 in k
25.266 * [backup-simplify]: Simplify 0 into 0
25.266 * [backup-simplify]: Simplify 0 into 0
25.266 * [backup-simplify]: Simplify 0 into 0
25.267 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.267 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
25.269 * [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
25.269 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
25.270 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
25.270 * [backup-simplify]: Simplify (+ 0 0) into 0
25.271 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.272 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
25.273 * [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
25.273 * [taylor]: Taking taylor expansion of 0 in k
25.273 * [backup-simplify]: Simplify 0 into 0
25.273 * [backup-simplify]: Simplify 0 into 0
25.273 * [backup-simplify]: Simplify 0 into 0
25.273 * [backup-simplify]: Simplify 0 into 0
25.274 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.275 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
25.278 * [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
25.279 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
25.279 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
25.280 * [backup-simplify]: Simplify (+ 0 0) into 0
25.281 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.282 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
25.283 * [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
25.283 * [taylor]: Taking taylor expansion of 0 in k
25.283 * [backup-simplify]: Simplify 0 into 0
25.283 * [backup-simplify]: Simplify 0 into 0
25.284 * [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)))))
25.284 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 1)
25.291 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
25.291 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
25.291 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
25.291 * [taylor]: Taking taylor expansion of 2 in n
25.291 * [backup-simplify]: Simplify 2 into 2
25.291 * [taylor]: Taking taylor expansion of (* n PI) in n
25.291 * [taylor]: Taking taylor expansion of n in n
25.291 * [backup-simplify]: Simplify 0 into 0
25.291 * [backup-simplify]: Simplify 1 into 1
25.291 * [taylor]: Taking taylor expansion of PI in n
25.291 * [backup-simplify]: Simplify PI into PI
25.291 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
25.291 * [taylor]: Taking taylor expansion of 2 in n
25.291 * [backup-simplify]: Simplify 2 into 2
25.291 * [taylor]: Taking taylor expansion of (* n PI) in n
25.291 * [taylor]: Taking taylor expansion of n in n
25.291 * [backup-simplify]: Simplify 0 into 0
25.291 * [backup-simplify]: Simplify 1 into 1
25.291 * [taylor]: Taking taylor expansion of PI in n
25.291 * [backup-simplify]: Simplify PI into PI
25.292 * [backup-simplify]: Simplify (* 0 PI) into 0
25.293 * [backup-simplify]: Simplify (* 2 0) into 0
25.293 * [backup-simplify]: Simplify 0 into 0
25.294 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
25.296 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
25.296 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.297 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
25.298 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
25.298 * [backup-simplify]: Simplify 0 into 0
25.299 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
25.300 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
25.300 * [backup-simplify]: Simplify 0 into 0
25.300 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
25.301 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
25.301 * [backup-simplify]: Simplify 0 into 0
25.302 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
25.303 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
25.303 * [backup-simplify]: Simplify 0 into 0
25.304 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
25.305 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
25.305 * [backup-simplify]: Simplify 0 into 0
25.306 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
25.307 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
25.307 * [backup-simplify]: Simplify 0 into 0
25.308 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
25.308 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
25.308 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
25.308 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
25.308 * [taylor]: Taking taylor expansion of 2 in n
25.308 * [backup-simplify]: Simplify 2 into 2
25.308 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.308 * [taylor]: Taking taylor expansion of PI in n
25.308 * [backup-simplify]: Simplify PI into PI
25.308 * [taylor]: Taking taylor expansion of n in n
25.308 * [backup-simplify]: Simplify 0 into 0
25.308 * [backup-simplify]: Simplify 1 into 1
25.308 * [backup-simplify]: Simplify (/ PI 1) into PI
25.308 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
25.308 * [taylor]: Taking taylor expansion of 2 in n
25.308 * [backup-simplify]: Simplify 2 into 2
25.308 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.309 * [taylor]: Taking taylor expansion of PI in n
25.309 * [backup-simplify]: Simplify PI into PI
25.309 * [taylor]: Taking taylor expansion of n in n
25.309 * [backup-simplify]: Simplify 0 into 0
25.309 * [backup-simplify]: Simplify 1 into 1
25.309 * [backup-simplify]: Simplify (/ PI 1) into PI
25.309 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.309 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.310 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
25.310 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
25.311 * [backup-simplify]: Simplify 0 into 0
25.311 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.312 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
25.312 * [backup-simplify]: Simplify 0 into 0
25.312 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.313 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
25.313 * [backup-simplify]: Simplify 0 into 0
25.314 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.315 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
25.315 * [backup-simplify]: Simplify 0 into 0
25.315 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.316 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
25.316 * [backup-simplify]: Simplify 0 into 0
25.317 * [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
25.318 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
25.318 * [backup-simplify]: Simplify 0 into 0
25.318 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
25.319 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
25.319 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
25.319 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
25.319 * [taylor]: Taking taylor expansion of -2 in n
25.319 * [backup-simplify]: Simplify -2 into -2
25.319 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.319 * [taylor]: Taking taylor expansion of PI in n
25.319 * [backup-simplify]: Simplify PI into PI
25.319 * [taylor]: Taking taylor expansion of n in n
25.319 * [backup-simplify]: Simplify 0 into 0
25.319 * [backup-simplify]: Simplify 1 into 1
25.319 * [backup-simplify]: Simplify (/ PI 1) into PI
25.319 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
25.319 * [taylor]: Taking taylor expansion of -2 in n
25.319 * [backup-simplify]: Simplify -2 into -2
25.319 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.319 * [taylor]: Taking taylor expansion of PI in n
25.319 * [backup-simplify]: Simplify PI into PI
25.319 * [taylor]: Taking taylor expansion of n in n
25.319 * [backup-simplify]: Simplify 0 into 0
25.319 * [backup-simplify]: Simplify 1 into 1
25.319 * [backup-simplify]: Simplify (/ PI 1) into PI
25.320 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.320 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.321 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
25.321 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
25.321 * [backup-simplify]: Simplify 0 into 0
25.322 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.322 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
25.322 * [backup-simplify]: Simplify 0 into 0
25.323 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.324 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
25.324 * [backup-simplify]: Simplify 0 into 0
25.324 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.325 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
25.325 * [backup-simplify]: Simplify 0 into 0
25.326 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.327 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
25.327 * [backup-simplify]: Simplify 0 into 0
25.327 * [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
25.329 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
25.329 * [backup-simplify]: Simplify 0 into 0
25.329 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
25.329 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1 1)
25.330 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
25.330 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
25.330 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
25.330 * [taylor]: Taking taylor expansion of 2 in n
25.330 * [backup-simplify]: Simplify 2 into 2
25.330 * [taylor]: Taking taylor expansion of (* n PI) in n
25.330 * [taylor]: Taking taylor expansion of n in n
25.330 * [backup-simplify]: Simplify 0 into 0
25.330 * [backup-simplify]: Simplify 1 into 1
25.330 * [taylor]: Taking taylor expansion of PI in n
25.330 * [backup-simplify]: Simplify PI into PI
25.330 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
25.330 * [taylor]: Taking taylor expansion of 2 in n
25.330 * [backup-simplify]: Simplify 2 into 2
25.330 * [taylor]: Taking taylor expansion of (* n PI) in n
25.330 * [taylor]: Taking taylor expansion of n in n
25.330 * [backup-simplify]: Simplify 0 into 0
25.330 * [backup-simplify]: Simplify 1 into 1
25.330 * [taylor]: Taking taylor expansion of PI in n
25.330 * [backup-simplify]: Simplify PI into PI
25.330 * [backup-simplify]: Simplify (* 0 PI) into 0
25.331 * [backup-simplify]: Simplify (* 2 0) into 0
25.331 * [backup-simplify]: Simplify 0 into 0
25.332 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
25.333 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
25.333 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.334 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
25.334 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
25.334 * [backup-simplify]: Simplify 0 into 0
25.335 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
25.336 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
25.336 * [backup-simplify]: Simplify 0 into 0
25.337 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
25.337 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
25.337 * [backup-simplify]: Simplify 0 into 0
25.338 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
25.339 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
25.339 * [backup-simplify]: Simplify 0 into 0
25.340 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
25.341 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
25.341 * [backup-simplify]: Simplify 0 into 0
25.343 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
25.344 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
25.344 * [backup-simplify]: Simplify 0 into 0
25.344 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
25.344 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
25.344 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
25.345 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
25.345 * [taylor]: Taking taylor expansion of 2 in n
25.345 * [backup-simplify]: Simplify 2 into 2
25.345 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.345 * [taylor]: Taking taylor expansion of PI in n
25.345 * [backup-simplify]: Simplify PI into PI
25.345 * [taylor]: Taking taylor expansion of n in n
25.345 * [backup-simplify]: Simplify 0 into 0
25.345 * [backup-simplify]: Simplify 1 into 1
25.345 * [backup-simplify]: Simplify (/ PI 1) into PI
25.345 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
25.345 * [taylor]: Taking taylor expansion of 2 in n
25.345 * [backup-simplify]: Simplify 2 into 2
25.345 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.345 * [taylor]: Taking taylor expansion of PI in n
25.345 * [backup-simplify]: Simplify PI into PI
25.345 * [taylor]: Taking taylor expansion of n in n
25.345 * [backup-simplify]: Simplify 0 into 0
25.345 * [backup-simplify]: Simplify 1 into 1
25.345 * [backup-simplify]: Simplify (/ PI 1) into PI
25.346 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.346 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.347 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
25.347 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
25.347 * [backup-simplify]: Simplify 0 into 0
25.348 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.348 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
25.349 * [backup-simplify]: Simplify 0 into 0
25.349 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.350 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
25.350 * [backup-simplify]: Simplify 0 into 0
25.351 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.351 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
25.351 * [backup-simplify]: Simplify 0 into 0
25.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.353 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
25.353 * [backup-simplify]: Simplify 0 into 0
25.354 * [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
25.355 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
25.355 * [backup-simplify]: Simplify 0 into 0
25.355 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
25.355 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
25.355 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
25.355 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
25.355 * [taylor]: Taking taylor expansion of -2 in n
25.355 * [backup-simplify]: Simplify -2 into -2
25.355 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.355 * [taylor]: Taking taylor expansion of PI in n
25.356 * [backup-simplify]: Simplify PI into PI
25.356 * [taylor]: Taking taylor expansion of n in n
25.356 * [backup-simplify]: Simplify 0 into 0
25.356 * [backup-simplify]: Simplify 1 into 1
25.356 * [backup-simplify]: Simplify (/ PI 1) into PI
25.356 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
25.356 * [taylor]: Taking taylor expansion of -2 in n
25.356 * [backup-simplify]: Simplify -2 into -2
25.356 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.356 * [taylor]: Taking taylor expansion of PI in n
25.356 * [backup-simplify]: Simplify PI into PI
25.356 * [taylor]: Taking taylor expansion of n in n
25.356 * [backup-simplify]: Simplify 0 into 0
25.356 * [backup-simplify]: Simplify 1 into 1
25.356 * [backup-simplify]: Simplify (/ PI 1) into PI
25.357 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.357 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.358 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
25.358 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
25.358 * [backup-simplify]: Simplify 0 into 0
25.359 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.359 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
25.359 * [backup-simplify]: Simplify 0 into 0
25.360 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.361 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
25.361 * [backup-simplify]: Simplify 0 into 0
25.361 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.362 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
25.362 * [backup-simplify]: Simplify 0 into 0
25.363 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.364 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
25.364 * [backup-simplify]: Simplify 0 into 0
25.364 * [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
25.365 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
25.366 * [backup-simplify]: Simplify 0 into 0
25.366 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
25.366 * * * [progress]: simplifying candidates
25.366 * * * * [progress]: [ 1 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))))) (sqrt k))))>
25.366 * * * * [progress]: [ 2 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))))) (sqrt k))))>
25.366 * * * * [progress]: [ 3 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))) (sqrt k))))>
25.366 * * * * [progress]: [ 4 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))) (sqrt k))))>
25.366 * * * * [progress]: [ 5 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))) (sqrt k))))>
25.366 * * * * [progress]: [ 6 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))) (sqrt k))))>
25.366 * * * * [progress]: [ 7 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))) (sqrt k))))>
25.366 * * * * [progress]: [ 8 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)))) (sqrt k))))>
25.367 * * * * [progress]: [ 9 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))) (sqrt k))))>
25.367 * * * * [progress]: [ 10 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))) (sqrt k))))>
25.367 * * * * [progress]: [ 11 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (sqrt k))))>
25.367 * * * * [progress]: [ 12 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2))))) (sqrt k))))>
25.367 * * * * [progress]: [ 13 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))))) (sqrt k))))>
25.367 * * * * [progress]: [ 14 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (sqrt k))))>
25.367 * * * * [progress]: [ 15 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))))) (sqrt k))))>
25.367 * * * * [progress]: [ 16 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))))) (sqrt k))))>
25.367 * * * * [progress]: [ 17 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))) (sqrt k))))>
25.367 * * * * [progress]: [ 18 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1)) (sqrt k))))>
25.367 * * * * [progress]: [ 19 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (sqrt k))))>
25.367 * * * * [progress]: [ 20 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (sqrt k))))>
25.367 * * * * [progress]: [ 21 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (sqrt k))))>
25.367 * * * * [progress]: [ 22 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (sqrt k))))>
25.367 * * * * [progress]: [ 23 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (sqrt k))))>
25.367 * * * * [progress]: [ 24 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k))))>
25.367 * * * * [progress]: [ 25 / 102 ] 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)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
25.367 * * * * [progress]: [ 26 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (sqrt k))))>
25.367 * * * * [progress]: [ 27 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.367 * * * * [progress]: [ 28 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.367 * * * * [progress]: [ 29 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.367 * * * * [progress]: [ 30 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.367 * * * * [progress]: [ 31 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 32 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 33 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 34 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 35 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 36 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 37 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 38 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 39 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 40 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 41 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 42 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 43 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 44 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1)) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 45 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 46 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 47 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 48 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 49 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 50 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 51 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 52 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 53 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 54 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (sqrt k))))>
25.368 * * * * [progress]: [ 55 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 56 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 57 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 58 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 59 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 60 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 61 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 62 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 63 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 64 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 65 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 66 / 102 ] 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))))>
25.369 * * * * [progress]: [ 67 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 68 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 69 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 70 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 71 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 72 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 73 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 74 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 75 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 76 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 77 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.369 * * * * [progress]: [ 78 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 79 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 80 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 81 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 82 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 83 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 84 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 85 / 102 ] 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))))>
25.370 * * * * [progress]: [ 86 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 87 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 88 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 89 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 90 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 91 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))) (sqrt k))))>
25.370 * * * * [progress]: [ 92 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k))))>
25.370 * * * * [progress]: [ 93 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))))>
25.370 * * * * [progress]: [ 94 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 95 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 96 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 97 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 98 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 99 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 100 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 101 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.370 * * * * [progress]: [ 102 / 102 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
25.371 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
25.373 * * [simplify]: iteration 1: (123 enodes)
25.414 * * [simplify]: iteration 2: (339 enodes)
25.795 * * [simplify]: iteration 3: (1098 enodes)
27.200 * * [simplify]: Extracting #0: cost 31 inf + 0
27.201 * * [simplify]: Extracting #1: cost 329 inf + 0
27.204 * * [simplify]: Extracting #2: cost 758 inf + 2956
27.213 * * [simplify]: Extracting #3: cost 890 inf + 35208
27.244 * * [simplify]: Extracting #4: cost 459 inf + 175306
27.309 * * [simplify]: Extracting #5: cost 130 inf + 298687
27.406 * * [simplify]: Extracting #6: cost 21 inf + 331348
27.528 * * [simplify]: Extracting #7: cost 1 inf + 336270
27.662 * * [simplify]: Extracting #8: cost 0 inf + 336145
27.796 * [simplify]: Simplified to:
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ k 2))
  (pow (* 2 (* PI n)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 (* PI n)) (sqrt (- 1/2 (/ k 2))))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* 2 (* PI n)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* 2 (* PI n))
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ (- k) 2))
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ (- k) 2))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (exp (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* (* (pow (* 2 (* PI n)) (- 1/2 (/ k 2))) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ k 2))
  (pow (* 2 (* PI n)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 (* PI n)) (sqrt (- 1/2 (/ k 2))))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* 2 (* PI n)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* 2 (* PI n))
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ (- k) 2))
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ (- k) 2))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (exp (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* (* (pow (* 2 (* PI n)) (- 1/2 (/ k 2))) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (exp (+ (* PI n) (* PI n)))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (* (cbrt (* 2 (* PI n))) (cbrt (* 2 (* PI n))))
  (cbrt (* 2 (* PI n)))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (sqrt (* 2 (* PI n)))
  (sqrt (* 2 (* PI n)))
  (* n 2)
  (* (cbrt n) (* PI 2))
  (* (sqrt n) (* PI 2))
  (* 2 (* PI n))
  (real->posit16 (* 2 (* PI n)))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (exp (+ (* PI n) (* PI n)))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (* (cbrt (* 2 (* PI n))) (cbrt (* 2 (* PI n))))
  (cbrt (* 2 (* PI n)))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (sqrt (* 2 (* PI n)))
  (sqrt (* 2 (* PI n)))
  (* n 2)
  (* (cbrt n) (* PI 2))
  (* (sqrt n) (* PI 2))
  (* 2 (* PI n))
  (real->posit16 (* 2 (* PI n)))
  (+ (* (* k (* (sqrt (* 2 (* PI n))) (+ (log n) (log (* PI 2))))) -1/2) (+ (+ (* (* (* 1/4 (log (* PI 2))) (log n)) (* (sqrt (* 2 (* PI n))) (* k k))) (sqrt (* 2 (* PI n)))) (* (* 1/8 (* k k)) (+ (* (log n) (* (sqrt (* 2 (* PI n))) (log n))) (* (sqrt (* 2 (* PI n))) (* (log (* PI 2)) (log (* PI 2))))))))
  (exp (* (log (* 2 (* PI n))) (- 1/2 (* k 1/2))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))
  (+ (* (* k (* (sqrt (* 2 (* PI n))) (+ (log n) (log (* PI 2))))) -1/2) (+ (+ (* (* (* 1/4 (log (* PI 2))) (log n)) (* (sqrt (* 2 (* PI n))) (* k k))) (sqrt (* 2 (* PI n)))) (* (* 1/8 (* k k)) (+ (* (log n) (* (sqrt (* 2 (* PI n))) (log n))) (* (sqrt (* 2 (* PI n))) (* (log (* PI 2)) (log (* PI 2))))))))
  (exp (* (log (* 2 (* PI n))) (- 1/2 (* k 1/2))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
27.816 * * * [progress]: adding candidates to table
29.369 * [progress]: [Phase 3 of 3] Extracting.
29.369 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))> #<alt (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (- (/ k 2)))) (sqrt k)))> #<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)))))> #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))> #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k))) (sqrt (cbrt k))))>)
29.371 * * * [regime-changes]: Trying 2 branch expressions: (n k)
29.371 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))> #<alt (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (- (/ k 2)))) (sqrt k)))> #<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)))))> #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))> #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k))) (sqrt (cbrt k))))>)
29.473 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2)))))> #<alt (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (- (/ k 2)))) (sqrt k)))> #<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)))))> #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))> #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k))) (sqrt (cbrt k))))>)
29.528 * * * [regime]: Found split indices: #<option (#s(si 0 255))>
29.528 * [simplify]: Simplifying:
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 2))))
29.528 * * [simplify]: iteration 1: (18 enodes)
29.530 * * [simplify]: iteration 2: (22 enodes)
29.531 * * [simplify]: Extracting #0: cost 1 inf + 0
29.531 * * [simplify]: Extracting #1: cost 3 inf + 0
29.531 * * [simplify]: Extracting #2: cost 7 inf + 0
29.531 * * [simplify]: Extracting #3: cost 14 inf + 0
29.532 * * [simplify]: Extracting #4: cost 11 inf + 45
29.532 * * [simplify]: Extracting #5: cost 8 inf + 130
29.532 * * [simplify]: Extracting #6: cost 3 inf + 1379
29.532 * * [simplify]: Extracting #7: cost 1 inf + 2459
29.532 * * [simplify]: Extracting #8: cost 0 inf + 3414
29.532 * [simplify]: Simplified to:
  (/ (pow (* (* PI 2) n) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (pow (* (* PI 2) n) (- 1/2 (/ k 2))) 1/2)))
38.360 * [regime-testing]: Baseline error score: 0.40386153235836036
38.362 * [regime-testing]: Oracle error score: 0.02618975535646077
38.367 * [regime-testing]: End program error score: 0.40386153235836036