60.475 * [progress]: [Phase 1 of 3] Setting up.
0.003 * * * [progress]: [1/2] Preparing points
0.224 * * * [progress]: [2/2] Setting up program.
0.229 * [progress]: [Phase 2 of 3] Improving.
0.230 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.230 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.230 * * [simplify]: iteration 0: 13 enodes
0.233 * * [simplify]: iteration 1: 31 enodes
0.257 * * [simplify]: iteration 2: 62 enodes
0.272 * * [simplify]: iteration 3: 124 enodes
0.311 * * [simplify]: iteration 4: 327 enodes
0.577 * * [simplify]: iteration 5: 929 enodes
1.623 * * [simplify]: iteration 6: 2719 enodes
2.474 * * [simplify]: iteration complete: 5000 enodes
2.474 * * [simplify]: Extracting #0: cost 1 inf + 0
2.474 * * [simplify]: Extracting #1: cost 61 inf + 0
2.476 * * [simplify]: Extracting #2: cost 488 inf + 1
2.481 * * [simplify]: Extracting #3: cost 953 inf + 92
2.497 * * [simplify]: Extracting #4: cost 921 inf + 18841
2.527 * * [simplify]: Extracting #5: cost 645 inf + 66373
2.595 * * [simplify]: Extracting #6: cost 241 inf + 329522
2.699 * * [simplify]: Extracting #7: cost 5 inf + 560024
2.814 * * [simplify]: Extracting #8: cost 0 inf + 561759
2.917 * * [simplify]: Extracting #9: cost 0 inf + 561250
3.032 * [simplify]: Simplified to:
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
3.038 * * [progress]: iteration 1 / 4
3.038 * * * [progress]: picking best candidate
3.044 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
3.044 * * * [progress]: localizing error
3.071 * * * [progress]: generating rewritten candidates
3.071 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
3.088 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
3.103 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
3.130 * * * [progress]: generating series expansions
3.130 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
3.130 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
3.130 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
3.130 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
3.130 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
3.130 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
3.130 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.130 * [taylor]: Taking taylor expansion of 1/2 in k
3.131 * [backup-simplify]: Simplify 1/2 into 1/2
3.131 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.131 * [taylor]: Taking taylor expansion of 1/2 in k
3.131 * [backup-simplify]: Simplify 1/2 into 1/2
3.131 * [taylor]: Taking taylor expansion of k in k
3.131 * [backup-simplify]: Simplify 0 into 0
3.131 * [backup-simplify]: Simplify 1 into 1
3.131 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
3.131 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
3.131 * [taylor]: Taking taylor expansion of 2 in k
3.131 * [backup-simplify]: Simplify 2 into 2
3.131 * [taylor]: Taking taylor expansion of (* n PI) in k
3.131 * [taylor]: Taking taylor expansion of n in k
3.131 * [backup-simplify]: Simplify n into n
3.131 * [taylor]: Taking taylor expansion of PI in k
3.131 * [backup-simplify]: Simplify PI into PI
3.131 * [backup-simplify]: Simplify (* n PI) into (* n PI)
3.131 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
3.131 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
3.132 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.132 * [backup-simplify]: Simplify (- 0) into 0
3.133 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.133 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
3.133 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
3.133 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.133 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.133 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.133 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.133 * [taylor]: Taking taylor expansion of 1/2 in n
3.133 * [backup-simplify]: Simplify 1/2 into 1/2
3.133 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.133 * [taylor]: Taking taylor expansion of 1/2 in n
3.133 * [backup-simplify]: Simplify 1/2 into 1/2
3.134 * [taylor]: Taking taylor expansion of k in n
3.134 * [backup-simplify]: Simplify k into k
3.134 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.134 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.134 * [taylor]: Taking taylor expansion of 2 in n
3.134 * [backup-simplify]: Simplify 2 into 2
3.134 * [taylor]: Taking taylor expansion of (* n PI) in n
3.134 * [taylor]: Taking taylor expansion of n in n
3.134 * [backup-simplify]: Simplify 0 into 0
3.134 * [backup-simplify]: Simplify 1 into 1
3.134 * [taylor]: Taking taylor expansion of PI in n
3.134 * [backup-simplify]: Simplify PI into PI
3.134 * [backup-simplify]: Simplify (* 0 PI) into 0
3.135 * [backup-simplify]: Simplify (* 2 0) into 0
3.137 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.138 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.139 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.139 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.140 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.140 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.141 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.143 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.144 * [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)))))
3.144 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.144 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.144 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.144 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.144 * [taylor]: Taking taylor expansion of 1/2 in n
3.144 * [backup-simplify]: Simplify 1/2 into 1/2
3.144 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.145 * [taylor]: Taking taylor expansion of 1/2 in n
3.145 * [backup-simplify]: Simplify 1/2 into 1/2
3.145 * [taylor]: Taking taylor expansion of k in n
3.145 * [backup-simplify]: Simplify k into k
3.145 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.145 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.145 * [taylor]: Taking taylor expansion of 2 in n
3.145 * [backup-simplify]: Simplify 2 into 2
3.145 * [taylor]: Taking taylor expansion of (* n PI) in n
3.145 * [taylor]: Taking taylor expansion of n in n
3.145 * [backup-simplify]: Simplify 0 into 0
3.145 * [backup-simplify]: Simplify 1 into 1
3.145 * [taylor]: Taking taylor expansion of PI in n
3.145 * [backup-simplify]: Simplify PI into PI
3.145 * [backup-simplify]: Simplify (* 0 PI) into 0
3.146 * [backup-simplify]: Simplify (* 2 0) into 0
3.148 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.149 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.151 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.151 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.151 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.151 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.152 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.153 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.154 * [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)))))
3.154 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
3.154 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
3.154 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.154 * [taylor]: Taking taylor expansion of 1/2 in k
3.154 * [backup-simplify]: Simplify 1/2 into 1/2
3.154 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.154 * [taylor]: Taking taylor expansion of 1/2 in k
3.154 * [backup-simplify]: Simplify 1/2 into 1/2
3.154 * [taylor]: Taking taylor expansion of k in k
3.154 * [backup-simplify]: Simplify 0 into 0
3.154 * [backup-simplify]: Simplify 1 into 1
3.154 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
3.154 * [taylor]: Taking taylor expansion of (log n) in k
3.154 * [taylor]: Taking taylor expansion of n in k
3.154 * [backup-simplify]: Simplify n into n
3.154 * [backup-simplify]: Simplify (log n) into (log n)
3.154 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.154 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.155 * [taylor]: Taking taylor expansion of 2 in k
3.155 * [backup-simplify]: Simplify 2 into 2
3.155 * [taylor]: Taking taylor expansion of PI in k
3.155 * [backup-simplify]: Simplify PI into PI
3.155 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.156 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.156 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.156 * [backup-simplify]: Simplify (- 0) into 0
3.156 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.157 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.158 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
3.158 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
3.159 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
3.160 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.161 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
3.162 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.162 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
3.162 * [backup-simplify]: Simplify (- 0) into 0
3.162 * [backup-simplify]: Simplify (+ 0 0) into 0
3.167 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.167 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
3.169 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
3.169 * [taylor]: Taking taylor expansion of 0 in k
3.169 * [backup-simplify]: Simplify 0 into 0
3.169 * [backup-simplify]: Simplify 0 into 0
3.169 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
3.170 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.171 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.171 * [backup-simplify]: Simplify (+ 0 0) into 0
3.172 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
3.172 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.172 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.173 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
3.175 * [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)))))))
3.177 * [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)))))))
3.178 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.179 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.181 * [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
3.182 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
3.183 * [backup-simplify]: Simplify (- 0) into 0
3.183 * [backup-simplify]: Simplify (+ 0 0) into 0
3.185 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.186 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.189 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.189 * [taylor]: Taking taylor expansion of 0 in k
3.189 * [backup-simplify]: Simplify 0 into 0
3.189 * [backup-simplify]: Simplify 0 into 0
3.189 * [backup-simplify]: Simplify 0 into 0
3.191 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
3.192 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.195 * [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
3.196 * [backup-simplify]: Simplify (+ 0 0) into 0
3.197 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
3.197 * [backup-simplify]: Simplify (- 0) into 0
3.198 * [backup-simplify]: Simplify (+ 0 0) into 0
3.199 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.204 * [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)))))
3.209 * [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)))))
3.220 * [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)))))
3.221 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
3.221 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
3.221 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
3.221 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
3.221 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
3.221 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
3.221 * [taylor]: Taking taylor expansion of 1/2 in k
3.221 * [backup-simplify]: Simplify 1/2 into 1/2
3.221 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.221 * [taylor]: Taking taylor expansion of 1/2 in k
3.221 * [backup-simplify]: Simplify 1/2 into 1/2
3.221 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.221 * [taylor]: Taking taylor expansion of k in k
3.221 * [backup-simplify]: Simplify 0 into 0
3.221 * [backup-simplify]: Simplify 1 into 1
3.221 * [backup-simplify]: Simplify (/ 1 1) into 1
3.221 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
3.221 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
3.221 * [taylor]: Taking taylor expansion of 2 in k
3.221 * [backup-simplify]: Simplify 2 into 2
3.221 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.221 * [taylor]: Taking taylor expansion of PI in k
3.221 * [backup-simplify]: Simplify PI into PI
3.221 * [taylor]: Taking taylor expansion of n in k
3.221 * [backup-simplify]: Simplify n into n
3.221 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.221 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
3.221 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
3.222 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.222 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.222 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.222 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
3.222 * [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))))
3.223 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
3.223 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
3.223 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
3.223 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
3.223 * [taylor]: Taking taylor expansion of 1/2 in n
3.223 * [backup-simplify]: Simplify 1/2 into 1/2
3.223 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.223 * [taylor]: Taking taylor expansion of 1/2 in n
3.223 * [backup-simplify]: Simplify 1/2 into 1/2
3.223 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.223 * [taylor]: Taking taylor expansion of k in n
3.223 * [backup-simplify]: Simplify k into k
3.223 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.223 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
3.223 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.223 * [taylor]: Taking taylor expansion of 2 in n
3.223 * [backup-simplify]: Simplify 2 into 2
3.223 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.223 * [taylor]: Taking taylor expansion of PI in n
3.223 * [backup-simplify]: Simplify PI into PI
3.223 * [taylor]: Taking taylor expansion of n in n
3.223 * [backup-simplify]: Simplify 0 into 0
3.223 * [backup-simplify]: Simplify 1 into 1
3.223 * [backup-simplify]: Simplify (/ PI 1) into PI
3.224 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.224 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.224 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.225 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
3.225 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
3.226 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.226 * [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)))
3.227 * [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))))
3.227 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
3.227 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
3.227 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
3.227 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
3.227 * [taylor]: Taking taylor expansion of 1/2 in n
3.227 * [backup-simplify]: Simplify 1/2 into 1/2
3.227 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.227 * [taylor]: Taking taylor expansion of 1/2 in n
3.227 * [backup-simplify]: Simplify 1/2 into 1/2
3.227 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.227 * [taylor]: Taking taylor expansion of k in n
3.227 * [backup-simplify]: Simplify k into k
3.227 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.227 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
3.227 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.227 * [taylor]: Taking taylor expansion of 2 in n
3.227 * [backup-simplify]: Simplify 2 into 2
3.227 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.227 * [taylor]: Taking taylor expansion of PI in n
3.227 * [backup-simplify]: Simplify PI into PI
3.227 * [taylor]: Taking taylor expansion of n in n
3.227 * [backup-simplify]: Simplify 0 into 0
3.227 * [backup-simplify]: Simplify 1 into 1
3.228 * [backup-simplify]: Simplify (/ PI 1) into PI
3.228 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.229 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.229 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.229 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
3.229 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
3.230 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.231 * [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)))
3.231 * [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))))
3.231 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
3.231 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
3.231 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
3.231 * [taylor]: Taking taylor expansion of 1/2 in k
3.231 * [backup-simplify]: Simplify 1/2 into 1/2
3.231 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.231 * [taylor]: Taking taylor expansion of 1/2 in k
3.231 * [backup-simplify]: Simplify 1/2 into 1/2
3.232 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.232 * [taylor]: Taking taylor expansion of k in k
3.232 * [backup-simplify]: Simplify 0 into 0
3.232 * [backup-simplify]: Simplify 1 into 1
3.232 * [backup-simplify]: Simplify (/ 1 1) into 1
3.232 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
3.232 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.232 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.232 * [taylor]: Taking taylor expansion of 2 in k
3.232 * [backup-simplify]: Simplify 2 into 2
3.232 * [taylor]: Taking taylor expansion of PI in k
3.232 * [backup-simplify]: Simplify PI into PI
3.232 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.233 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.233 * [taylor]: Taking taylor expansion of (log n) in k
3.233 * [taylor]: Taking taylor expansion of n in k
3.233 * [backup-simplify]: Simplify n into n
3.233 * [backup-simplify]: Simplify (log n) into (log n)
3.233 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.233 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.234 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.234 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.234 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
3.235 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
3.236 * [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))))
3.237 * [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))))
3.237 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.238 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.239 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.239 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.239 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
3.239 * [backup-simplify]: Simplify (- 0) into 0
3.240 * [backup-simplify]: Simplify (+ 0 0) into 0
3.241 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.242 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
3.243 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.243 * [taylor]: Taking taylor expansion of 0 in k
3.243 * [backup-simplify]: Simplify 0 into 0
3.243 * [backup-simplify]: Simplify 0 into 0
3.243 * [backup-simplify]: Simplify 0 into 0
3.244 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.244 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.246 * [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
3.246 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.247 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
3.247 * [backup-simplify]: Simplify (- 0) into 0
3.247 * [backup-simplify]: Simplify (+ 0 0) into 0
3.248 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.250 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
3.252 * [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
3.252 * [taylor]: Taking taylor expansion of 0 in k
3.252 * [backup-simplify]: Simplify 0 into 0
3.252 * [backup-simplify]: Simplify 0 into 0
3.253 * [backup-simplify]: Simplify 0 into 0
3.253 * [backup-simplify]: Simplify 0 into 0
3.254 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.255 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.261 * [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
3.262 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.263 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
3.263 * [backup-simplify]: Simplify (- 0) into 0
3.263 * [backup-simplify]: Simplify (+ 0 0) into 0
3.265 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.266 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
3.268 * [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
3.268 * [taylor]: Taking taylor expansion of 0 in k
3.268 * [backup-simplify]: Simplify 0 into 0
3.268 * [backup-simplify]: Simplify 0 into 0
3.269 * [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)))))
3.269 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
3.269 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
3.269 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
3.269 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
3.269 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
3.269 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
3.269 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.269 * [taylor]: Taking taylor expansion of 1/2 in k
3.269 * [backup-simplify]: Simplify 1/2 into 1/2
3.269 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.269 * [taylor]: Taking taylor expansion of k in k
3.269 * [backup-simplify]: Simplify 0 into 0
3.269 * [backup-simplify]: Simplify 1 into 1
3.269 * [backup-simplify]: Simplify (/ 1 1) into 1
3.269 * [taylor]: Taking taylor expansion of 1/2 in k
3.269 * [backup-simplify]: Simplify 1/2 into 1/2
3.269 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
3.269 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
3.269 * [taylor]: Taking taylor expansion of -2 in k
3.269 * [backup-simplify]: Simplify -2 into -2
3.269 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.269 * [taylor]: Taking taylor expansion of PI in k
3.269 * [backup-simplify]: Simplify PI into PI
3.269 * [taylor]: Taking taylor expansion of n in k
3.269 * [backup-simplify]: Simplify n into n
3.270 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.270 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
3.270 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
3.270 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.270 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.270 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
3.270 * [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)))
3.270 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
3.270 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
3.270 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
3.270 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
3.270 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.270 * [taylor]: Taking taylor expansion of 1/2 in n
3.270 * [backup-simplify]: Simplify 1/2 into 1/2
3.271 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.271 * [taylor]: Taking taylor expansion of k in n
3.271 * [backup-simplify]: Simplify k into k
3.271 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.271 * [taylor]: Taking taylor expansion of 1/2 in n
3.271 * [backup-simplify]: Simplify 1/2 into 1/2
3.271 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
3.271 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.271 * [taylor]: Taking taylor expansion of -2 in n
3.271 * [backup-simplify]: Simplify -2 into -2
3.271 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.271 * [taylor]: Taking taylor expansion of PI in n
3.271 * [backup-simplify]: Simplify PI into PI
3.271 * [taylor]: Taking taylor expansion of n in n
3.271 * [backup-simplify]: Simplify 0 into 0
3.271 * [backup-simplify]: Simplify 1 into 1
3.271 * [backup-simplify]: Simplify (/ PI 1) into PI
3.271 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.272 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.272 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.272 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
3.273 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.274 * [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)))
3.275 * [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))))
3.275 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
3.275 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
3.275 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
3.275 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
3.275 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.275 * [taylor]: Taking taylor expansion of 1/2 in n
3.275 * [backup-simplify]: Simplify 1/2 into 1/2
3.275 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.275 * [taylor]: Taking taylor expansion of k in n
3.275 * [backup-simplify]: Simplify k into k
3.275 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.275 * [taylor]: Taking taylor expansion of 1/2 in n
3.275 * [backup-simplify]: Simplify 1/2 into 1/2
3.275 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
3.275 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.275 * [taylor]: Taking taylor expansion of -2 in n
3.275 * [backup-simplify]: Simplify -2 into -2
3.275 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.275 * [taylor]: Taking taylor expansion of PI in n
3.275 * [backup-simplify]: Simplify PI into PI
3.275 * [taylor]: Taking taylor expansion of n in n
3.275 * [backup-simplify]: Simplify 0 into 0
3.275 * [backup-simplify]: Simplify 1 into 1
3.276 * [backup-simplify]: Simplify (/ PI 1) into PI
3.276 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.277 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.277 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.277 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
3.278 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.283 * [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)))
3.284 * [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))))
3.284 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
3.284 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
3.284 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
3.284 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.284 * [taylor]: Taking taylor expansion of 1/2 in k
3.284 * [backup-simplify]: Simplify 1/2 into 1/2
3.284 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.284 * [taylor]: Taking taylor expansion of k in k
3.284 * [backup-simplify]: Simplify 0 into 0
3.284 * [backup-simplify]: Simplify 1 into 1
3.284 * [backup-simplify]: Simplify (/ 1 1) into 1
3.284 * [taylor]: Taking taylor expansion of 1/2 in k
3.284 * [backup-simplify]: Simplify 1/2 into 1/2
3.284 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
3.284 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
3.284 * [taylor]: Taking taylor expansion of (* -2 PI) in k
3.284 * [taylor]: Taking taylor expansion of -2 in k
3.284 * [backup-simplify]: Simplify -2 into -2
3.285 * [taylor]: Taking taylor expansion of PI in k
3.285 * [backup-simplify]: Simplify PI into PI
3.285 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.286 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.286 * [taylor]: Taking taylor expansion of (log n) in k
3.286 * [taylor]: Taking taylor expansion of n in k
3.286 * [backup-simplify]: Simplify n into n
3.286 * [backup-simplify]: Simplify (log n) into (log n)
3.286 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.286 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.286 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.287 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
3.288 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
3.288 * [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))))
3.289 * [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))))
3.290 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.290 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
3.291 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
3.291 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.292 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
3.292 * [backup-simplify]: Simplify (+ 0 0) into 0
3.293 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.295 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
3.297 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.297 * [taylor]: Taking taylor expansion of 0 in k
3.297 * [backup-simplify]: Simplify 0 into 0
3.297 * [backup-simplify]: Simplify 0 into 0
3.297 * [backup-simplify]: Simplify 0 into 0
3.298 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.299 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
3.303 * [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
3.303 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.304 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
3.305 * [backup-simplify]: Simplify (+ 0 0) into 0
3.306 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.308 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
3.310 * [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
3.310 * [taylor]: Taking taylor expansion of 0 in k
3.310 * [backup-simplify]: Simplify 0 into 0
3.310 * [backup-simplify]: Simplify 0 into 0
3.310 * [backup-simplify]: Simplify 0 into 0
3.310 * [backup-simplify]: Simplify 0 into 0
3.310 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.311 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.315 * [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
3.315 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.316 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
3.316 * [backup-simplify]: Simplify (+ 0 0) into 0
3.317 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.318 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
3.320 * [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
3.320 * [taylor]: Taking taylor expansion of 0 in k
3.320 * [backup-simplify]: Simplify 0 into 0
3.320 * [backup-simplify]: Simplify 0 into 0
3.321 * [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)))))
3.321 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
3.321 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI))
3.321 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
3.321 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.321 * [taylor]: Taking taylor expansion of 2 in n
3.321 * [backup-simplify]: Simplify 2 into 2
3.321 * [taylor]: Taking taylor expansion of (* n PI) in n
3.321 * [taylor]: Taking taylor expansion of n in n
3.321 * [backup-simplify]: Simplify 0 into 0
3.321 * [backup-simplify]: Simplify 1 into 1
3.321 * [taylor]: Taking taylor expansion of PI in n
3.321 * [backup-simplify]: Simplify PI into PI
3.321 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.321 * [taylor]: Taking taylor expansion of 2 in n
3.321 * [backup-simplify]: Simplify 2 into 2
3.321 * [taylor]: Taking taylor expansion of (* n PI) in n
3.321 * [taylor]: Taking taylor expansion of n in n
3.321 * [backup-simplify]: Simplify 0 into 0
3.321 * [backup-simplify]: Simplify 1 into 1
3.321 * [taylor]: Taking taylor expansion of PI in n
3.321 * [backup-simplify]: Simplify PI into PI
3.321 * [backup-simplify]: Simplify (* 0 PI) into 0
3.322 * [backup-simplify]: Simplify (* 2 0) into 0
3.322 * [backup-simplify]: Simplify 0 into 0
3.323 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.324 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.324 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.325 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.325 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
3.325 * [backup-simplify]: Simplify 0 into 0
3.326 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.327 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.327 * [backup-simplify]: Simplify 0 into 0
3.328 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.329 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
3.329 * [backup-simplify]: Simplify 0 into 0
3.330 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.330 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
3.331 * [backup-simplify]: Simplify 0 into 0
3.332 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.333 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
3.333 * [backup-simplify]: Simplify 0 into 0
3.334 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
3.335 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
3.335 * [backup-simplify]: Simplify 0 into 0
3.335 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
3.335 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n))
3.336 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
3.336 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.336 * [taylor]: Taking taylor expansion of 2 in n
3.336 * [backup-simplify]: Simplify 2 into 2
3.336 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.336 * [taylor]: Taking taylor expansion of PI in n
3.336 * [backup-simplify]: Simplify PI into PI
3.336 * [taylor]: Taking taylor expansion of n in n
3.336 * [backup-simplify]: Simplify 0 into 0
3.336 * [backup-simplify]: Simplify 1 into 1
3.336 * [backup-simplify]: Simplify (/ PI 1) into PI
3.336 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.336 * [taylor]: Taking taylor expansion of 2 in n
3.336 * [backup-simplify]: Simplify 2 into 2
3.336 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.336 * [taylor]: Taking taylor expansion of PI in n
3.336 * [backup-simplify]: Simplify PI into PI
3.336 * [taylor]: Taking taylor expansion of n in n
3.336 * [backup-simplify]: Simplify 0 into 0
3.336 * [backup-simplify]: Simplify 1 into 1
3.337 * [backup-simplify]: Simplify (/ PI 1) into PI
3.337 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.338 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.339 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.340 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.340 * [backup-simplify]: Simplify 0 into 0
3.341 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.342 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.342 * [backup-simplify]: Simplify 0 into 0
3.343 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.344 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.345 * [backup-simplify]: Simplify 0 into 0
3.346 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.347 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.347 * [backup-simplify]: Simplify 0 into 0
3.348 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.350 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.350 * [backup-simplify]: Simplify 0 into 0
3.351 * [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
3.352 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.352 * [backup-simplify]: Simplify 0 into 0
3.353 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
3.353 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n))
3.353 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
3.353 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.353 * [taylor]: Taking taylor expansion of -2 in n
3.353 * [backup-simplify]: Simplify -2 into -2
3.353 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.353 * [taylor]: Taking taylor expansion of PI in n
3.353 * [backup-simplify]: Simplify PI into PI
3.353 * [taylor]: Taking taylor expansion of n in n
3.353 * [backup-simplify]: Simplify 0 into 0
3.353 * [backup-simplify]: Simplify 1 into 1
3.354 * [backup-simplify]: Simplify (/ PI 1) into PI
3.354 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.354 * [taylor]: Taking taylor expansion of -2 in n
3.354 * [backup-simplify]: Simplify -2 into -2
3.354 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.354 * [taylor]: Taking taylor expansion of PI in n
3.354 * [backup-simplify]: Simplify PI into PI
3.354 * [taylor]: Taking taylor expansion of n in n
3.354 * [backup-simplify]: Simplify 0 into 0
3.354 * [backup-simplify]: Simplify 1 into 1
3.354 * [backup-simplify]: Simplify (/ PI 1) into PI
3.355 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.355 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.356 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.357 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
3.357 * [backup-simplify]: Simplify 0 into 0
3.358 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.359 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
3.359 * [backup-simplify]: Simplify 0 into 0
3.360 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.361 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.361 * [backup-simplify]: Simplify 0 into 0
3.362 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.363 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.363 * [backup-simplify]: Simplify 0 into 0
3.364 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.366 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.366 * [backup-simplify]: Simplify 0 into 0
3.367 * [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
3.369 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.369 * [backup-simplify]: Simplify 0 into 0
3.369 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
3.369 * * * * [progress]: [ 3 / 3 ] generating series at (2)
3.370 * [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))))
3.370 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
3.370 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
3.370 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.370 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.370 * [taylor]: Taking taylor expansion of k in k
3.370 * [backup-simplify]: Simplify 0 into 0
3.370 * [backup-simplify]: Simplify 1 into 1
3.370 * [backup-simplify]: Simplify (/ 1 1) into 1
3.371 * [backup-simplify]: Simplify (sqrt 0) into 0
3.372 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.372 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
3.372 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
3.372 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
3.372 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.372 * [taylor]: Taking taylor expansion of 1/2 in k
3.372 * [backup-simplify]: Simplify 1/2 into 1/2
3.372 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.372 * [taylor]: Taking taylor expansion of 1/2 in k
3.372 * [backup-simplify]: Simplify 1/2 into 1/2
3.372 * [taylor]: Taking taylor expansion of k in k
3.372 * [backup-simplify]: Simplify 0 into 0
3.372 * [backup-simplify]: Simplify 1 into 1
3.372 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
3.372 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
3.372 * [taylor]: Taking taylor expansion of 2 in k
3.372 * [backup-simplify]: Simplify 2 into 2
3.372 * [taylor]: Taking taylor expansion of (* n PI) in k
3.372 * [taylor]: Taking taylor expansion of n in k
3.372 * [backup-simplify]: Simplify n into n
3.372 * [taylor]: Taking taylor expansion of PI in k
3.372 * [backup-simplify]: Simplify PI into PI
3.373 * [backup-simplify]: Simplify (* n PI) into (* n PI)
3.373 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
3.373 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
3.373 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.373 * [backup-simplify]: Simplify (- 0) into 0
3.374 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.374 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
3.374 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
3.374 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
3.374 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
3.374 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.374 * [taylor]: Taking taylor expansion of k in n
3.374 * [backup-simplify]: Simplify k into k
3.374 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.374 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
3.374 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.374 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
3.374 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.375 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.375 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.375 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.375 * [taylor]: Taking taylor expansion of 1/2 in n
3.375 * [backup-simplify]: Simplify 1/2 into 1/2
3.375 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.375 * [taylor]: Taking taylor expansion of 1/2 in n
3.375 * [backup-simplify]: Simplify 1/2 into 1/2
3.375 * [taylor]: Taking taylor expansion of k in n
3.375 * [backup-simplify]: Simplify k into k
3.375 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.375 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.375 * [taylor]: Taking taylor expansion of 2 in n
3.375 * [backup-simplify]: Simplify 2 into 2
3.375 * [taylor]: Taking taylor expansion of (* n PI) in n
3.375 * [taylor]: Taking taylor expansion of n in n
3.375 * [backup-simplify]: Simplify 0 into 0
3.375 * [backup-simplify]: Simplify 1 into 1
3.375 * [taylor]: Taking taylor expansion of PI in n
3.375 * [backup-simplify]: Simplify PI into PI
3.376 * [backup-simplify]: Simplify (* 0 PI) into 0
3.376 * [backup-simplify]: Simplify (* 2 0) into 0
3.377 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.378 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.379 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.379 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.379 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.379 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.380 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.380 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.381 * [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)))))
3.381 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
3.381 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
3.381 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.381 * [taylor]: Taking taylor expansion of k in n
3.381 * [backup-simplify]: Simplify k into k
3.381 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.381 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
3.381 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.381 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
3.381 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.381 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.382 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.382 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.382 * [taylor]: Taking taylor expansion of 1/2 in n
3.382 * [backup-simplify]: Simplify 1/2 into 1/2
3.382 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.382 * [taylor]: Taking taylor expansion of 1/2 in n
3.382 * [backup-simplify]: Simplify 1/2 into 1/2
3.382 * [taylor]: Taking taylor expansion of k in n
3.382 * [backup-simplify]: Simplify k into k
3.382 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.382 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.382 * [taylor]: Taking taylor expansion of 2 in n
3.382 * [backup-simplify]: Simplify 2 into 2
3.382 * [taylor]: Taking taylor expansion of (* n PI) in n
3.382 * [taylor]: Taking taylor expansion of n in n
3.382 * [backup-simplify]: Simplify 0 into 0
3.382 * [backup-simplify]: Simplify 1 into 1
3.382 * [taylor]: Taking taylor expansion of PI in n
3.382 * [backup-simplify]: Simplify PI into PI
3.382 * [backup-simplify]: Simplify (* 0 PI) into 0
3.382 * [backup-simplify]: Simplify (* 2 0) into 0
3.383 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.384 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.385 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.385 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.385 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.385 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.386 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.387 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.388 * [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)))))
3.389 * [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)))
3.389 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
3.389 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
3.389 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
3.389 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.389 * [taylor]: Taking taylor expansion of 1/2 in k
3.389 * [backup-simplify]: Simplify 1/2 into 1/2
3.389 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.389 * [taylor]: Taking taylor expansion of 1/2 in k
3.389 * [backup-simplify]: Simplify 1/2 into 1/2
3.389 * [taylor]: Taking taylor expansion of k in k
3.389 * [backup-simplify]: Simplify 0 into 0
3.389 * [backup-simplify]: Simplify 1 into 1
3.389 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
3.389 * [taylor]: Taking taylor expansion of (log n) in k
3.389 * [taylor]: Taking taylor expansion of n in k
3.389 * [backup-simplify]: Simplify n into n
3.389 * [backup-simplify]: Simplify (log n) into (log n)
3.389 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.389 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.389 * [taylor]: Taking taylor expansion of 2 in k
3.389 * [backup-simplify]: Simplify 2 into 2
3.389 * [taylor]: Taking taylor expansion of PI in k
3.389 * [backup-simplify]: Simplify PI into PI
3.389 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.390 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.390 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.391 * [backup-simplify]: Simplify (- 0) into 0
3.391 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.391 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.392 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
3.393 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
3.393 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.393 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.393 * [taylor]: Taking taylor expansion of k in k
3.393 * [backup-simplify]: Simplify 0 into 0
3.393 * [backup-simplify]: Simplify 1 into 1
3.393 * [backup-simplify]: Simplify (/ 1 1) into 1
3.393 * [backup-simplify]: Simplify (sqrt 0) into 0
3.394 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.399 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
3.399 * [backup-simplify]: Simplify 0 into 0
3.400 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.401 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
3.402 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.402 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
3.402 * [backup-simplify]: Simplify (- 0) into 0
3.403 * [backup-simplify]: Simplify (+ 0 0) into 0
3.404 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.404 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
3.405 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
3.406 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
3.406 * [taylor]: Taking taylor expansion of 0 in k
3.406 * [backup-simplify]: Simplify 0 into 0
3.407 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
3.407 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.408 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.409 * [backup-simplify]: Simplify (+ 0 0) into 0
3.409 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
3.409 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.410 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.410 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
3.412 * [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)))))))
3.415 * [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)))))))
3.416 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
3.417 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.417 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.419 * [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
3.420 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
3.420 * [backup-simplify]: Simplify (- 0) into 0
3.420 * [backup-simplify]: Simplify (+ 0 0) into 0
3.421 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.422 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.424 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.424 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.424 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
3.425 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
3.426 * [taylor]: Taking taylor expansion of 0 in k
3.426 * [backup-simplify]: Simplify 0 into 0
3.426 * [backup-simplify]: Simplify 0 into 0
3.426 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
3.428 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.429 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
3.430 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.431 * [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
3.432 * [backup-simplify]: Simplify (+ 0 0) into 0
3.432 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
3.433 * [backup-simplify]: Simplify (- 0) into 0
3.433 * [backup-simplify]: Simplify (+ 0 0) into 0
3.435 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.440 * [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)))))
3.449 * [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))))))))
3.453 * [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))))))))
3.454 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.456 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
3.461 * [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
3.462 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
3.463 * [backup-simplify]: Simplify (- 0) into 0
3.463 * [backup-simplify]: Simplify (+ 0 0) into 0
3.465 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.466 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
3.469 * [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
3.470 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.471 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
3.473 * [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
3.473 * [taylor]: Taking taylor expansion of 0 in k
3.473 * [backup-simplify]: Simplify 0 into 0
3.473 * [backup-simplify]: Simplify 0 into 0
3.473 * [backup-simplify]: Simplify 0 into 0
3.474 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.478 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.481 * [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
3.483 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.488 * [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
3.489 * [backup-simplify]: Simplify (+ 0 0) into 0
3.490 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
3.490 * [backup-simplify]: Simplify (- 0) into 0
3.491 * [backup-simplify]: Simplify (+ 0 0) into 0
3.493 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
3.499 * [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)))))))
3.523 * [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))))))))))))))
3.537 * [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))))))))))))))
3.557 * [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))))))))))))))))))))))
3.558 * [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)))))
3.558 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
3.558 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
3.558 * [taylor]: Taking taylor expansion of (sqrt k) in k
3.558 * [taylor]: Taking taylor expansion of k in k
3.558 * [backup-simplify]: Simplify 0 into 0
3.558 * [backup-simplify]: Simplify 1 into 1
3.558 * [backup-simplify]: Simplify (sqrt 0) into 0
3.560 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.560 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
3.560 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
3.560 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
3.560 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
3.560 * [taylor]: Taking taylor expansion of 1/2 in k
3.560 * [backup-simplify]: Simplify 1/2 into 1/2
3.560 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.560 * [taylor]: Taking taylor expansion of 1/2 in k
3.560 * [backup-simplify]: Simplify 1/2 into 1/2
3.560 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.560 * [taylor]: Taking taylor expansion of k in k
3.560 * [backup-simplify]: Simplify 0 into 0
3.560 * [backup-simplify]: Simplify 1 into 1
3.560 * [backup-simplify]: Simplify (/ 1 1) into 1
3.560 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
3.560 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
3.560 * [taylor]: Taking taylor expansion of 2 in k
3.561 * [backup-simplify]: Simplify 2 into 2
3.561 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.561 * [taylor]: Taking taylor expansion of PI in k
3.561 * [backup-simplify]: Simplify PI into PI
3.561 * [taylor]: Taking taylor expansion of n in k
3.561 * [backup-simplify]: Simplify n into n
3.561 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.561 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
3.561 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
3.561 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.562 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.562 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.562 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
3.562 * [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))))
3.562 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
3.562 * [taylor]: Taking taylor expansion of (sqrt k) in n
3.562 * [taylor]: Taking taylor expansion of k in n
3.562 * [backup-simplify]: Simplify k into k
3.562 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
3.562 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
3.562 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
3.562 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
3.563 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
3.563 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
3.563 * [taylor]: Taking taylor expansion of 1/2 in n
3.563 * [backup-simplify]: Simplify 1/2 into 1/2
3.563 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.563 * [taylor]: Taking taylor expansion of 1/2 in n
3.563 * [backup-simplify]: Simplify 1/2 into 1/2
3.563 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.563 * [taylor]: Taking taylor expansion of k in n
3.563 * [backup-simplify]: Simplify k into k
3.563 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.563 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
3.563 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.563 * [taylor]: Taking taylor expansion of 2 in n
3.563 * [backup-simplify]: Simplify 2 into 2
3.563 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.563 * [taylor]: Taking taylor expansion of PI in n
3.563 * [backup-simplify]: Simplify PI into PI
3.563 * [taylor]: Taking taylor expansion of n in n
3.563 * [backup-simplify]: Simplify 0 into 0
3.563 * [backup-simplify]: Simplify 1 into 1
3.563 * [backup-simplify]: Simplify (/ PI 1) into PI
3.564 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.565 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.565 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.565 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
3.565 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
3.566 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.567 * [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)))
3.569 * [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))))
3.569 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
3.569 * [taylor]: Taking taylor expansion of (sqrt k) in n
3.569 * [taylor]: Taking taylor expansion of k in n
3.569 * [backup-simplify]: Simplify k into k
3.569 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
3.569 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
3.569 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
3.569 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
3.569 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
3.569 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
3.569 * [taylor]: Taking taylor expansion of 1/2 in n
3.569 * [backup-simplify]: Simplify 1/2 into 1/2
3.569 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.569 * [taylor]: Taking taylor expansion of 1/2 in n
3.569 * [backup-simplify]: Simplify 1/2 into 1/2
3.569 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.569 * [taylor]: Taking taylor expansion of k in n
3.569 * [backup-simplify]: Simplify k into k
3.569 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.569 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
3.569 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.569 * [taylor]: Taking taylor expansion of 2 in n
3.569 * [backup-simplify]: Simplify 2 into 2
3.569 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.569 * [taylor]: Taking taylor expansion of PI in n
3.569 * [backup-simplify]: Simplify PI into PI
3.569 * [taylor]: Taking taylor expansion of n in n
3.569 * [backup-simplify]: Simplify 0 into 0
3.569 * [backup-simplify]: Simplify 1 into 1
3.570 * [backup-simplify]: Simplify (/ PI 1) into PI
3.570 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.571 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.571 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.572 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
3.572 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
3.573 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.574 * [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)))
3.575 * [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))))
3.576 * [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))
3.576 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
3.576 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
3.577 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
3.577 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
3.577 * [taylor]: Taking taylor expansion of 1/2 in k
3.577 * [backup-simplify]: Simplify 1/2 into 1/2
3.577 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.577 * [taylor]: Taking taylor expansion of 1/2 in k
3.577 * [backup-simplify]: Simplify 1/2 into 1/2
3.577 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.577 * [taylor]: Taking taylor expansion of k in k
3.577 * [backup-simplify]: Simplify 0 into 0
3.577 * [backup-simplify]: Simplify 1 into 1
3.577 * [backup-simplify]: Simplify (/ 1 1) into 1
3.577 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
3.577 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.577 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.577 * [taylor]: Taking taylor expansion of 2 in k
3.577 * [backup-simplify]: Simplify 2 into 2
3.577 * [taylor]: Taking taylor expansion of PI in k
3.577 * [backup-simplify]: Simplify PI into PI
3.578 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.579 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.579 * [taylor]: Taking taylor expansion of (log n) in k
3.579 * [taylor]: Taking taylor expansion of n in k
3.579 * [backup-simplify]: Simplify n into n
3.579 * [backup-simplify]: Simplify (log n) into (log n)
3.579 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.580 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.580 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.580 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.581 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
3.582 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
3.583 * [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))))
3.583 * [taylor]: Taking taylor expansion of (sqrt k) in k
3.583 * [taylor]: Taking taylor expansion of k in k
3.583 * [backup-simplify]: Simplify 0 into 0
3.583 * [backup-simplify]: Simplify 1 into 1
3.584 * [backup-simplify]: Simplify (sqrt 0) into 0
3.585 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.586 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
3.586 * [backup-simplify]: Simplify 0 into 0
3.588 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.589 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.591 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.591 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.592 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
3.592 * [backup-simplify]: Simplify (- 0) into 0
3.593 * [backup-simplify]: Simplify (+ 0 0) into 0
3.594 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.595 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
3.597 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.599 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
3.599 * [taylor]: Taking taylor expansion of 0 in k
3.599 * [backup-simplify]: Simplify 0 into 0
3.599 * [backup-simplify]: Simplify 0 into 0
3.600 * [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))))))
3.602 * [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))))))
3.603 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.604 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.608 * [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
3.608 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.609 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
3.609 * [backup-simplify]: Simplify (- 0) into 0
3.610 * [backup-simplify]: Simplify (+ 0 0) into 0
3.611 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.613 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
3.616 * [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
3.616 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
3.618 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
3.618 * [taylor]: Taking taylor expansion of 0 in k
3.618 * [backup-simplify]: Simplify 0 into 0
3.618 * [backup-simplify]: Simplify 0 into 0
3.618 * [backup-simplify]: Simplify 0 into 0
3.622 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.624 * [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))))))
3.625 * [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))))))
3.626 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.628 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.633 * [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
3.634 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.635 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
3.635 * [backup-simplify]: Simplify (- 0) into 0
3.636 * [backup-simplify]: Simplify (+ 0 0) into 0
3.637 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.639 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
3.642 * [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
3.642 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
3.644 * [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
3.644 * [taylor]: Taking taylor expansion of 0 in k
3.645 * [backup-simplify]: Simplify 0 into 0
3.645 * [backup-simplify]: Simplify 0 into 0
3.645 * [backup-simplify]: Simplify 0 into 0
3.645 * [backup-simplify]: Simplify 0 into 0
3.649 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.651 * [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))))))
3.652 * [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))))))
3.656 * [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))))))))
3.657 * [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)))
3.657 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
3.657 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
3.657 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
3.657 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
3.657 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
3.657 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
3.657 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.657 * [taylor]: Taking taylor expansion of 1/2 in k
3.657 * [backup-simplify]: Simplify 1/2 into 1/2
3.657 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.657 * [taylor]: Taking taylor expansion of k in k
3.657 * [backup-simplify]: Simplify 0 into 0
3.657 * [backup-simplify]: Simplify 1 into 1
3.658 * [backup-simplify]: Simplify (/ 1 1) into 1
3.658 * [taylor]: Taking taylor expansion of 1/2 in k
3.658 * [backup-simplify]: Simplify 1/2 into 1/2
3.658 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
3.658 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
3.658 * [taylor]: Taking taylor expansion of -2 in k
3.658 * [backup-simplify]: Simplify -2 into -2
3.658 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.658 * [taylor]: Taking taylor expansion of PI in k
3.658 * [backup-simplify]: Simplify PI into PI
3.658 * [taylor]: Taking taylor expansion of n in k
3.658 * [backup-simplify]: Simplify n into n
3.658 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.658 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
3.658 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
3.659 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.659 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.659 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
3.659 * [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)))
3.659 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
3.659 * [taylor]: Taking taylor expansion of (/ -1 k) in k
3.660 * [taylor]: Taking taylor expansion of -1 in k
3.660 * [backup-simplify]: Simplify -1 into -1
3.660 * [taylor]: Taking taylor expansion of k in k
3.660 * [backup-simplify]: Simplify 0 into 0
3.660 * [backup-simplify]: Simplify 1 into 1
3.660 * [backup-simplify]: Simplify (/ -1 1) into -1
3.660 * [backup-simplify]: Simplify (sqrt 0) into 0
3.667 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
3.667 * [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))))
3.667 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
3.667 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
3.667 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
3.667 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
3.667 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
3.667 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.667 * [taylor]: Taking taylor expansion of 1/2 in n
3.667 * [backup-simplify]: Simplify 1/2 into 1/2
3.668 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.668 * [taylor]: Taking taylor expansion of k in n
3.668 * [backup-simplify]: Simplify k into k
3.668 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.668 * [taylor]: Taking taylor expansion of 1/2 in n
3.668 * [backup-simplify]: Simplify 1/2 into 1/2
3.668 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
3.668 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.668 * [taylor]: Taking taylor expansion of -2 in n
3.668 * [backup-simplify]: Simplify -2 into -2
3.668 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.668 * [taylor]: Taking taylor expansion of PI in n
3.668 * [backup-simplify]: Simplify PI into PI
3.668 * [taylor]: Taking taylor expansion of n in n
3.668 * [backup-simplify]: Simplify 0 into 0
3.668 * [backup-simplify]: Simplify 1 into 1
3.668 * [backup-simplify]: Simplify (/ PI 1) into PI
3.669 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.670 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.670 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.670 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
3.672 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.673 * [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)))
3.674 * [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))))
3.675 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
3.675 * [taylor]: Taking taylor expansion of (/ -1 k) in n
3.675 * [taylor]: Taking taylor expansion of -1 in n
3.675 * [backup-simplify]: Simplify -1 into -1
3.675 * [taylor]: Taking taylor expansion of k in n
3.675 * [backup-simplify]: Simplify k into k
3.675 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
3.675 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
3.675 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
3.675 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
3.676 * [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)))
3.676 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
3.676 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
3.676 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
3.677 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
3.677 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
3.677 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.677 * [taylor]: Taking taylor expansion of 1/2 in n
3.677 * [backup-simplify]: Simplify 1/2 into 1/2
3.677 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.677 * [taylor]: Taking taylor expansion of k in n
3.677 * [backup-simplify]: Simplify k into k
3.677 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.677 * [taylor]: Taking taylor expansion of 1/2 in n
3.677 * [backup-simplify]: Simplify 1/2 into 1/2
3.677 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
3.677 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.677 * [taylor]: Taking taylor expansion of -2 in n
3.677 * [backup-simplify]: Simplify -2 into -2
3.677 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.677 * [taylor]: Taking taylor expansion of PI in n
3.677 * [backup-simplify]: Simplify PI into PI
3.677 * [taylor]: Taking taylor expansion of n in n
3.677 * [backup-simplify]: Simplify 0 into 0
3.677 * [backup-simplify]: Simplify 1 into 1
3.678 * [backup-simplify]: Simplify (/ PI 1) into PI
3.678 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.679 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.679 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.679 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
3.680 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.681 * [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)))
3.682 * [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))))
3.682 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
3.682 * [taylor]: Taking taylor expansion of (/ -1 k) in n
3.682 * [taylor]: Taking taylor expansion of -1 in n
3.682 * [backup-simplify]: Simplify -1 into -1
3.682 * [taylor]: Taking taylor expansion of k in n
3.682 * [backup-simplify]: Simplify k into k
3.682 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
3.682 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
3.682 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
3.682 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
3.683 * [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)))
3.683 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
3.683 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
3.683 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
3.683 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
3.683 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.683 * [taylor]: Taking taylor expansion of 1/2 in k
3.683 * [backup-simplify]: Simplify 1/2 into 1/2
3.683 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.683 * [taylor]: Taking taylor expansion of k in k
3.683 * [backup-simplify]: Simplify 0 into 0
3.683 * [backup-simplify]: Simplify 1 into 1
3.684 * [backup-simplify]: Simplify (/ 1 1) into 1
3.684 * [taylor]: Taking taylor expansion of 1/2 in k
3.684 * [backup-simplify]: Simplify 1/2 into 1/2
3.684 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
3.684 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
3.684 * [taylor]: Taking taylor expansion of (* -2 PI) in k
3.684 * [taylor]: Taking taylor expansion of -2 in k
3.684 * [backup-simplify]: Simplify -2 into -2
3.684 * [taylor]: Taking taylor expansion of PI in k
3.684 * [backup-simplify]: Simplify PI into PI
3.684 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.685 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.685 * [taylor]: Taking taylor expansion of (log n) in k
3.685 * [taylor]: Taking taylor expansion of n in k
3.685 * [backup-simplify]: Simplify n into n
3.685 * [backup-simplify]: Simplify (log n) into (log n)
3.685 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.685 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.685 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.686 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
3.687 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
3.688 * [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))))
3.688 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
3.688 * [taylor]: Taking taylor expansion of (/ -1 k) in k
3.688 * [taylor]: Taking taylor expansion of -1 in k
3.688 * [backup-simplify]: Simplify -1 into -1
3.688 * [taylor]: Taking taylor expansion of k in k
3.688 * [backup-simplify]: Simplify 0 into 0
3.688 * [backup-simplify]: Simplify 1 into 1
3.688 * [backup-simplify]: Simplify (/ -1 1) into -1
3.688 * [backup-simplify]: Simplify (sqrt 0) into 0
3.689 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
3.690 * [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)))))
3.691 * [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)))))
3.691 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.692 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
3.693 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
3.693 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.693 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
3.693 * [backup-simplify]: Simplify (+ 0 0) into 0
3.694 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.695 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
3.696 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.697 * [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
3.697 * [taylor]: Taking taylor expansion of 0 in k
3.697 * [backup-simplify]: Simplify 0 into 0
3.697 * [backup-simplify]: Simplify 0 into 0
3.698 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
3.700 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.701 * [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))))))
3.702 * [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))))))
3.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.703 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
3.705 * [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
3.705 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.706 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
3.706 * [backup-simplify]: Simplify (+ 0 0) into 0
3.707 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.708 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
3.709 * [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
3.709 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.710 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
3.711 * [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
3.711 * [taylor]: Taking taylor expansion of 0 in k
3.711 * [backup-simplify]: Simplify 0 into 0
3.711 * [backup-simplify]: Simplify 0 into 0
3.711 * [backup-simplify]: Simplify 0 into 0
3.712 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.714 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.716 * [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))))))
3.717 * [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))))))
3.719 * [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)))))))))))
3.720 * * * [progress]: simplifying candidates
3.720 * * * * [progress]: [ 1 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
3.720 * * * * [progress]: [ 2 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
3.720 * * * * [progress]: [ 3 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
3.720 * * * * [progress]: [ 4 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
3.720 * * * * [progress]: [ 5 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
3.720 * * * * [progress]: [ 6 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
3.720 * * * * [progress]: [ 7 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
3.720 * * * * [progress]: [ 8 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
3.720 * * * * [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)))>
3.720 * * * * [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)))>
3.720 * * * * [progress]: [ 11 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
3.720 * * * * [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)))>
3.720 * * * * [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)))>
3.720 * * * * [progress]: [ 14 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
3.720 * * * * [progress]: [ 15 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))>
3.720 * * * * [progress]: [ 16 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))>
3.720 * * * * [progress]: [ 17 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k)))>
3.720 * * * * [progress]: [ 18 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k)))>
3.720 * * * * [progress]: [ 19 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
3.720 * * * * [progress]: [ 20 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
3.720 * * * * [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)))>
3.721 * * * * [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)))>
3.721 * * * * [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)))>
3.721 * * * * [progress]: [ 24 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))>
3.721 * * * * [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)))>
3.721 * * * * [progress]: [ 26 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
3.721 * * * * [progress]: [ 27 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 28 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 29 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 30 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (+ (log n) (log 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 31 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log (* n 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 32 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 33 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [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)))>
3.721 * * * * [progress]: [ 35 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [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)))>
3.721 * * * * [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)))>
3.721 * * * * [progress]: [ 38 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 39 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* (* n 2) PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 40 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (* (cbrt PI) (cbrt PI))) (cbrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 41 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 42 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) 1) PI) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 43 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 44 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 45 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))>
3.721 * * * * [progress]: [ 46 / 127 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) 1))>
3.721 * * * * [progress]: [ 47 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
3.721 * * * * [progress]: [ 48 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
3.722 * * * * [progress]: [ 49 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
3.722 * * * * [progress]: [ 50 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
3.722 * * * * [progress]: [ 51 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
3.722 * * * * [progress]: [ 52 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
3.722 * * * * [progress]: [ 53 / 127 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
3.722 * * * * [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)))))>
3.722 * * * * [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)))))>
3.722 * * * * [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)))))>
3.722 * * * * [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)))))>
3.722 * * * * [progress]: [ 58 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (- (sqrt k))))>
3.722 * * * * [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)))))>
3.722 * * * * [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)))))>
3.722 * * * * [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)))))>
3.722 * * * * [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))))>
3.722 * * * * [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)))))>
3.722 * * * * [progress]: [ 64 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) 1) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
3.722 * * * * [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)))))>
3.722 * * * * [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)))))>
3.722 * * * * [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)))))>
3.722 * * * * [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))))>
3.722 * * * * [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)))))>
3.722 * * * * [progress]: [ 70 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) 1) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
3.722 * * * * [progress]: [ 71 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
3.722 * * * * [progress]: [ 72 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
3.722 * * * * [progress]: [ 73 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
3.723 * * * * [progress]: [ 74 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))>
3.723 * * * * [progress]: [ 75 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
3.723 * * * * [progress]: [ 76 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) 1) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))>
3.723 * * * * [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)))))>
3.723 * * * * [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)))))>
3.723 * * * * [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)))))>
3.723 * * * * [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))))>
3.723 * * * * [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)))))>
3.723 * * * * [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))))>
3.723 * * * * [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)))))>
3.723 * * * * [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)))))>
3.723 * * * * [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)))))>
3.723 * * * * [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))))>
3.723 * * * * [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)))))>
3.723 * * * * [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))))>
3.723 * * * * [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)))))>
3.723 * * * * [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)))))>
3.723 * * * * [progress]: [ 91 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
3.723 * * * * [progress]: [ 92 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
3.723 * * * * [progress]: [ 93 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
3.723 * * * * [progress]: [ 94 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
3.723 * * * * [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)))))>
3.723 * * * * [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)))))>
3.723 * * * * [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)))))>
3.723 * * * * [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))))>
3.724 * * * * [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)))))>
3.724 * * * * [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))))>
3.724 * * * * [progress]: [ 101 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
3.724 * * * * [progress]: [ 102 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
3.724 * * * * [progress]: [ 103 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))>
3.724 * * * * [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))))>
3.724 * * * * [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))))>
3.724 * * * * [progress]: [ 106 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
3.724 * * * * [progress]: [ 107 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k)))>
3.724 * * * * [progress]: [ 108 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
3.724 * * * * [progress]: [ 109 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k)))>
3.724 * * * * [progress]: [ 110 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))))>
3.724 * * * * [progress]: [ 111 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))))>
3.724 * * * * [progress]: [ 112 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))))>
3.724 * * * * [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)))))))>
3.724 * * * * [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)))))))>
3.724 * * * * [progress]: [ 115 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))>
3.724 * * * * [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)))))>
3.724 * * * * [progress]: [ 117 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))))>
3.724 * * * * [progress]: [ 118 / 127 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
3.724 * * * * [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)))>
3.724 * * * * [progress]: [ 120 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
3.724 * * * * [progress]: [ 121 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
3.724 * * * * [progress]: [ 122 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.724 * * * * [progress]: [ 123 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.724 * * * * [progress]: [ 124 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.725 * * * * [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)))))))))))))))))))))))>
3.725 * * * * [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)))))))))>
3.725 * * * * [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))))))))))))>
3.726 * [simplify]: Simplifying:
  (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log 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 2) (- 1/2 (/ k 2)))
  (pow 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 2)) (log PI))
  (log (* (* n 2) PI))
  (exp (* (* n 2) PI))
  (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))
  (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) 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 PI) (cbrt PI)))
  (* (* n 2) (sqrt PI))
  (* (* n 2) 1)
  (* 2 PI)
  (real->posit16 (* (* n 2) PI))
  (- (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (+ (log (* n 2)) (log 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 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) 1)
  (/ (pow 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 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)))))))))))
3.730 * * [simplify]: iteration 0: 271 enodes
3.828 * * [simplify]: iteration 1: 662 enodes
4.183 * * [simplify]: iteration 2: 2241 enodes
5.028 * * [simplify]: iteration complete: 5008 enodes
5.028 * * [simplify]: Extracting #0: cost 96 inf + 0
5.029 * * [simplify]: Extracting #1: cost 556 inf + 1
5.032 * * [simplify]: Extracting #2: cost 1197 inf + 932
5.047 * * [simplify]: Extracting #3: cost 1527 inf + 33350
5.101 * * [simplify]: Extracting #4: cost 1063 inf + 205576
5.192 * * [simplify]: Extracting #5: cost 381 inf + 501395
5.373 * * [simplify]: Extracting #6: cost 148 inf + 646155
5.528 * * [simplify]: Extracting #7: cost 56 inf + 693103
5.700 * * [simplify]: Extracting #8: cost 3 inf + 723366
5.903 * * [simplify]: Extracting #9: cost 0 inf + 713906
6.099 * * [simplify]: Extracting #10: cost 0 inf + 709106
6.279 * * [simplify]: Extracting #11: cost 0 inf + 708436
6.457 * [simplify]: Simplified to:
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (- 1/2 (* 1/2 k))
  (- 1/2 (* 1/2 k))
  (- 1/2 (* 1/2 k))
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (/ k 2))
  (pow (* (* 2 PI) n) (* (cbrt (- 1/2 (* 1/2 k))) (cbrt (- 1/2 (* 1/2 k)))))
  (pow (* (* 2 PI) n) (sqrt (- 1/2 (* 1/2 k))))
  (* (* 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) (* -1/2 k))
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (* -1/2 k))
  (pow (* n 2) (- 1/2 (* 1/2 k)))
  (pow PI (- 1/2 (* 1/2 k)))
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (exp (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (* (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (* (* (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (pow (* (* 2 PI) n) (- 1/4 (/ k 4)))
  (pow (* (* 2 PI) n) (- 1/4 (/ k 4)))
  (real->posit16 (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (log (* (* 2 PI) n))
  (log (* (* 2 PI) n))
  (log (* (* 2 PI) n))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* 2 PI) n) (* (* (* 2 PI) n) (* (* 2 PI) n)))
  (* (* (* 2 PI) n) (* (* (* 2 PI) n) (* (* 2 PI) n)))
  (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n)))
  (cbrt (* (* 2 PI) n))
  (* (* (* 2 PI) n) (* (* (* 2 PI) n) (* (* 2 PI) n)))
  (sqrt (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (* (* (cbrt PI) (* n 2)) (cbrt PI))
  (* 2 (* n (sqrt PI)))
  (* n 2)
  (* 2 PI)
  (real->posit16 (* (* 2 PI) n))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (exp (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (* (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) k) (* (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))))
  (* (cbrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))) (cbrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))))
  (cbrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (* (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)) (* (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)) (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))))
  (sqrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (sqrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (- (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (- (sqrt k))
  (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (cbrt (sqrt k)))
  (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))
  (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (cbrt (sqrt k)))
  (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))
  (/ (/ (pow (* n 2) (- 1/2 (* 1/2 k))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (cbrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (* 1/2 k))) (fabs (cbrt k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt (cbrt k)))
  (/ (pow (* n 2) (- 1/2 (* 1/2 k))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt (sqrt k)))
  (pow (* n 2) (- 1/2 (* 1/2 k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k))
  (/ (pow (* n 2) (- 1/2 (* 1/2 k))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt (sqrt k)))
  (pow (* n 2) (- 1/2 (* 1/2 k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k))
  (* (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (sqrt k))) (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (sqrt k))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (sqrt k)))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (/ (fabs (cbrt k)) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (cbrt k)))
  (* (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (* (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt k))
  (* (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (* (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt k))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (sqrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (fabs (cbrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (cbrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt k))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))
  1
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))
  1
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (/ (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (fabs (cbrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))
  (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))
  (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))
  (/ (sqrt k) (pow (* (* 2 PI) n) (* -1/2 k)))
  (/ (sqrt k) (pow (* (* 2 PI) n) (* -1/2 k)))
  (/ (sqrt k) (pow PI (- 1/2 (* 1/2 k))))
  (/ (sqrt k) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (sqrt k) (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (sqrt k) (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- 1/4 (/ k 4))))
  (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
  (real->posit16 (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (- (+ (+ (* (log (* 2 PI)) (* (* (* (* k k) (log n)) (sqrt (* (* 2 PI) n))) 1/4)) (sqrt (* (* 2 PI) n))) (* (* (* k k) 1/8) (+ (* (sqrt (* (* 2 PI) n)) (* (log (* 2 PI)) (log (* 2 PI)))) (* (sqrt (* (* 2 PI) n)) (* (log n) (log n)))))) (/ (* (* k (sqrt (* (* 2 PI) n))) (log (* (* 2 PI) n))) 2))
  (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n)))))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (+ (+ (* (- (log (* 2 PI))) (* (* (* k k) (* +nan.0 (sqrt (* (* 2 PI) n)))) (log n))) (* (* (* k k) (* +nan.0 (sqrt (* (* 2 PI) n)))) (- (log (* 2 PI)) (* (log n) (log n))))) (+ (+ (- (* k (* +nan.0 (sqrt (* (* 2 PI) n)))) (* +nan.0 (sqrt (* (* 2 PI) n)))) (* (* (* k k) (* +nan.0 (sqrt (* (* 2 PI) n)))) (- (* (log (* 2 PI)) (log (* 2 PI))) (log n)))) (- (* (* k k) (* +nan.0 (sqrt (* (* 2 PI) n)))) (* +nan.0 (* (* k (sqrt (* (* 2 PI) n))) (- (log (* 2 PI)) (log n)))))))
  (+ (/ (* (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (- +nan.0)) (* (* k k) k)) (* +nan.0 (- (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) k) (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (* k k)))))
  (+ (- (* (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) k) +nan.0)) (* +nan.0 (- (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k)) (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))))))
6.472 * * * [progress]: adding candidates to table
6.997 * * [progress]: iteration 2 / 4
6.997 * * * [progress]: picking best candidate
7.029 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
7.029 * * * [progress]: localizing error
7.065 * * * [progress]: generating rewritten candidates
7.065 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
7.094 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1 2)
7.105 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
7.137 * * * [progress]: generating series expansions
7.137 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
7.138 * [backup-simplify]: Simplify (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
7.138 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
7.138 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
7.138 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
7.138 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
7.138 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
7.138 * [taylor]: Taking taylor expansion of 1/2 in k
7.138 * [backup-simplify]: Simplify 1/2 into 1/2
7.138 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
7.138 * [taylor]: Taking taylor expansion of 1/2 in k
7.138 * [backup-simplify]: Simplify 1/2 into 1/2
7.138 * [taylor]: Taking taylor expansion of k in k
7.138 * [backup-simplify]: Simplify 0 into 0
7.138 * [backup-simplify]: Simplify 1 into 1
7.138 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
7.138 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
7.138 * [taylor]: Taking taylor expansion of 2 in k
7.138 * [backup-simplify]: Simplify 2 into 2
7.138 * [taylor]: Taking taylor expansion of (* n PI) in k
7.138 * [taylor]: Taking taylor expansion of n in k
7.138 * [backup-simplify]: Simplify n into n
7.138 * [taylor]: Taking taylor expansion of PI in k
7.138 * [backup-simplify]: Simplify PI into PI
7.138 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.138 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
7.139 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
7.139 * [backup-simplify]: Simplify (* 1/2 0) into 0
7.140 * [backup-simplify]: Simplify (- 0) into 0
7.140 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.140 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
7.140 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
7.140 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
7.140 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
7.141 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
7.141 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
7.141 * [taylor]: Taking taylor expansion of 1/2 in n
7.141 * [backup-simplify]: Simplify 1/2 into 1/2
7.141 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
7.141 * [taylor]: Taking taylor expansion of 1/2 in n
7.141 * [backup-simplify]: Simplify 1/2 into 1/2
7.141 * [taylor]: Taking taylor expansion of k in n
7.141 * [backup-simplify]: Simplify k into k
7.141 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.141 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.141 * [taylor]: Taking taylor expansion of 2 in n
7.141 * [backup-simplify]: Simplify 2 into 2
7.141 * [taylor]: Taking taylor expansion of (* n PI) in n
7.141 * [taylor]: Taking taylor expansion of n in n
7.141 * [backup-simplify]: Simplify 0 into 0
7.141 * [backup-simplify]: Simplify 1 into 1
7.141 * [taylor]: Taking taylor expansion of PI in n
7.141 * [backup-simplify]: Simplify PI into PI
7.141 * [backup-simplify]: Simplify (* 0 PI) into 0
7.142 * [backup-simplify]: Simplify (* 2 0) into 0
7.144 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.145 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.146 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.146 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
7.146 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
7.146 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
7.148 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.149 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
7.150 * [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)))))
7.150 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
7.150 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
7.150 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
7.150 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
7.150 * [taylor]: Taking taylor expansion of 1/2 in n
7.150 * [backup-simplify]: Simplify 1/2 into 1/2
7.150 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
7.150 * [taylor]: Taking taylor expansion of 1/2 in n
7.150 * [backup-simplify]: Simplify 1/2 into 1/2
7.150 * [taylor]: Taking taylor expansion of k in n
7.150 * [backup-simplify]: Simplify k into k
7.151 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.151 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.151 * [taylor]: Taking taylor expansion of 2 in n
7.151 * [backup-simplify]: Simplify 2 into 2
7.151 * [taylor]: Taking taylor expansion of (* n PI) in n
7.151 * [taylor]: Taking taylor expansion of n in n
7.151 * [backup-simplify]: Simplify 0 into 0
7.151 * [backup-simplify]: Simplify 1 into 1
7.151 * [taylor]: Taking taylor expansion of PI in n
7.151 * [backup-simplify]: Simplify PI into PI
7.151 * [backup-simplify]: Simplify (* 0 PI) into 0
7.152 * [backup-simplify]: Simplify (* 2 0) into 0
7.154 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.155 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.156 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.157 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
7.157 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
7.157 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
7.158 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.159 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
7.161 * [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)))))
7.161 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
7.161 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
7.161 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
7.161 * [taylor]: Taking taylor expansion of 1/2 in k
7.161 * [backup-simplify]: Simplify 1/2 into 1/2
7.161 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
7.161 * [taylor]: Taking taylor expansion of 1/2 in k
7.161 * [backup-simplify]: Simplify 1/2 into 1/2
7.161 * [taylor]: Taking taylor expansion of k in k
7.161 * [backup-simplify]: Simplify 0 into 0
7.161 * [backup-simplify]: Simplify 1 into 1
7.161 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
7.161 * [taylor]: Taking taylor expansion of (log n) in k
7.161 * [taylor]: Taking taylor expansion of n in k
7.161 * [backup-simplify]: Simplify n into n
7.161 * [backup-simplify]: Simplify (log n) into (log n)
7.161 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.161 * [taylor]: Taking taylor expansion of (* 2 PI) in k
7.161 * [taylor]: Taking taylor expansion of 2 in k
7.161 * [backup-simplify]: Simplify 2 into 2
7.161 * [taylor]: Taking taylor expansion of PI in k
7.161 * [backup-simplify]: Simplify PI into PI
7.162 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.163 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.163 * [backup-simplify]: Simplify (* 1/2 0) into 0
7.164 * [backup-simplify]: Simplify (- 0) into 0
7.164 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.165 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.166 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
7.167 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
7.168 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
7.170 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.171 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
7.172 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.173 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
7.173 * [backup-simplify]: Simplify (- 0) into 0
7.174 * [backup-simplify]: Simplify (+ 0 0) into 0
7.175 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.177 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
7.179 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.179 * [taylor]: Taking taylor expansion of 0 in k
7.179 * [backup-simplify]: Simplify 0 into 0
7.179 * [backup-simplify]: Simplify 0 into 0
7.180 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
7.181 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.182 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.183 * [backup-simplify]: Simplify (+ 0 0) into 0
7.184 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
7.184 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.184 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.186 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
7.189 * [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)))))))
7.192 * [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)))))))
7.193 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.195 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.198 * [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
7.199 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
7.199 * [backup-simplify]: Simplify (- 0) into 0
7.200 * [backup-simplify]: Simplify (+ 0 0) into 0
7.201 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.203 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.205 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.205 * [taylor]: Taking taylor expansion of 0 in k
7.205 * [backup-simplify]: Simplify 0 into 0
7.205 * [backup-simplify]: Simplify 0 into 0
7.205 * [backup-simplify]: Simplify 0 into 0
7.207 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
7.208 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.212 * [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
7.213 * [backup-simplify]: Simplify (+ 0 0) into 0
7.214 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
7.214 * [backup-simplify]: Simplify (- 0) into 0
7.215 * [backup-simplify]: Simplify (+ 0 0) into 0
7.217 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.221 * [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)))))
7.226 * [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)))))
7.236 * [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)))))
7.237 * [backup-simplify]: Simplify (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
7.237 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
7.237 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
7.237 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
7.237 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
7.237 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
7.237 * [taylor]: Taking taylor expansion of 1/2 in k
7.237 * [backup-simplify]: Simplify 1/2 into 1/2
7.237 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.237 * [taylor]: Taking taylor expansion of 1/2 in k
7.237 * [backup-simplify]: Simplify 1/2 into 1/2
7.237 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.237 * [taylor]: Taking taylor expansion of k in k
7.237 * [backup-simplify]: Simplify 0 into 0
7.237 * [backup-simplify]: Simplify 1 into 1
7.238 * [backup-simplify]: Simplify (/ 1 1) into 1
7.238 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
7.238 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
7.238 * [taylor]: Taking taylor expansion of 2 in k
7.238 * [backup-simplify]: Simplify 2 into 2
7.238 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.238 * [taylor]: Taking taylor expansion of PI in k
7.238 * [backup-simplify]: Simplify PI into PI
7.238 * [taylor]: Taking taylor expansion of n in k
7.238 * [backup-simplify]: Simplify n into n
7.238 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.238 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
7.238 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
7.239 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.239 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.240 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.240 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
7.240 * [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))))
7.240 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
7.240 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
7.240 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
7.240 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
7.240 * [taylor]: Taking taylor expansion of 1/2 in n
7.240 * [backup-simplify]: Simplify 1/2 into 1/2
7.240 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.240 * [taylor]: Taking taylor expansion of 1/2 in n
7.240 * [backup-simplify]: Simplify 1/2 into 1/2
7.240 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.240 * [taylor]: Taking taylor expansion of k in n
7.240 * [backup-simplify]: Simplify k into k
7.240 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.240 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
7.240 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.240 * [taylor]: Taking taylor expansion of 2 in n
7.240 * [backup-simplify]: Simplify 2 into 2
7.240 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.240 * [taylor]: Taking taylor expansion of PI in n
7.240 * [backup-simplify]: Simplify PI into PI
7.240 * [taylor]: Taking taylor expansion of n in n
7.240 * [backup-simplify]: Simplify 0 into 0
7.241 * [backup-simplify]: Simplify 1 into 1
7.241 * [backup-simplify]: Simplify (/ PI 1) into PI
7.242 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.243 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.243 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.243 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
7.243 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
7.244 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.246 * [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)))
7.247 * [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))))
7.247 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
7.247 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
7.247 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
7.247 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
7.247 * [taylor]: Taking taylor expansion of 1/2 in n
7.247 * [backup-simplify]: Simplify 1/2 into 1/2
7.247 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.247 * [taylor]: Taking taylor expansion of 1/2 in n
7.247 * [backup-simplify]: Simplify 1/2 into 1/2
7.247 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.247 * [taylor]: Taking taylor expansion of k in n
7.247 * [backup-simplify]: Simplify k into k
7.247 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.247 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
7.247 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.247 * [taylor]: Taking taylor expansion of 2 in n
7.247 * [backup-simplify]: Simplify 2 into 2
7.247 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.247 * [taylor]: Taking taylor expansion of PI in n
7.247 * [backup-simplify]: Simplify PI into PI
7.247 * [taylor]: Taking taylor expansion of n in n
7.247 * [backup-simplify]: Simplify 0 into 0
7.247 * [backup-simplify]: Simplify 1 into 1
7.248 * [backup-simplify]: Simplify (/ PI 1) into PI
7.248 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.250 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.250 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.250 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
7.250 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
7.251 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.252 * [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)))
7.254 * [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))))
7.254 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
7.254 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
7.254 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
7.254 * [taylor]: Taking taylor expansion of 1/2 in k
7.254 * [backup-simplify]: Simplify 1/2 into 1/2
7.254 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.254 * [taylor]: Taking taylor expansion of 1/2 in k
7.254 * [backup-simplify]: Simplify 1/2 into 1/2
7.254 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.254 * [taylor]: Taking taylor expansion of k in k
7.254 * [backup-simplify]: Simplify 0 into 0
7.254 * [backup-simplify]: Simplify 1 into 1
7.254 * [backup-simplify]: Simplify (/ 1 1) into 1
7.254 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
7.255 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.255 * [taylor]: Taking taylor expansion of (* 2 PI) in k
7.255 * [taylor]: Taking taylor expansion of 2 in k
7.255 * [backup-simplify]: Simplify 2 into 2
7.255 * [taylor]: Taking taylor expansion of PI in k
7.255 * [backup-simplify]: Simplify PI into PI
7.255 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.256 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.256 * [taylor]: Taking taylor expansion of (log n) in k
7.256 * [taylor]: Taking taylor expansion of n in k
7.256 * [backup-simplify]: Simplify n into n
7.256 * [backup-simplify]: Simplify (log n) into (log n)
7.257 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.257 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.258 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.258 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.259 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
7.260 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
7.261 * [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))))
7.262 * [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))))
7.263 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.264 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.273 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.273 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.274 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
7.275 * [backup-simplify]: Simplify (- 0) into 0
7.275 * [backup-simplify]: Simplify (+ 0 0) into 0
7.277 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.278 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
7.280 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
7.280 * [taylor]: Taking taylor expansion of 0 in k
7.280 * [backup-simplify]: Simplify 0 into 0
7.280 * [backup-simplify]: Simplify 0 into 0
7.280 * [backup-simplify]: Simplify 0 into 0
7.281 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.282 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.286 * [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
7.286 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.288 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
7.288 * [backup-simplify]: Simplify (- 0) into 0
7.288 * [backup-simplify]: Simplify (+ 0 0) into 0
7.289 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.290 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
7.292 * [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
7.292 * [taylor]: Taking taylor expansion of 0 in k
7.292 * [backup-simplify]: Simplify 0 into 0
7.292 * [backup-simplify]: Simplify 0 into 0
7.292 * [backup-simplify]: Simplify 0 into 0
7.292 * [backup-simplify]: Simplify 0 into 0
7.293 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.293 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.296 * [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
7.297 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.297 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
7.298 * [backup-simplify]: Simplify (- 0) into 0
7.298 * [backup-simplify]: Simplify (+ 0 0) into 0
7.299 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.300 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
7.302 * [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
7.302 * [taylor]: Taking taylor expansion of 0 in k
7.302 * [backup-simplify]: Simplify 0 into 0
7.302 * [backup-simplify]: Simplify 0 into 0
7.302 * [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)))))
7.303 * [backup-simplify]: Simplify (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
7.303 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
7.303 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
7.303 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
7.303 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
7.303 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
7.303 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.303 * [taylor]: Taking taylor expansion of 1/2 in k
7.303 * [backup-simplify]: Simplify 1/2 into 1/2
7.303 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.303 * [taylor]: Taking taylor expansion of k in k
7.303 * [backup-simplify]: Simplify 0 into 0
7.303 * [backup-simplify]: Simplify 1 into 1
7.303 * [backup-simplify]: Simplify (/ 1 1) into 1
7.303 * [taylor]: Taking taylor expansion of 1/2 in k
7.303 * [backup-simplify]: Simplify 1/2 into 1/2
7.303 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
7.303 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
7.303 * [taylor]: Taking taylor expansion of -2 in k
7.303 * [backup-simplify]: Simplify -2 into -2
7.303 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.303 * [taylor]: Taking taylor expansion of PI in k
7.303 * [backup-simplify]: Simplify PI into PI
7.303 * [taylor]: Taking taylor expansion of n in k
7.303 * [backup-simplify]: Simplify n into n
7.303 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.303 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
7.303 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
7.304 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.304 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.304 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
7.304 * [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)))
7.304 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
7.304 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
7.304 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
7.304 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
7.304 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.304 * [taylor]: Taking taylor expansion of 1/2 in n
7.304 * [backup-simplify]: Simplify 1/2 into 1/2
7.304 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.304 * [taylor]: Taking taylor expansion of k in n
7.304 * [backup-simplify]: Simplify k into k
7.304 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.304 * [taylor]: Taking taylor expansion of 1/2 in n
7.304 * [backup-simplify]: Simplify 1/2 into 1/2
7.304 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
7.304 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.304 * [taylor]: Taking taylor expansion of -2 in n
7.304 * [backup-simplify]: Simplify -2 into -2
7.304 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.304 * [taylor]: Taking taylor expansion of PI in n
7.304 * [backup-simplify]: Simplify PI into PI
7.304 * [taylor]: Taking taylor expansion of n in n
7.304 * [backup-simplify]: Simplify 0 into 0
7.304 * [backup-simplify]: Simplify 1 into 1
7.305 * [backup-simplify]: Simplify (/ PI 1) into PI
7.305 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.306 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.306 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.306 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
7.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.307 * [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)))
7.308 * [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))))
7.308 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
7.308 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
7.308 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
7.308 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
7.308 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.308 * [taylor]: Taking taylor expansion of 1/2 in n
7.308 * [backup-simplify]: Simplify 1/2 into 1/2
7.308 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.308 * [taylor]: Taking taylor expansion of k in n
7.308 * [backup-simplify]: Simplify k into k
7.308 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.308 * [taylor]: Taking taylor expansion of 1/2 in n
7.309 * [backup-simplify]: Simplify 1/2 into 1/2
7.309 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
7.309 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.309 * [taylor]: Taking taylor expansion of -2 in n
7.309 * [backup-simplify]: Simplify -2 into -2
7.309 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.309 * [taylor]: Taking taylor expansion of PI in n
7.309 * [backup-simplify]: Simplify PI into PI
7.309 * [taylor]: Taking taylor expansion of n in n
7.309 * [backup-simplify]: Simplify 0 into 0
7.309 * [backup-simplify]: Simplify 1 into 1
7.309 * [backup-simplify]: Simplify (/ PI 1) into PI
7.309 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.310 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.310 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.310 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
7.311 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.312 * [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)))
7.312 * [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))))
7.313 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
7.313 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
7.313 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
7.313 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.313 * [taylor]: Taking taylor expansion of 1/2 in k
7.313 * [backup-simplify]: Simplify 1/2 into 1/2
7.313 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.313 * [taylor]: Taking taylor expansion of k in k
7.313 * [backup-simplify]: Simplify 0 into 0
7.313 * [backup-simplify]: Simplify 1 into 1
7.313 * [backup-simplify]: Simplify (/ 1 1) into 1
7.313 * [taylor]: Taking taylor expansion of 1/2 in k
7.313 * [backup-simplify]: Simplify 1/2 into 1/2
7.313 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
7.313 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
7.313 * [taylor]: Taking taylor expansion of (* -2 PI) in k
7.313 * [taylor]: Taking taylor expansion of -2 in k
7.313 * [backup-simplify]: Simplify -2 into -2
7.313 * [taylor]: Taking taylor expansion of PI in k
7.313 * [backup-simplify]: Simplify PI into PI
7.313 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.314 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.314 * [taylor]: Taking taylor expansion of (log n) in k
7.314 * [taylor]: Taking taylor expansion of n in k
7.314 * [backup-simplify]: Simplify n into n
7.314 * [backup-simplify]: Simplify (log n) into (log n)
7.314 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.315 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.315 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.315 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
7.316 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
7.317 * [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))))
7.318 * [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))))
7.318 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.319 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
7.320 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
7.320 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.320 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
7.321 * [backup-simplify]: Simplify (+ 0 0) into 0
7.321 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.322 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
7.323 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
7.323 * [taylor]: Taking taylor expansion of 0 in k
7.324 * [backup-simplify]: Simplify 0 into 0
7.324 * [backup-simplify]: Simplify 0 into 0
7.324 * [backup-simplify]: Simplify 0 into 0
7.324 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.325 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
7.327 * [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
7.327 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.328 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
7.328 * [backup-simplify]: Simplify (+ 0 0) into 0
7.329 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.330 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
7.331 * [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
7.331 * [taylor]: Taking taylor expansion of 0 in k
7.331 * [backup-simplify]: Simplify 0 into 0
7.331 * [backup-simplify]: Simplify 0 into 0
7.331 * [backup-simplify]: Simplify 0 into 0
7.331 * [backup-simplify]: Simplify 0 into 0
7.332 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.333 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.337 * [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
7.337 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.338 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
7.338 * [backup-simplify]: Simplify (+ 0 0) into 0
7.339 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.340 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
7.341 * [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
7.342 * [taylor]: Taking taylor expansion of 0 in k
7.342 * [backup-simplify]: Simplify 0 into 0
7.342 * [backup-simplify]: Simplify 0 into 0
7.342 * [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)))))
7.342 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1 2)
7.343 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.343 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0
7.343 * [taylor]: Taking taylor expansion of (* n PI) in n
7.343 * [taylor]: Taking taylor expansion of n in n
7.343 * [backup-simplify]: Simplify 0 into 0
7.343 * [backup-simplify]: Simplify 1 into 1
7.343 * [taylor]: Taking taylor expansion of PI in n
7.343 * [backup-simplify]: Simplify PI into PI
7.343 * [taylor]: Taking taylor expansion of (* n PI) in n
7.343 * [taylor]: Taking taylor expansion of n in n
7.343 * [backup-simplify]: Simplify 0 into 0
7.343 * [backup-simplify]: Simplify 1 into 1
7.343 * [taylor]: Taking taylor expansion of PI in n
7.343 * [backup-simplify]: Simplify PI into PI
7.343 * [backup-simplify]: Simplify (* 0 PI) into 0
7.343 * [backup-simplify]: Simplify 0 into 0
7.344 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.344 * [backup-simplify]: Simplify PI into PI
7.345 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.345 * [backup-simplify]: Simplify 0 into 0
7.345 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.346 * [backup-simplify]: Simplify 0 into 0
7.346 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.346 * [backup-simplify]: Simplify 0 into 0
7.347 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
7.347 * [backup-simplify]: Simplify 0 into 0
7.349 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
7.349 * [backup-simplify]: Simplify 0 into 0
7.351 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
7.351 * [backup-simplify]: Simplify 0 into 0
7.351 * [backup-simplify]: Simplify (* PI n) into (* n PI)
7.351 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n)
7.351 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0
7.351 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.351 * [taylor]: Taking taylor expansion of PI in n
7.351 * [backup-simplify]: Simplify PI into PI
7.351 * [taylor]: Taking taylor expansion of n in n
7.351 * [backup-simplify]: Simplify 0 into 0
7.351 * [backup-simplify]: Simplify 1 into 1
7.352 * [backup-simplify]: Simplify (/ PI 1) into PI
7.352 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.352 * [taylor]: Taking taylor expansion of PI in n
7.352 * [backup-simplify]: Simplify PI into PI
7.352 * [taylor]: Taking taylor expansion of n in n
7.352 * [backup-simplify]: Simplify 0 into 0
7.352 * [backup-simplify]: Simplify 1 into 1
7.353 * [backup-simplify]: Simplify (/ PI 1) into PI
7.353 * [backup-simplify]: Simplify PI into PI
7.354 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.354 * [backup-simplify]: Simplify 0 into 0
7.355 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.355 * [backup-simplify]: Simplify 0 into 0
7.356 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.356 * [backup-simplify]: Simplify 0 into 0
7.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.357 * [backup-simplify]: Simplify 0 into 0
7.358 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.358 * [backup-simplify]: Simplify 0 into 0
7.359 * [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
7.359 * [backup-simplify]: Simplify 0 into 0
7.359 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI)
7.359 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n))
7.359 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0
7.359 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
7.359 * [taylor]: Taking taylor expansion of -1 in n
7.359 * [backup-simplify]: Simplify -1 into -1
7.359 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.360 * [taylor]: Taking taylor expansion of PI in n
7.360 * [backup-simplify]: Simplify PI into PI
7.360 * [taylor]: Taking taylor expansion of n in n
7.360 * [backup-simplify]: Simplify 0 into 0
7.360 * [backup-simplify]: Simplify 1 into 1
7.360 * [backup-simplify]: Simplify (/ PI 1) into PI
7.360 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
7.360 * [taylor]: Taking taylor expansion of -1 in n
7.360 * [backup-simplify]: Simplify -1 into -1
7.360 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.360 * [taylor]: Taking taylor expansion of PI in n
7.360 * [backup-simplify]: Simplify PI into PI
7.360 * [taylor]: Taking taylor expansion of n in n
7.360 * [backup-simplify]: Simplify 0 into 0
7.360 * [backup-simplify]: Simplify 1 into 1
7.361 * [backup-simplify]: Simplify (/ PI 1) into PI
7.361 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
7.362 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
7.363 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.363 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0
7.363 * [backup-simplify]: Simplify 0 into 0
7.364 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.365 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0
7.365 * [backup-simplify]: Simplify 0 into 0
7.367 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.368 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.368 * [backup-simplify]: Simplify 0 into 0
7.369 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.370 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.370 * [backup-simplify]: Simplify 0 into 0
7.371 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.373 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
7.373 * [backup-simplify]: Simplify 0 into 0
7.374 * [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
7.376 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
7.376 * [backup-simplify]: Simplify 0 into 0
7.376 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI)
7.376 * * * * [progress]: [ 3 / 3 ] generating series at (2)
7.377 * [backup-simplify]: Simplify (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))))
7.377 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
7.377 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
7.377 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.377 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.377 * [taylor]: Taking taylor expansion of k in k
7.377 * [backup-simplify]: Simplify 0 into 0
7.377 * [backup-simplify]: Simplify 1 into 1
7.377 * [backup-simplify]: Simplify (/ 1 1) into 1
7.377 * [backup-simplify]: Simplify (sqrt 0) into 0
7.379 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.379 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
7.379 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
7.379 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
7.379 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
7.379 * [taylor]: Taking taylor expansion of 1/2 in k
7.379 * [backup-simplify]: Simplify 1/2 into 1/2
7.379 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
7.379 * [taylor]: Taking taylor expansion of 1/2 in k
7.379 * [backup-simplify]: Simplify 1/2 into 1/2
7.379 * [taylor]: Taking taylor expansion of k in k
7.379 * [backup-simplify]: Simplify 0 into 0
7.379 * [backup-simplify]: Simplify 1 into 1
7.379 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
7.379 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
7.379 * [taylor]: Taking taylor expansion of 2 in k
7.379 * [backup-simplify]: Simplify 2 into 2
7.379 * [taylor]: Taking taylor expansion of (* n PI) in k
7.379 * [taylor]: Taking taylor expansion of n in k
7.379 * [backup-simplify]: Simplify n into n
7.379 * [taylor]: Taking taylor expansion of PI in k
7.379 * [backup-simplify]: Simplify PI into PI
7.379 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.380 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
7.380 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
7.380 * [backup-simplify]: Simplify (* 1/2 0) into 0
7.380 * [backup-simplify]: Simplify (- 0) into 0
7.381 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.381 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
7.381 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
7.381 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
7.381 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
7.381 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.381 * [taylor]: Taking taylor expansion of k in n
7.381 * [backup-simplify]: Simplify k into k
7.381 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.381 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
7.381 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.382 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
7.382 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
7.382 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
7.382 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
7.382 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
7.382 * [taylor]: Taking taylor expansion of 1/2 in n
7.382 * [backup-simplify]: Simplify 1/2 into 1/2
7.382 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
7.382 * [taylor]: Taking taylor expansion of 1/2 in n
7.382 * [backup-simplify]: Simplify 1/2 into 1/2
7.382 * [taylor]: Taking taylor expansion of k in n
7.382 * [backup-simplify]: Simplify k into k
7.382 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.382 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.382 * [taylor]: Taking taylor expansion of 2 in n
7.382 * [backup-simplify]: Simplify 2 into 2
7.382 * [taylor]: Taking taylor expansion of (* n PI) in n
7.382 * [taylor]: Taking taylor expansion of n in n
7.382 * [backup-simplify]: Simplify 0 into 0
7.382 * [backup-simplify]: Simplify 1 into 1
7.382 * [taylor]: Taking taylor expansion of PI in n
7.382 * [backup-simplify]: Simplify PI into PI
7.388 * [backup-simplify]: Simplify (* 0 PI) into 0
7.389 * [backup-simplify]: Simplify (* 2 0) into 0
7.390 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.392 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.393 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.393 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
7.393 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
7.393 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
7.395 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.396 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
7.397 * [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)))))
7.397 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
7.397 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
7.397 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.397 * [taylor]: Taking taylor expansion of k in n
7.397 * [backup-simplify]: Simplify k into k
7.397 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.397 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
7.397 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.398 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
7.398 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
7.398 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
7.398 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
7.398 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
7.398 * [taylor]: Taking taylor expansion of 1/2 in n
7.398 * [backup-simplify]: Simplify 1/2 into 1/2
7.398 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
7.398 * [taylor]: Taking taylor expansion of 1/2 in n
7.398 * [backup-simplify]: Simplify 1/2 into 1/2
7.398 * [taylor]: Taking taylor expansion of k in n
7.398 * [backup-simplify]: Simplify k into k
7.398 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.398 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.398 * [taylor]: Taking taylor expansion of 2 in n
7.398 * [backup-simplify]: Simplify 2 into 2
7.398 * [taylor]: Taking taylor expansion of (* n PI) in n
7.398 * [taylor]: Taking taylor expansion of n in n
7.398 * [backup-simplify]: Simplify 0 into 0
7.398 * [backup-simplify]: Simplify 1 into 1
7.398 * [taylor]: Taking taylor expansion of PI in n
7.398 * [backup-simplify]: Simplify PI into PI
7.399 * [backup-simplify]: Simplify (* 0 PI) into 0
7.399 * [backup-simplify]: Simplify (* 2 0) into 0
7.401 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.402 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.403 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.403 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
7.403 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
7.403 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
7.405 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.405 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
7.406 * [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)))))
7.407 * [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)))
7.407 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
7.407 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
7.407 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
7.407 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
7.407 * [taylor]: Taking taylor expansion of 1/2 in k
7.407 * [backup-simplify]: Simplify 1/2 into 1/2
7.407 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
7.407 * [taylor]: Taking taylor expansion of 1/2 in k
7.407 * [backup-simplify]: Simplify 1/2 into 1/2
7.407 * [taylor]: Taking taylor expansion of k in k
7.407 * [backup-simplify]: Simplify 0 into 0
7.407 * [backup-simplify]: Simplify 1 into 1
7.407 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
7.407 * [taylor]: Taking taylor expansion of (log n) in k
7.407 * [taylor]: Taking taylor expansion of n in k
7.407 * [backup-simplify]: Simplify n into n
7.407 * [backup-simplify]: Simplify (log n) into (log n)
7.407 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.407 * [taylor]: Taking taylor expansion of (* 2 PI) in k
7.407 * [taylor]: Taking taylor expansion of 2 in k
7.407 * [backup-simplify]: Simplify 2 into 2
7.407 * [taylor]: Taking taylor expansion of PI in k
7.407 * [backup-simplify]: Simplify PI into PI
7.408 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.408 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.408 * [backup-simplify]: Simplify (* 1/2 0) into 0
7.409 * [backup-simplify]: Simplify (- 0) into 0
7.409 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.410 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.410 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
7.411 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
7.411 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.411 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.411 * [taylor]: Taking taylor expansion of k in k
7.411 * [backup-simplify]: Simplify 0 into 0
7.411 * [backup-simplify]: Simplify 1 into 1
7.411 * [backup-simplify]: Simplify (/ 1 1) into 1
7.412 * [backup-simplify]: Simplify (sqrt 0) into 0
7.412 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.413 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
7.413 * [backup-simplify]: Simplify 0 into 0
7.414 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.414 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
7.415 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.416 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
7.416 * [backup-simplify]: Simplify (- 0) into 0
7.416 * [backup-simplify]: Simplify (+ 0 0) into 0
7.417 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.418 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
7.419 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.420 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
7.420 * [taylor]: Taking taylor expansion of 0 in k
7.420 * [backup-simplify]: Simplify 0 into 0
7.420 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
7.421 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.422 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.422 * [backup-simplify]: Simplify (+ 0 0) into 0
7.422 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
7.423 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.423 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.424 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
7.426 * [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)))))))
7.429 * [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)))))))
7.429 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
7.430 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.431 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.433 * [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
7.434 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
7.434 * [backup-simplify]: Simplify (- 0) into 0
7.434 * [backup-simplify]: Simplify (+ 0 0) into 0
7.435 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.436 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.437 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.438 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.438 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
7.439 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
7.439 * [taylor]: Taking taylor expansion of 0 in k
7.439 * [backup-simplify]: Simplify 0 into 0
7.439 * [backup-simplify]: Simplify 0 into 0
7.440 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
7.442 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.443 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
7.443 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.445 * [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
7.445 * [backup-simplify]: Simplify (+ 0 0) into 0
7.446 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
7.446 * [backup-simplify]: Simplify (- 0) into 0
7.446 * [backup-simplify]: Simplify (+ 0 0) into 0
7.448 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.450 * [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)))))
7.456 * [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))))))))
7.460 * [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))))))))
7.461 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.462 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
7.465 * [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
7.466 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
7.466 * [backup-simplify]: Simplify (- 0) into 0
7.466 * [backup-simplify]: Simplify (+ 0 0) into 0
7.467 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.468 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
7.470 * [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
7.470 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.471 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
7.472 * [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
7.472 * [taylor]: Taking taylor expansion of 0 in k
7.472 * [backup-simplify]: Simplify 0 into 0
7.472 * [backup-simplify]: Simplify 0 into 0
7.472 * [backup-simplify]: Simplify 0 into 0
7.473 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.475 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.477 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
7.478 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.491 * [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
7.492 * [backup-simplify]: Simplify (+ 0 0) into 0
7.493 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
7.494 * [backup-simplify]: Simplify (- 0) into 0
7.494 * [backup-simplify]: Simplify (+ 0 0) into 0
7.496 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
7.503 * [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)))))))
7.521 * [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))))))))))))))
7.531 * [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))))))))))))))
7.543 * [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))))))))))))))))))))))
7.543 * [backup-simplify]: Simplify (/ (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
7.543 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
7.543 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
7.543 * [taylor]: Taking taylor expansion of (sqrt k) in k
7.543 * [taylor]: Taking taylor expansion of k in k
7.543 * [backup-simplify]: Simplify 0 into 0
7.543 * [backup-simplify]: Simplify 1 into 1
7.543 * [backup-simplify]: Simplify (sqrt 0) into 0
7.544 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.544 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
7.544 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
7.544 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
7.544 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
7.544 * [taylor]: Taking taylor expansion of 1/2 in k
7.544 * [backup-simplify]: Simplify 1/2 into 1/2
7.544 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.544 * [taylor]: Taking taylor expansion of 1/2 in k
7.544 * [backup-simplify]: Simplify 1/2 into 1/2
7.544 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.544 * [taylor]: Taking taylor expansion of k in k
7.544 * [backup-simplify]: Simplify 0 into 0
7.544 * [backup-simplify]: Simplify 1 into 1
7.545 * [backup-simplify]: Simplify (/ 1 1) into 1
7.545 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
7.545 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
7.545 * [taylor]: Taking taylor expansion of 2 in k
7.545 * [backup-simplify]: Simplify 2 into 2
7.545 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.545 * [taylor]: Taking taylor expansion of PI in k
7.545 * [backup-simplify]: Simplify PI into PI
7.545 * [taylor]: Taking taylor expansion of n in k
7.545 * [backup-simplify]: Simplify n into n
7.545 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.545 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
7.545 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
7.546 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.546 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.546 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.546 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
7.546 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
7.546 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
7.546 * [taylor]: Taking taylor expansion of (sqrt k) in n
7.546 * [taylor]: Taking taylor expansion of k in n
7.546 * [backup-simplify]: Simplify k into k
7.546 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
7.546 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
7.547 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
7.547 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
7.547 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
7.547 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
7.547 * [taylor]: Taking taylor expansion of 1/2 in n
7.547 * [backup-simplify]: Simplify 1/2 into 1/2
7.547 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.547 * [taylor]: Taking taylor expansion of 1/2 in n
7.547 * [backup-simplify]: Simplify 1/2 into 1/2
7.547 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.547 * [taylor]: Taking taylor expansion of k in n
7.547 * [backup-simplify]: Simplify k into k
7.547 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.547 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
7.547 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.547 * [taylor]: Taking taylor expansion of 2 in n
7.547 * [backup-simplify]: Simplify 2 into 2
7.547 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.547 * [taylor]: Taking taylor expansion of PI in n
7.547 * [backup-simplify]: Simplify PI into PI
7.547 * [taylor]: Taking taylor expansion of n in n
7.547 * [backup-simplify]: Simplify 0 into 0
7.547 * [backup-simplify]: Simplify 1 into 1
7.547 * [backup-simplify]: Simplify (/ PI 1) into PI
7.548 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.548 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.548 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.548 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
7.548 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
7.549 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.550 * [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)))
7.551 * [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))))
7.551 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
7.551 * [taylor]: Taking taylor expansion of (sqrt k) in n
7.551 * [taylor]: Taking taylor expansion of k in n
7.551 * [backup-simplify]: Simplify k into k
7.551 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
7.551 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
7.551 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
7.551 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
7.551 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
7.551 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
7.551 * [taylor]: Taking taylor expansion of 1/2 in n
7.551 * [backup-simplify]: Simplify 1/2 into 1/2
7.551 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.551 * [taylor]: Taking taylor expansion of 1/2 in n
7.551 * [backup-simplify]: Simplify 1/2 into 1/2
7.551 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.551 * [taylor]: Taking taylor expansion of k in n
7.551 * [backup-simplify]: Simplify k into k
7.551 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.551 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
7.551 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.551 * [taylor]: Taking taylor expansion of 2 in n
7.551 * [backup-simplify]: Simplify 2 into 2
7.551 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.551 * [taylor]: Taking taylor expansion of PI in n
7.551 * [backup-simplify]: Simplify PI into PI
7.551 * [taylor]: Taking taylor expansion of n in n
7.551 * [backup-simplify]: Simplify 0 into 0
7.551 * [backup-simplify]: Simplify 1 into 1
7.552 * [backup-simplify]: Simplify (/ PI 1) into PI
7.552 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.553 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.553 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.553 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
7.553 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
7.554 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.554 * [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)))
7.555 * [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))))
7.556 * [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))
7.556 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
7.556 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
7.556 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
7.556 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
7.556 * [taylor]: Taking taylor expansion of 1/2 in k
7.556 * [backup-simplify]: Simplify 1/2 into 1/2
7.556 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.556 * [taylor]: Taking taylor expansion of 1/2 in k
7.556 * [backup-simplify]: Simplify 1/2 into 1/2
7.556 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.556 * [taylor]: Taking taylor expansion of k in k
7.556 * [backup-simplify]: Simplify 0 into 0
7.556 * [backup-simplify]: Simplify 1 into 1
7.556 * [backup-simplify]: Simplify (/ 1 1) into 1
7.557 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
7.557 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.557 * [taylor]: Taking taylor expansion of (* 2 PI) in k
7.557 * [taylor]: Taking taylor expansion of 2 in k
7.557 * [backup-simplify]: Simplify 2 into 2
7.557 * [taylor]: Taking taylor expansion of PI in k
7.557 * [backup-simplify]: Simplify PI into PI
7.557 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.558 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.558 * [taylor]: Taking taylor expansion of (log n) in k
7.558 * [taylor]: Taking taylor expansion of n in k
7.558 * [backup-simplify]: Simplify n into n
7.558 * [backup-simplify]: Simplify (log n) into (log n)
7.558 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.558 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.558 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.558 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.559 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
7.560 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
7.561 * [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))))
7.561 * [taylor]: Taking taylor expansion of (sqrt k) in k
7.561 * [taylor]: Taking taylor expansion of k in k
7.561 * [backup-simplify]: Simplify 0 into 0
7.561 * [backup-simplify]: Simplify 1 into 1
7.561 * [backup-simplify]: Simplify (sqrt 0) into 0
7.562 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.562 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
7.562 * [backup-simplify]: Simplify 0 into 0
7.563 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.563 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.564 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.565 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.565 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
7.565 * [backup-simplify]: Simplify (- 0) into 0
7.565 * [backup-simplify]: Simplify (+ 0 0) into 0
7.566 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.567 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
7.568 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
7.569 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
7.569 * [taylor]: Taking taylor expansion of 0 in k
7.569 * [backup-simplify]: Simplify 0 into 0
7.569 * [backup-simplify]: Simplify 0 into 0
7.570 * [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))))))
7.571 * [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))))))
7.571 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.572 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.574 * [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
7.574 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.575 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
7.575 * [backup-simplify]: Simplify (- 0) into 0
7.575 * [backup-simplify]: Simplify (+ 0 0) into 0
7.576 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.577 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
7.578 * [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
7.579 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
7.580 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
7.580 * [taylor]: Taking taylor expansion of 0 in k
7.580 * [backup-simplify]: Simplify 0 into 0
7.580 * [backup-simplify]: Simplify 0 into 0
7.580 * [backup-simplify]: Simplify 0 into 0
7.582 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.583 * [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))))))
7.584 * [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))))))
7.585 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.586 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.595 * [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
7.595 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.598 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
7.598 * [backup-simplify]: Simplify (- 0) into 0
7.598 * [backup-simplify]: Simplify (+ 0 0) into 0
7.600 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.602 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
7.605 * [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
7.606 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
7.608 * [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
7.608 * [taylor]: Taking taylor expansion of 0 in k
7.608 * [backup-simplify]: Simplify 0 into 0
7.608 * [backup-simplify]: Simplify 0 into 0
7.608 * [backup-simplify]: Simplify 0 into 0
7.608 * [backup-simplify]: Simplify 0 into 0
7.612 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.614 * [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))))))
7.616 * [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))))))
7.620 * [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))))))))
7.620 * [backup-simplify]: Simplify (/ (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
7.620 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
7.620 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
7.621 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
7.621 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
7.621 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
7.621 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
7.621 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.621 * [taylor]: Taking taylor expansion of 1/2 in k
7.621 * [backup-simplify]: Simplify 1/2 into 1/2
7.621 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.621 * [taylor]: Taking taylor expansion of k in k
7.621 * [backup-simplify]: Simplify 0 into 0
7.621 * [backup-simplify]: Simplify 1 into 1
7.621 * [backup-simplify]: Simplify (/ 1 1) into 1
7.621 * [taylor]: Taking taylor expansion of 1/2 in k
7.621 * [backup-simplify]: Simplify 1/2 into 1/2
7.621 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
7.621 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
7.621 * [taylor]: Taking taylor expansion of -2 in k
7.621 * [backup-simplify]: Simplify -2 into -2
7.621 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.622 * [taylor]: Taking taylor expansion of PI in k
7.622 * [backup-simplify]: Simplify PI into PI
7.622 * [taylor]: Taking taylor expansion of n in k
7.622 * [backup-simplify]: Simplify n into n
7.622 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.622 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
7.622 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
7.622 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.623 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.623 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
7.623 * [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)))
7.623 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
7.623 * [taylor]: Taking taylor expansion of (/ -1 k) in k
7.623 * [taylor]: Taking taylor expansion of -1 in k
7.623 * [backup-simplify]: Simplify -1 into -1
7.623 * [taylor]: Taking taylor expansion of k in k
7.623 * [backup-simplify]: Simplify 0 into 0
7.623 * [backup-simplify]: Simplify 1 into 1
7.624 * [backup-simplify]: Simplify (/ -1 1) into -1
7.624 * [backup-simplify]: Simplify (sqrt 0) into 0
7.625 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
7.626 * [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))))
7.626 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
7.626 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
7.626 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
7.626 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
7.626 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
7.626 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.626 * [taylor]: Taking taylor expansion of 1/2 in n
7.626 * [backup-simplify]: Simplify 1/2 into 1/2
7.626 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.626 * [taylor]: Taking taylor expansion of k in n
7.626 * [backup-simplify]: Simplify k into k
7.626 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.626 * [taylor]: Taking taylor expansion of 1/2 in n
7.626 * [backup-simplify]: Simplify 1/2 into 1/2
7.626 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
7.626 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.626 * [taylor]: Taking taylor expansion of -2 in n
7.626 * [backup-simplify]: Simplify -2 into -2
7.626 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.626 * [taylor]: Taking taylor expansion of PI in n
7.626 * [backup-simplify]: Simplify PI into PI
7.626 * [taylor]: Taking taylor expansion of n in n
7.626 * [backup-simplify]: Simplify 0 into 0
7.626 * [backup-simplify]: Simplify 1 into 1
7.627 * [backup-simplify]: Simplify (/ PI 1) into PI
7.628 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.629 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.629 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.629 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
7.631 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.632 * [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)))
7.633 * [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))))
7.633 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
7.633 * [taylor]: Taking taylor expansion of (/ -1 k) in n
7.633 * [taylor]: Taking taylor expansion of -1 in n
7.633 * [backup-simplify]: Simplify -1 into -1
7.633 * [taylor]: Taking taylor expansion of k in n
7.633 * [backup-simplify]: Simplify k into k
7.633 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
7.633 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
7.634 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
7.634 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
7.635 * [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)))
7.635 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
7.635 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
7.635 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
7.635 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
7.635 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
7.635 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.635 * [taylor]: Taking taylor expansion of 1/2 in n
7.635 * [backup-simplify]: Simplify 1/2 into 1/2
7.635 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.635 * [taylor]: Taking taylor expansion of k in n
7.635 * [backup-simplify]: Simplify k into k
7.635 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.635 * [taylor]: Taking taylor expansion of 1/2 in n
7.636 * [backup-simplify]: Simplify 1/2 into 1/2
7.636 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
7.636 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.636 * [taylor]: Taking taylor expansion of -2 in n
7.636 * [backup-simplify]: Simplify -2 into -2
7.636 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.636 * [taylor]: Taking taylor expansion of PI in n
7.636 * [backup-simplify]: Simplify PI into PI
7.636 * [taylor]: Taking taylor expansion of n in n
7.636 * [backup-simplify]: Simplify 0 into 0
7.636 * [backup-simplify]: Simplify 1 into 1
7.636 * [backup-simplify]: Simplify (/ PI 1) into PI
7.637 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.638 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.638 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.638 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
7.640 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.641 * [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)))
7.642 * [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))))
7.642 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
7.642 * [taylor]: Taking taylor expansion of (/ -1 k) in n
7.642 * [taylor]: Taking taylor expansion of -1 in n
7.642 * [backup-simplify]: Simplify -1 into -1
7.642 * [taylor]: Taking taylor expansion of k in n
7.642 * [backup-simplify]: Simplify k into k
7.642 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
7.642 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
7.642 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
7.643 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
7.644 * [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)))
7.644 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
7.644 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
7.644 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
7.644 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
7.644 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.644 * [taylor]: Taking taylor expansion of 1/2 in k
7.644 * [backup-simplify]: Simplify 1/2 into 1/2
7.644 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.644 * [taylor]: Taking taylor expansion of k in k
7.644 * [backup-simplify]: Simplify 0 into 0
7.644 * [backup-simplify]: Simplify 1 into 1
7.645 * [backup-simplify]: Simplify (/ 1 1) into 1
7.645 * [taylor]: Taking taylor expansion of 1/2 in k
7.645 * [backup-simplify]: Simplify 1/2 into 1/2
7.645 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
7.645 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
7.645 * [taylor]: Taking taylor expansion of (* -2 PI) in k
7.645 * [taylor]: Taking taylor expansion of -2 in k
7.645 * [backup-simplify]: Simplify -2 into -2
7.645 * [taylor]: Taking taylor expansion of PI in k
7.645 * [backup-simplify]: Simplify PI into PI
7.645 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.647 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.647 * [taylor]: Taking taylor expansion of (log n) in k
7.647 * [taylor]: Taking taylor expansion of n in k
7.647 * [backup-simplify]: Simplify n into n
7.647 * [backup-simplify]: Simplify (log n) into (log n)
7.647 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.648 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.648 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.649 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
7.650 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
7.652 * [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))))
7.652 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
7.652 * [taylor]: Taking taylor expansion of (/ -1 k) in k
7.652 * [taylor]: Taking taylor expansion of -1 in k
7.652 * [backup-simplify]: Simplify -1 into -1
7.652 * [taylor]: Taking taylor expansion of k in k
7.652 * [backup-simplify]: Simplify 0 into 0
7.652 * [backup-simplify]: Simplify 1 into 1
7.652 * [backup-simplify]: Simplify (/ -1 1) into -1
7.653 * [backup-simplify]: Simplify (sqrt 0) into 0
7.654 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
7.656 * [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)))))
7.657 * [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)))))
7.658 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.659 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
7.661 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
7.661 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.661 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
7.662 * [backup-simplify]: Simplify (+ 0 0) into 0
7.663 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.665 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
7.667 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
7.668 * [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
7.668 * [taylor]: Taking taylor expansion of 0 in k
7.668 * [backup-simplify]: Simplify 0 into 0
7.668 * [backup-simplify]: Simplify 0 into 0
7.669 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
7.672 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.674 * [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))))))
7.676 * [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))))))
7.677 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.678 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
7.682 * [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
7.683 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.684 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
7.684 * [backup-simplify]: Simplify (+ 0 0) into 0
7.686 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.687 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
7.690 * [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
7.690 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.691 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
7.692 * [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
7.692 * [taylor]: Taking taylor expansion of 0 in k
7.692 * [backup-simplify]: Simplify 0 into 0
7.692 * [backup-simplify]: Simplify 0 into 0
7.692 * [backup-simplify]: Simplify 0 into 0
7.693 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.698 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.702 * [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))))))
7.703 * [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))))))
7.708 * [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)))))))))))
7.708 * * * [progress]: simplifying candidates
7.708 * * * * [progress]: [ 1 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log 2) (+ (log n) (log PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
7.708 * * * * [progress]: [ 2 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log 2) (log (* n PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
7.708 * * * * [progress]: [ 3 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
7.708 * * * * [progress]: [ 4 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
7.708 * * * * [progress]: [ 5 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
7.708 * * * * [progress]: [ 6 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
7.709 * * * * [progress]: [ 7 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
7.709 * * * * [progress]: [ 8 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) 1/2) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
7.709 * * * * [progress]: [ 9 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* 2 (* n PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
7.709 * * * * [progress]: [ 10 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* 2 (* n PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
7.709 * * * * [progress]: [ 11 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* 2 (* n PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
7.709 * * * * [progress]: [ 12 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* 2 (* n PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))>
7.709 * * * * [progress]: [ 13 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* 2 (* n PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))>
7.709 * * * * [progress]: [ 14 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* 2 (* n PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
7.709 * * * * [progress]: [ 15 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 2 (* n PI)) 1/2) (pow (* 2 (* n PI)) (- (/ k 2)))) (sqrt k)))>
7.709 * * * * [progress]: [ 16 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 2 (* n PI)) 1/2) (pow (* 2 (* n PI)) (- (/ k 2)))) (sqrt k)))>
7.709 * * * * [progress]: [ 17 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>
7.709 * * * * [progress]: [ 18 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
7.709 * * * * [progress]: [ 19 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
7.709 * * * * [progress]: [ 20 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
7.709 * * * * [progress]: [ 21 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
7.710 * * * * [progress]: [ 22 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
7.710 * * * * [progress]: [ 23 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
7.710 * * * * [progress]: [ 24 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
7.710 * * * * [progress]: [ 25 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
7.710 * * * * [progress]: [ 26 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
7.710 * * * * [progress]: [ 27 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (pow (* n PI) 1)) (- 1/2 (/ k 2))) (sqrt k)))>
7.710 * * * * [progress]: [ 28 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (pow (* n PI) 1)) (- 1/2 (/ k 2))) (sqrt k)))>
7.710 * * * * [progress]: [ 29 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (exp (+ (log n) (log PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.710 * * * * [progress]: [ 30 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (exp (log (* n PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.710 * * * * [progress]: [ 31 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (log (exp (* n PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.710 * * * * [progress]: [ 32 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (cbrt (* (* (* n n) n) (* (* PI PI) PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.710 * * * * [progress]: [ 33 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.710 * * * * [progress]: [ 34 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (cbrt (* (* (* n PI) (* n PI)) (* n PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.710 * * * * [progress]: [ 35 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* (sqrt (* n PI)) (sqrt (* n PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.710 * * * * [progress]: [ 36 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* 1 (* n PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.710 * * * * [progress]: [ 37 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.711 * * * * [progress]: [ 38 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* (* n (* (cbrt PI) (cbrt PI))) (cbrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.711 * * * * [progress]: [ 39 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* (* n (sqrt PI)) (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.711 * * * * [progress]: [ 40 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* (* n 1) PI)) (- 1/2 (/ k 2))) (sqrt k)))>
7.711 * * * * [progress]: [ 41 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.711 * * * * [progress]: [ 42 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* (sqrt n) (* (sqrt n) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.711 * * * * [progress]: [ 43 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* 1 (* n PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.711 * * * * [progress]: [ 44 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (posit16->real (real->posit16 (* n PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.711 * * * * [progress]: [ 45 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* PI n)) (- 1/2 (/ k 2))) (sqrt k)))>
7.711 * * * * [progress]: [ 46 / 127 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) 1))>
7.711 * * * * [progress]: [ 47 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log 2) (+ (log n) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
7.711 * * * * [progress]: [ 48 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log 2) (log (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
7.711 * * * * [progress]: [ 49 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
7.711 * * * * [progress]: [ 50 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
7.711 * * * * [progress]: [ 51 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
7.711 * * * * [progress]: [ 52 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
7.711 * * * * [progress]: [ 53 / 127 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
7.712 * * * * [progress]: [ 54 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
7.712 * * * * [progress]: [ 55 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
7.712 * * * * [progress]: [ 56 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
7.712 * * * * [progress]: [ 57 / 127 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
7.712 * * * * [progress]: [ 58 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (- (sqrt k))))>
7.712 * * * * [progress]: [ 59 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
7.712 * * * * [progress]: [ 60 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (cbrt k)))))>
7.712 * * * * [progress]: [ 61 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
7.712 * * * * [progress]: [ 62 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (sqrt 1)) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))))>
7.712 * * * * [progress]: [ 63 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
7.712 * * * * [progress]: [ 64 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) 1) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))))>
7.712 * * * * [progress]: [ 65 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
7.712 * * * * [progress]: [ 66 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (cbrt k)))))>
7.712 * * * * [progress]: [ 67 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
7.713 * * * * [progress]: [ 68 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (sqrt 1)) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))))>
7.713 * * * * [progress]: [ 69 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
7.713 * * * * [progress]: [ 70 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) 1) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))))>
7.713 * * * * [progress]: [ 71 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
7.713 * * * * [progress]: [ 72 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
7.713 * * * * [progress]: [ 73 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
7.713 * * * * [progress]: [ 74 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
7.713 * * * * [progress]: [ 75 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
7.713 * * * * [progress]: [ 76 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
7.713 * * * * [progress]: [ 77 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
7.713 * * * * [progress]: [ 78 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
7.713 * * * * [progress]: [ 79 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
7.713 * * * * [progress]: [ 80 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt 1)) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
7.713 * * * * [progress]: [ 81 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
7.713 * * * * [progress]: [ 82 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
7.714 * * * * [progress]: [ 83 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
7.714 * * * * [progress]: [ 84 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
7.714 * * * * [progress]: [ 85 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
7.714 * * * * [progress]: [ 86 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
7.714 * * * * [progress]: [ 87 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
7.714 * * * * [progress]: [ 88 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
7.714 * * * * [progress]: [ 89 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
7.714 * * * * [progress]: [ 90 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
7.714 * * * * [progress]: [ 91 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
7.714 * * * * [progress]: [ 92 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))))>
7.714 * * * * [progress]: [ 93 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
7.714 * * * * [progress]: [ 94 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))))>
7.714 * * * * [progress]: [ 95 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))>
7.714 * * * * [progress]: [ 96 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))>
7.714 * * * * [progress]: [ 97 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
7.715 * * * * [progress]: [ 98 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
7.715 * * * * [progress]: [ 99 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
7.715 * * * * [progress]: [ 100 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
7.715 * * * * [progress]: [ 101 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))))>
7.715 * * * * [progress]: [ 102 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
7.715 * * * * [progress]: [ 103 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))>
7.715 * * * * [progress]: [ 104 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
7.715 * * * * [progress]: [ 105 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
7.715 * * * * [progress]: [ 106 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
7.715 * * * * [progress]: [ 107 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k)))>
7.715 * * * * [progress]: [ 108 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
7.715 * * * * [progress]: [ 109 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
7.715 * * * * [progress]: [ 110 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) 1/2) (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2))))))>
7.715 * * * * [progress]: [ 111 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) 1/2) (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2))))))>
7.715 * * * * [progress]: [ 112 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow 2 (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2))))))>
7.716 * * * * [progress]: [ 113 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))>
7.716 * * * * [progress]: [ 114 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))>
7.716 * * * * [progress]: [ 115 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))>
7.716 * * * * [progress]: [ 116 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)))))>
7.716 * * * * [progress]: [ 117 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) 1/2) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))))>
7.716 * * * * [progress]: [ 118 / 127 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
7.716 * * * * [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)))>
7.716 * * * * [progress]: [ 120 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
7.716 * * * * [progress]: [ 121 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
7.716 * * * * [progress]: [ 122 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
7.716 * * * * [progress]: [ 123 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
7.716 * * * * [progress]: [ 124 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
7.716 * * * * [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)))))))))))))))))))))))>
7.716 * * * * [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)))))))))>
7.717 * * * * [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))))))))))))>
7.719 * [simplify]: Simplifying:
  (* (+ (log 2) (+ (log n) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log 2) (log (* n PI))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* 2 (* n PI)) 1/2)
  (pow (* 2 (* n PI)) (/ k 2))
  (pow (* 2 (* n PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 (* n PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* 2 (* n PI)) 1)
  (pow (* 2 (* n PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* 2 (* n PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* 2 (* n PI)) 1)
  (pow (* 2 (* n PI)) 1/2)
  (pow (* 2 (* n PI)) (- (/ k 2)))
  (pow (* 2 (* n PI)) 1/2)
  (pow (* 2 (* n PI)) (- (/ k 2)))
  (pow 2 (- 1/2 (/ k 2)))
  (pow (* n PI) (- 1/2 (/ k 2)))
  (log (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (exp (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (* n PI)
  (+ (log n) (log PI))
  (log (* n PI))
  (exp (* n PI))
  (* (* (* n n) n) (* (* PI PI) PI))
  (* (cbrt (* n PI)) (cbrt (* n PI)))
  (cbrt (* n PI))
  (* (* (* n PI) (* n PI)) (* n PI))
  (sqrt (* n PI))
  (sqrt (* n PI))
  (* (sqrt n) (sqrt PI))
  (* (sqrt n) (sqrt PI))
  (* n (* (cbrt PI) (cbrt PI)))
  (* n (sqrt PI))
  (* n 1)
  (* (cbrt n) PI)
  (* (sqrt n) PI)
  (* n PI)
  (real->posit16 (* n PI))
  (- (* (+ (log 2) (+ (log n) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (+ (log 2) (log (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (log (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (log (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (exp (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (* (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (pow (* 2 (* n PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) 1/2) (sqrt 1))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))
  (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) 1/2) 1)
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))
  (/ (pow (* 2 (* n PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) 1/2) (sqrt 1))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))
  (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) 1/2) 1)
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))
  (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow 2 (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow 2 (- 1/2 (/ k 2))) 1)
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt 1))
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1)
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt 1))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1)
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))
  (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))
  (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) 1)
  (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) 1)
  (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2))))
  (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2))))
  (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)))
  (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))
  (real->posit16 (/ (pow (* 2 (* n 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)))))
  (* n PI)
  (* n PI)
  (* 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)))))))))))
7.725 * * [simplify]: iteration 0: 268 enodes
7.849 * * [simplify]: iteration 1: 630 enodes
8.058 * * [simplify]: iteration 2: 1943 enodes
8.770 * * [simplify]: iteration complete: 5001 enodes
8.770 * * [simplify]: Extracting #0: cost 101 inf + 0
8.771 * * [simplify]: Extracting #1: cost 495 inf + 2
8.774 * * [simplify]: Extracting #2: cost 1138 inf + 2031
8.788 * * [simplify]: Extracting #3: cost 1629 inf + 30540
8.854 * * [simplify]: Extracting #4: cost 1171 inf + 254304
9.011 * * [simplify]: Extracting #5: cost 375 inf + 686790
9.242 * * [simplify]: Extracting #6: cost 144 inf + 833087
9.448 * * [simplify]: Extracting #7: cost 57 inf + 855804
9.696 * * [simplify]: Extracting #8: cost 6 inf + 886142
9.942 * * [simplify]: Extracting #9: cost 0 inf + 884672
10.125 * * [simplify]: Extracting #10: cost 0 inf + 883502
10.320 * [simplify]: Simplified to:
  (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* 2 (* n PI)))
  (pow (* 2 (* n PI)) (/ k 2))
  (pow (* 2 (* n PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 (* n PI)) (sqrt (- 1/2 (/ k 2))))
  (* 2 (* n PI))
  (pow (* 2 (* n PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* 2 (* n PI)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* 2 (* n PI))
  (sqrt (* 2 (* n PI)))
  (pow (* 2 (* n PI)) (- (/ k 2)))
  (sqrt (* 2 (* n PI)))
  (pow (* 2 (* n PI)) (- (/ k 2)))
  (pow 2 (- 1/2 (/ k 2)))
  (pow (* PI n) (- 1/2 (/ k 2)))
  (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))
  (exp (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (pow (* 2 (* n PI)) (- 1/4 (/ k 4)))
  (pow (* 2 (* n PI)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (* PI n)
  (log (* PI n))
  (log (* PI n))
  (exp (* PI n))
  (* (* (* PI n) n) (* PI (* PI n)))
  (* (cbrt (* PI n)) (cbrt (* PI n)))
  (cbrt (* PI n))
  (* (* (* PI n) n) (* PI (* PI n)))
  (sqrt (* PI n))
  (sqrt (* PI n))
  (* (sqrt PI) (sqrt n))
  (* (sqrt PI) (sqrt n))
  (* n (* (cbrt PI) (cbrt PI)))
  (* (sqrt PI) n)
  n
  (* PI (cbrt n))
  (* (sqrt n) PI)
  (* PI n)
  (real->posit16 (* PI n))
  (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (exp (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (sqrt k) k))
  (* (cbrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) (* (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (sqrt (* 2 (* n PI))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* 2 (* n PI))) (fabs (cbrt k)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* 2 (* n PI))) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* 2 (* n PI)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* 2 (* n PI))) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* 2 (* n PI)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* 2 (* n PI))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* 2 (* n PI))) (fabs (cbrt k)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* 2 (* n PI))) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* 2 (* n PI)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* 2 (* n PI))) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* 2 (* n PI)))
  (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))
  (/ (/ (pow 2 (- 1/2 (/ k 2))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* PI n) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow 2 (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow 2 (- 1/2 (/ k 2)))
  (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow 2 (- 1/2 (/ k 2)))
  (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt k))
  (* (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (fabs (cbrt k)) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (* (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (* (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (fabs (cbrt k)))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  1
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  1
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (cbrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (fabs (cbrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (cbrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* 2 (* n PI)) (- 1/4 (/ k 4)))
  (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt k))
  (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* 2 (* n PI)) (- 1/4 (/ k 4)))
  (/ (pow (* 2 (* n PI)) (- 1/4 (/ k 4))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))
  (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))
  (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2))))
  (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2))))
  (/ (sqrt k) (pow (* PI n) (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/4 (/ k 4))))
  (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))
  (real->posit16 (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (+ (* (* k k) (+ (* 1/8 (* (* (exp (/ (log (* 2 (* n PI))) 2)) (log n)) (log n))) (* (* (log (* PI 2)) 1/4) (* (exp (/ (log (* 2 (* n PI))) 2)) (log n))))) (- (+ (* 1/8 (* (* k k) (* (log (* PI 2)) (* (log (* PI 2)) (exp (/ (log (* 2 (* n PI))) 2)))))) (exp (/ (log (* 2 (* n PI))) 2))) (/ (* (* (exp (/ (log (* 2 (* n PI))) 2)) k) (log (* 2 (* n PI)))) 2)))
  (exp (* (log (* 2 (* n PI))) (- 1/2 (* k 1/2))))
  (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))
  (* PI n)
  (* PI n)
  (* PI n)
  (+ (+ (* (* (* (* (log (* PI 2)) (exp (/ (log (* 2 (* n PI))) 2))) (log n)) (* k k)) (- +nan.0)) (* (* (* k k) (* +nan.0 (exp (/ (log (* 2 (* n PI))) 2)))) (- (log (* PI 2)) (* (log n) (log n))))) (+ (- (* k (* +nan.0 (exp (/ (log (* 2 (* n PI))) 2)))) (* +nan.0 (exp (/ (log (* 2 (* n PI))) 2)))) (+ (* (* (* k k) (* +nan.0 (exp (/ (log (* 2 (* n PI))) 2)))) (- (* (log (* PI 2)) (log (* PI 2))) (log n))) (- (* (* k k) (* +nan.0 (exp (/ (log (* 2 (* n PI))) 2)))) (* +nan.0 (* (* (exp (/ (log (* 2 (* n PI))) 2)) k) (- (log (* PI 2)) (log n))))))))
  (- (+ (- (/ (* +nan.0 (exp (* (log (* 2 (* n PI))) (- 1/2 (* k 1/2))))) (* k (* k k))) (/ (* +nan.0 (exp (* (log (* 2 (* n PI))) (- 1/2 (* k 1/2))))) k)) (/ (* +nan.0 (exp (* (log (* 2 (* n PI))) (- 1/2 (* k 1/2))))) (* k k))))
  (- (+ (- (* +nan.0 (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))) k)) (* (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))) k) (/ +nan.0 k))) (* (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))) +nan.0)))
10.329 * * * [progress]: adding candidates to table
10.870 * * [progress]: iteration 3 / 4
10.870 * * * [progress]: picking best candidate
10.907 * * * * [pick]: Picked  #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>
10.907 * * * [progress]: localizing error
10.933 * * * [progress]: generating rewritten candidates
10.933 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2)
10.942 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 1)
10.947 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
10.970 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1)
10.991 * * * [progress]: generating series expansions
10.991 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2)
10.991 * [backup-simplify]: Simplify (pow (* n PI) (- 1/2 (/ k 2))) into (pow (* n PI) (- 1/2 (* 1/2 k)))
10.991 * [approximate]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in (n k) around 0
10.991 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k
10.991 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k
10.991 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k
10.991 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
10.991 * [taylor]: Taking taylor expansion of 1/2 in k
10.991 * [backup-simplify]: Simplify 1/2 into 1/2
10.991 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
10.991 * [taylor]: Taking taylor expansion of 1/2 in k
10.991 * [backup-simplify]: Simplify 1/2 into 1/2
10.991 * [taylor]: Taking taylor expansion of k in k
10.991 * [backup-simplify]: Simplify 0 into 0
10.991 * [backup-simplify]: Simplify 1 into 1
10.991 * [taylor]: Taking taylor expansion of (log (* n PI)) in k
10.991 * [taylor]: Taking taylor expansion of (* n PI) in k
10.991 * [taylor]: Taking taylor expansion of n in k
10.991 * [backup-simplify]: Simplify n into n
10.991 * [taylor]: Taking taylor expansion of PI in k
10.991 * [backup-simplify]: Simplify PI into PI
10.991 * [backup-simplify]: Simplify (* n PI) into (* n PI)
10.991 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI))
10.992 * [backup-simplify]: Simplify (* 1/2 0) into 0
10.992 * [backup-simplify]: Simplify (- 0) into 0
10.993 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
10.993 * [backup-simplify]: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI)))
10.993 * [backup-simplify]: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2)
10.993 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n
10.993 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n
10.993 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n
10.993 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
10.993 * [taylor]: Taking taylor expansion of 1/2 in n
10.993 * [backup-simplify]: Simplify 1/2 into 1/2
10.993 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
10.993 * [taylor]: Taking taylor expansion of 1/2 in n
10.993 * [backup-simplify]: Simplify 1/2 into 1/2
10.993 * [taylor]: Taking taylor expansion of k in n
10.993 * [backup-simplify]: Simplify k into k
10.993 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
10.993 * [taylor]: Taking taylor expansion of (* n PI) in n
10.993 * [taylor]: Taking taylor expansion of n in n
10.993 * [backup-simplify]: Simplify 0 into 0
10.993 * [backup-simplify]: Simplify 1 into 1
10.993 * [taylor]: Taking taylor expansion of PI in n
10.993 * [backup-simplify]: Simplify PI into PI
10.994 * [backup-simplify]: Simplify (* 0 PI) into 0
10.995 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.995 * [backup-simplify]: Simplify (log PI) into (log PI)
10.995 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
10.995 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
10.995 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
10.996 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
10.996 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
10.997 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
10.997 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n
10.997 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n
10.997 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n
10.997 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
10.997 * [taylor]: Taking taylor expansion of 1/2 in n
10.997 * [backup-simplify]: Simplify 1/2 into 1/2
10.997 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
10.997 * [taylor]: Taking taylor expansion of 1/2 in n
10.997 * [backup-simplify]: Simplify 1/2 into 1/2
10.997 * [taylor]: Taking taylor expansion of k in n
10.997 * [backup-simplify]: Simplify k into k
10.997 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
10.997 * [taylor]: Taking taylor expansion of (* n PI) in n
10.997 * [taylor]: Taking taylor expansion of n in n
10.997 * [backup-simplify]: Simplify 0 into 0
10.997 * [backup-simplify]: Simplify 1 into 1
10.997 * [taylor]: Taking taylor expansion of PI in n
10.997 * [backup-simplify]: Simplify PI into PI
10.997 * [backup-simplify]: Simplify (* 0 PI) into 0
10.998 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.999 * [backup-simplify]: Simplify (log PI) into (log PI)
10.999 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
10.999 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
10.999 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
10.999 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.000 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
11.000 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
11.000 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) in k
11.000 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) in k
11.000 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.000 * [taylor]: Taking taylor expansion of 1/2 in k
11.000 * [backup-simplify]: Simplify 1/2 into 1/2
11.000 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.000 * [taylor]: Taking taylor expansion of 1/2 in k
11.000 * [backup-simplify]: Simplify 1/2 into 1/2
11.000 * [taylor]: Taking taylor expansion of k in k
11.000 * [backup-simplify]: Simplify 0 into 0
11.000 * [backup-simplify]: Simplify 1 into 1
11.000 * [taylor]: Taking taylor expansion of (+ (log PI) (log n)) in k
11.000 * [taylor]: Taking taylor expansion of (log PI) in k
11.000 * [taylor]: Taking taylor expansion of PI in k
11.000 * [backup-simplify]: Simplify PI into PI
11.001 * [backup-simplify]: Simplify (log PI) into (log PI)
11.001 * [taylor]: Taking taylor expansion of (log n) in k
11.001 * [taylor]: Taking taylor expansion of n in k
11.001 * [backup-simplify]: Simplify n into n
11.001 * [backup-simplify]: Simplify (log n) into (log n)
11.001 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.001 * [backup-simplify]: Simplify (- 0) into 0
11.002 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.002 * [backup-simplify]: Simplify (+ (log PI) (log n)) into (+ (log PI) (log n))
11.002 * [backup-simplify]: Simplify (* 1/2 (+ (log PI) (log n))) into (* 1/2 (+ (log PI) (log n)))
11.002 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n))))
11.003 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n))))
11.003 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.004 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
11.005 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
11.005 * [backup-simplify]: Simplify (- 0) into 0
11.005 * [backup-simplify]: Simplify (+ 0 0) into 0
11.006 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.006 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log PI) (log n)))) into 0
11.007 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
11.007 * [taylor]: Taking taylor expansion of 0 in k
11.007 * [backup-simplify]: Simplify 0 into 0
11.007 * [backup-simplify]: Simplify 0 into 0
11.008 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
11.008 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
11.009 * [backup-simplify]: Simplify (+ 0 0) into 0
11.009 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
11.009 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.010 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.010 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log PI) (log n)))) into (- (+ (* 1/2 (log PI)) (* 1/2 (log n))))
11.011 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n)))))
11.012 * [backup-simplify]: Simplify (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n)))))
11.013 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.015 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
11.015 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
11.016 * [backup-simplify]: Simplify (- 0) into 0
11.016 * [backup-simplify]: Simplify (+ 0 0) into 0
11.017 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.017 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log PI) (log n))))) into 0
11.018 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.018 * [taylor]: Taking taylor expansion of 0 in k
11.018 * [backup-simplify]: Simplify 0 into 0
11.018 * [backup-simplify]: Simplify 0 into 0
11.018 * [backup-simplify]: Simplify 0 into 0
11.020 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
11.021 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
11.022 * [backup-simplify]: Simplify (+ 0 0) into 0
11.022 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
11.023 * [backup-simplify]: Simplify (- 0) into 0
11.023 * [backup-simplify]: Simplify (+ 0 0) into 0
11.024 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log PI) (log n))))) into 0
11.025 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n))))))
11.027 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n))))))
11.030 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log PI) (log n)))))) into (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k)))))
11.031 * [backup-simplify]: Simplify (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))
11.031 * [approximate]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
11.031 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k
11.031 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k
11.031 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k
11.031 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.031 * [taylor]: Taking taylor expansion of 1/2 in k
11.031 * [backup-simplify]: Simplify 1/2 into 1/2
11.031 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.031 * [taylor]: Taking taylor expansion of 1/2 in k
11.031 * [backup-simplify]: Simplify 1/2 into 1/2
11.031 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.031 * [taylor]: Taking taylor expansion of k in k
11.031 * [backup-simplify]: Simplify 0 into 0
11.031 * [backup-simplify]: Simplify 1 into 1
11.031 * [backup-simplify]: Simplify (/ 1 1) into 1
11.031 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k
11.031 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.031 * [taylor]: Taking taylor expansion of PI in k
11.031 * [backup-simplify]: Simplify PI into PI
11.031 * [taylor]: Taking taylor expansion of n in k
11.031 * [backup-simplify]: Simplify n into n
11.031 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.031 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n))
11.032 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.032 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.032 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.032 * [backup-simplify]: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
11.032 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))
11.032 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.032 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
11.032 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
11.032 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.032 * [taylor]: Taking taylor expansion of 1/2 in n
11.032 * [backup-simplify]: Simplify 1/2 into 1/2
11.032 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.032 * [taylor]: Taking taylor expansion of 1/2 in n
11.032 * [backup-simplify]: Simplify 1/2 into 1/2
11.032 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.032 * [taylor]: Taking taylor expansion of k in n
11.032 * [backup-simplify]: Simplify k into k
11.032 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.032 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
11.032 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.032 * [taylor]: Taking taylor expansion of PI in n
11.033 * [backup-simplify]: Simplify PI into PI
11.033 * [taylor]: Taking taylor expansion of n in n
11.033 * [backup-simplify]: Simplify 0 into 0
11.033 * [backup-simplify]: Simplify 1 into 1
11.033 * [backup-simplify]: Simplify (/ PI 1) into PI
11.033 * [backup-simplify]: Simplify (log PI) into (log PI)
11.033 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.033 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.033 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.034 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.034 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
11.035 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
11.035 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.035 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
11.035 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
11.035 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.035 * [taylor]: Taking taylor expansion of 1/2 in n
11.035 * [backup-simplify]: Simplify 1/2 into 1/2
11.035 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.035 * [taylor]: Taking taylor expansion of 1/2 in n
11.035 * [backup-simplify]: Simplify 1/2 into 1/2
11.035 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.035 * [taylor]: Taking taylor expansion of k in n
11.035 * [backup-simplify]: Simplify k into k
11.035 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.035 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
11.035 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.035 * [taylor]: Taking taylor expansion of PI in n
11.035 * [backup-simplify]: Simplify PI into PI
11.035 * [taylor]: Taking taylor expansion of n in n
11.035 * [backup-simplify]: Simplify 0 into 0
11.035 * [backup-simplify]: Simplify 1 into 1
11.035 * [backup-simplify]: Simplify (/ PI 1) into PI
11.036 * [backup-simplify]: Simplify (log PI) into (log PI)
11.036 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.036 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.036 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.036 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.037 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
11.037 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
11.037 * [taylor]: Taking taylor expansion of (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
11.037 * [taylor]: Taking taylor expansion of (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
11.037 * [taylor]: Taking taylor expansion of (- (log PI) (log n)) in k
11.037 * [taylor]: Taking taylor expansion of (log PI) in k
11.037 * [taylor]: Taking taylor expansion of PI in k
11.037 * [backup-simplify]: Simplify PI into PI
11.037 * [backup-simplify]: Simplify (log PI) into (log PI)
11.038 * [taylor]: Taking taylor expansion of (log n) in k
11.038 * [taylor]: Taking taylor expansion of n in k
11.038 * [backup-simplify]: Simplify n into n
11.038 * [backup-simplify]: Simplify (log n) into (log n)
11.038 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.038 * [taylor]: Taking taylor expansion of 1/2 in k
11.038 * [backup-simplify]: Simplify 1/2 into 1/2
11.038 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.038 * [taylor]: Taking taylor expansion of 1/2 in k
11.038 * [backup-simplify]: Simplify 1/2 into 1/2
11.038 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.038 * [taylor]: Taking taylor expansion of k in k
11.038 * [backup-simplify]: Simplify 0 into 0
11.038 * [backup-simplify]: Simplify 1 into 1
11.038 * [backup-simplify]: Simplify (/ 1 1) into 1
11.038 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.038 * [backup-simplify]: Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n))
11.039 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.039 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.039 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.039 * [backup-simplify]: Simplify (* (- (log PI) (log n)) -1/2) into (* -1/2 (- (log PI) (log n)))
11.040 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
11.040 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
11.041 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.042 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
11.042 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.042 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.042 * [backup-simplify]: Simplify (- 0) into 0
11.043 * [backup-simplify]: Simplify (+ 0 0) into 0
11.043 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.044 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0
11.052 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.052 * [taylor]: Taking taylor expansion of 0 in k
11.052 * [backup-simplify]: Simplify 0 into 0
11.052 * [backup-simplify]: Simplify 0 into 0
11.052 * [backup-simplify]: Simplify 0 into 0
11.053 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.055 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
11.055 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.056 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.056 * [backup-simplify]: Simplify (- 0) into 0
11.057 * [backup-simplify]: Simplify (+ 0 0) into 0
11.057 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.058 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0
11.059 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.059 * [taylor]: Taking taylor expansion of 0 in k
11.059 * [backup-simplify]: Simplify 0 into 0
11.059 * [backup-simplify]: Simplify 0 into 0
11.059 * [backup-simplify]: Simplify 0 into 0
11.059 * [backup-simplify]: Simplify 0 into 0
11.060 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.063 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
11.063 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.064 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
11.064 * [backup-simplify]: Simplify (- 0) into 0
11.064 * [backup-simplify]: Simplify (+ 0 0) into 0
11.065 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.066 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0
11.067 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
11.067 * [taylor]: Taking taylor expansion of 0 in k
11.067 * [backup-simplify]: Simplify 0 into 0
11.067 * [backup-simplify]: Simplify 0 into 0
11.068 * [backup-simplify]: Simplify (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n)))))
11.068 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
11.068 * [approximate]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
11.068 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.068 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k
11.068 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k
11.068 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.068 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.068 * [taylor]: Taking taylor expansion of 1/2 in k
11.068 * [backup-simplify]: Simplify 1/2 into 1/2
11.068 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.068 * [taylor]: Taking taylor expansion of k in k
11.068 * [backup-simplify]: Simplify 0 into 0
11.068 * [backup-simplify]: Simplify 1 into 1
11.068 * [backup-simplify]: Simplify (/ 1 1) into 1
11.068 * [taylor]: Taking taylor expansion of 1/2 in k
11.068 * [backup-simplify]: Simplify 1/2 into 1/2
11.068 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k
11.068 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k
11.068 * [taylor]: Taking taylor expansion of -1 in k
11.068 * [backup-simplify]: Simplify -1 into -1
11.068 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.068 * [taylor]: Taking taylor expansion of PI in k
11.068 * [backup-simplify]: Simplify PI into PI
11.068 * [taylor]: Taking taylor expansion of n in k
11.068 * [backup-simplify]: Simplify n into n
11.068 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.068 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n))
11.069 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n)))
11.069 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.069 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.069 * [backup-simplify]: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
11.069 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
11.069 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.069 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
11.069 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
11.069 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.069 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.069 * [taylor]: Taking taylor expansion of 1/2 in n
11.069 * [backup-simplify]: Simplify 1/2 into 1/2
11.069 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.069 * [taylor]: Taking taylor expansion of k in n
11.069 * [backup-simplify]: Simplify k into k
11.070 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.070 * [taylor]: Taking taylor expansion of 1/2 in n
11.070 * [backup-simplify]: Simplify 1/2 into 1/2
11.070 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
11.070 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
11.070 * [taylor]: Taking taylor expansion of -1 in n
11.070 * [backup-simplify]: Simplify -1 into -1
11.070 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.070 * [taylor]: Taking taylor expansion of PI in n
11.070 * [backup-simplify]: Simplify PI into PI
11.070 * [taylor]: Taking taylor expansion of n in n
11.070 * [backup-simplify]: Simplify 0 into 0
11.070 * [backup-simplify]: Simplify 1 into 1
11.070 * [backup-simplify]: Simplify (/ PI 1) into PI
11.071 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
11.071 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
11.071 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.071 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.072 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.073 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
11.074 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
11.074 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.074 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
11.074 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
11.074 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.074 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.074 * [taylor]: Taking taylor expansion of 1/2 in n
11.074 * [backup-simplify]: Simplify 1/2 into 1/2
11.074 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.074 * [taylor]: Taking taylor expansion of k in n
11.074 * [backup-simplify]: Simplify k into k
11.074 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.074 * [taylor]: Taking taylor expansion of 1/2 in n
11.074 * [backup-simplify]: Simplify 1/2 into 1/2
11.074 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
11.074 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
11.074 * [taylor]: Taking taylor expansion of -1 in n
11.074 * [backup-simplify]: Simplify -1 into -1
11.074 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.074 * [taylor]: Taking taylor expansion of PI in n
11.074 * [backup-simplify]: Simplify PI into PI
11.074 * [taylor]: Taking taylor expansion of n in n
11.074 * [backup-simplify]: Simplify 0 into 0
11.074 * [backup-simplify]: Simplify 1 into 1
11.074 * [backup-simplify]: Simplify (/ PI 1) into PI
11.075 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
11.075 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
11.075 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.076 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.076 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.077 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
11.078 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
11.078 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) in k
11.078 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) in k
11.078 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.078 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.078 * [taylor]: Taking taylor expansion of 1/2 in k
11.078 * [backup-simplify]: Simplify 1/2 into 1/2
11.078 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.078 * [taylor]: Taking taylor expansion of k in k
11.078 * [backup-simplify]: Simplify 0 into 0
11.078 * [backup-simplify]: Simplify 1 into 1
11.078 * [backup-simplify]: Simplify (/ 1 1) into 1
11.078 * [taylor]: Taking taylor expansion of 1/2 in k
11.078 * [backup-simplify]: Simplify 1/2 into 1/2
11.078 * [taylor]: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k
11.078 * [taylor]: Taking taylor expansion of (log (* -1 PI)) in k
11.078 * [taylor]: Taking taylor expansion of (* -1 PI) in k
11.078 * [taylor]: Taking taylor expansion of -1 in k
11.078 * [backup-simplify]: Simplify -1 into -1
11.078 * [taylor]: Taking taylor expansion of PI in k
11.079 * [backup-simplify]: Simplify PI into PI
11.079 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
11.079 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
11.079 * [taylor]: Taking taylor expansion of (log n) in k
11.079 * [taylor]: Taking taylor expansion of n in k
11.080 * [backup-simplify]: Simplify n into n
11.080 * [backup-simplify]: Simplify (log n) into (log n)
11.080 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.080 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.080 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.081 * [backup-simplify]: Simplify (+ (log (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n))
11.082 * [backup-simplify]: Simplify (* 1/2 (- (log (* -1 PI)) (log n))) into (* 1/2 (- (log (* -1 PI)) (log n)))
11.082 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
11.083 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
11.084 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.084 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0
11.085 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0
11.085 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.085 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.086 * [backup-simplify]: Simplify (+ 0 0) into 0
11.087 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.087 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0
11.088 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
11.089 * [taylor]: Taking taylor expansion of 0 in k
11.089 * [backup-simplify]: Simplify 0 into 0
11.089 * [backup-simplify]: Simplify 0 into 0
11.089 * [backup-simplify]: Simplify 0 into 0
11.089 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.090 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0
11.092 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0
11.092 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.092 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.093 * [backup-simplify]: Simplify (+ 0 0) into 0
11.094 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.095 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0
11.096 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.096 * [taylor]: Taking taylor expansion of 0 in k
11.096 * [backup-simplify]: Simplify 0 into 0
11.096 * [backup-simplify]: Simplify 0 into 0
11.096 * [backup-simplify]: Simplify 0 into 0
11.096 * [backup-simplify]: Simplify 0 into 0
11.097 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.098 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.101 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -1 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -1 PI) 1)))) 6) into 0
11.101 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.102 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
11.102 * [backup-simplify]: Simplify (+ 0 0) into 0
11.103 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.104 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n)))))) into 0
11.106 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
11.106 * [taylor]: Taking taylor expansion of 0 in k
11.106 * [backup-simplify]: Simplify 0 into 0
11.106 * [backup-simplify]: Simplify 0 into 0
11.107 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))) into (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))
11.107 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 1)
11.107 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.107 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0
11.107 * [taylor]: Taking taylor expansion of (* n PI) in n
11.107 * [taylor]: Taking taylor expansion of n in n
11.107 * [backup-simplify]: Simplify 0 into 0
11.107 * [backup-simplify]: Simplify 1 into 1
11.107 * [taylor]: Taking taylor expansion of PI in n
11.107 * [backup-simplify]: Simplify PI into PI
11.107 * [taylor]: Taking taylor expansion of (* n PI) in n
11.107 * [taylor]: Taking taylor expansion of n in n
11.107 * [backup-simplify]: Simplify 0 into 0
11.107 * [backup-simplify]: Simplify 1 into 1
11.107 * [taylor]: Taking taylor expansion of PI in n
11.107 * [backup-simplify]: Simplify PI into PI
11.108 * [backup-simplify]: Simplify (* 0 PI) into 0
11.108 * [backup-simplify]: Simplify 0 into 0
11.109 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.109 * [backup-simplify]: Simplify PI into PI
11.109 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.109 * [backup-simplify]: Simplify 0 into 0
11.110 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.110 * [backup-simplify]: Simplify 0 into 0
11.111 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.111 * [backup-simplify]: Simplify 0 into 0
11.112 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.112 * [backup-simplify]: Simplify 0 into 0
11.113 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.113 * [backup-simplify]: Simplify 0 into 0
11.114 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
11.114 * [backup-simplify]: Simplify 0 into 0
11.114 * [backup-simplify]: Simplify (* PI n) into (* n PI)
11.114 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n)
11.114 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0
11.114 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.114 * [taylor]: Taking taylor expansion of PI in n
11.114 * [backup-simplify]: Simplify PI into PI
11.114 * [taylor]: Taking taylor expansion of n in n
11.114 * [backup-simplify]: Simplify 0 into 0
11.114 * [backup-simplify]: Simplify 1 into 1
11.114 * [backup-simplify]: Simplify (/ PI 1) into PI
11.114 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.115 * [taylor]: Taking taylor expansion of PI in n
11.115 * [backup-simplify]: Simplify PI into PI
11.115 * [taylor]: Taking taylor expansion of n in n
11.115 * [backup-simplify]: Simplify 0 into 0
11.115 * [backup-simplify]: Simplify 1 into 1
11.115 * [backup-simplify]: Simplify (/ PI 1) into PI
11.115 * [backup-simplify]: Simplify PI into PI
11.115 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.116 * [backup-simplify]: Simplify 0 into 0
11.116 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.116 * [backup-simplify]: Simplify 0 into 0
11.117 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.117 * [backup-simplify]: Simplify 0 into 0
11.118 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.118 * [backup-simplify]: Simplify 0 into 0
11.118 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.118 * [backup-simplify]: Simplify 0 into 0
11.119 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.119 * [backup-simplify]: Simplify 0 into 0
11.119 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI)
11.119 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n))
11.119 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0
11.119 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
11.119 * [taylor]: Taking taylor expansion of -1 in n
11.119 * [backup-simplify]: Simplify -1 into -1
11.119 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.119 * [taylor]: Taking taylor expansion of PI in n
11.119 * [backup-simplify]: Simplify PI into PI
11.119 * [taylor]: Taking taylor expansion of n in n
11.119 * [backup-simplify]: Simplify 0 into 0
11.119 * [backup-simplify]: Simplify 1 into 1
11.120 * [backup-simplify]: Simplify (/ PI 1) into PI
11.120 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
11.120 * [taylor]: Taking taylor expansion of -1 in n
11.120 * [backup-simplify]: Simplify -1 into -1
11.120 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.120 * [taylor]: Taking taylor expansion of PI in n
11.120 * [backup-simplify]: Simplify PI into PI
11.120 * [taylor]: Taking taylor expansion of n in n
11.120 * [backup-simplify]: Simplify 0 into 0
11.120 * [backup-simplify]: Simplify 1 into 1
11.120 * [backup-simplify]: Simplify (/ PI 1) into PI
11.121 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
11.121 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
11.121 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.122 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0
11.122 * [backup-simplify]: Simplify 0 into 0
11.123 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.123 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0
11.123 * [backup-simplify]: Simplify 0 into 0
11.124 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.125 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.125 * [backup-simplify]: Simplify 0 into 0
11.125 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.126 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.126 * [backup-simplify]: Simplify 0 into 0
11.127 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.127 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.128 * [backup-simplify]: Simplify 0 into 0
11.128 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.130 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.130 * [backup-simplify]: Simplify 0 into 0
11.131 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI)
11.131 * * * * [progress]: [ 3 / 4 ] generating series at (2)
11.131 * [backup-simplify]: Simplify (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) into (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k)))
11.131 * [approximate]: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (k n) around 0
11.131 * [taylor]: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n
11.131 * [taylor]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in n
11.131 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n
11.131 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n
11.131 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n
11.131 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
11.131 * [taylor]: Taking taylor expansion of 1/2 in n
11.131 * [backup-simplify]: Simplify 1/2 into 1/2
11.131 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
11.131 * [taylor]: Taking taylor expansion of 1/2 in n
11.131 * [backup-simplify]: Simplify 1/2 into 1/2
11.131 * [taylor]: Taking taylor expansion of k in n
11.131 * [backup-simplify]: Simplify k into k
11.131 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
11.131 * [taylor]: Taking taylor expansion of (* n PI) in n
11.131 * [taylor]: Taking taylor expansion of n in n
11.131 * [backup-simplify]: Simplify 0 into 0
11.132 * [backup-simplify]: Simplify 1 into 1
11.132 * [taylor]: Taking taylor expansion of PI in n
11.132 * [backup-simplify]: Simplify PI into PI
11.132 * [backup-simplify]: Simplify (* 0 PI) into 0
11.134 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.134 * [backup-simplify]: Simplify (log PI) into (log PI)
11.134 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
11.134 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
11.134 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
11.135 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.136 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
11.136 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
11.136 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in n
11.136 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in n
11.136 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in n
11.136 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
11.136 * [taylor]: Taking taylor expansion of 1/2 in n
11.136 * [backup-simplify]: Simplify 1/2 into 1/2
11.136 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
11.137 * [taylor]: Taking taylor expansion of 1/2 in n
11.137 * [backup-simplify]: Simplify 1/2 into 1/2
11.137 * [taylor]: Taking taylor expansion of k in n
11.137 * [backup-simplify]: Simplify k into k
11.137 * [taylor]: Taking taylor expansion of (log 2) in n
11.137 * [taylor]: Taking taylor expansion of 2 in n
11.137 * [backup-simplify]: Simplify 2 into 2
11.137 * [backup-simplify]: Simplify (log 2) into (log 2)
11.137 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
11.137 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
11.137 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
11.138 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k)))
11.138 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k))))
11.138 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
11.138 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.138 * [taylor]: Taking taylor expansion of k in n
11.138 * [backup-simplify]: Simplify k into k
11.138 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.138 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
11.139 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.139 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
11.139 * [taylor]: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k
11.139 * [taylor]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in k
11.139 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k
11.139 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k
11.139 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k
11.139 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.139 * [taylor]: Taking taylor expansion of 1/2 in k
11.139 * [backup-simplify]: Simplify 1/2 into 1/2
11.139 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.139 * [taylor]: Taking taylor expansion of 1/2 in k
11.139 * [backup-simplify]: Simplify 1/2 into 1/2
11.139 * [taylor]: Taking taylor expansion of k in k
11.139 * [backup-simplify]: Simplify 0 into 0
11.139 * [backup-simplify]: Simplify 1 into 1
11.139 * [taylor]: Taking taylor expansion of (log (* n PI)) in k
11.139 * [taylor]: Taking taylor expansion of (* n PI) in k
11.139 * [taylor]: Taking taylor expansion of n in k
11.139 * [backup-simplify]: Simplify n into n
11.139 * [taylor]: Taking taylor expansion of PI in k
11.139 * [backup-simplify]: Simplify PI into PI
11.139 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.139 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI))
11.140 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.140 * [backup-simplify]: Simplify (- 0) into 0
11.141 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.141 * [backup-simplify]: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI)))
11.141 * [backup-simplify]: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2)
11.141 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k
11.141 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k
11.141 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k
11.141 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.141 * [taylor]: Taking taylor expansion of 1/2 in k
11.141 * [backup-simplify]: Simplify 1/2 into 1/2
11.141 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.141 * [taylor]: Taking taylor expansion of 1/2 in k
11.141 * [backup-simplify]: Simplify 1/2 into 1/2
11.141 * [taylor]: Taking taylor expansion of k in k
11.141 * [backup-simplify]: Simplify 0 into 0
11.141 * [backup-simplify]: Simplify 1 into 1
11.141 * [taylor]: Taking taylor expansion of (log 2) in k
11.141 * [taylor]: Taking taylor expansion of 2 in k
11.141 * [backup-simplify]: Simplify 2 into 2
11.142 * [backup-simplify]: Simplify (log 2) into (log 2)
11.142 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.142 * [backup-simplify]: Simplify (- 0) into 0
11.143 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.144 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
11.145 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
11.145 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
11.145 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.145 * [taylor]: Taking taylor expansion of k in k
11.145 * [backup-simplify]: Simplify 0 into 0
11.145 * [backup-simplify]: Simplify 1 into 1
11.145 * [backup-simplify]: Simplify (/ 1 1) into 1
11.146 * [backup-simplify]: Simplify (sqrt 0) into 0
11.146 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.146 * [taylor]: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k
11.146 * [taylor]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in k
11.147 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k
11.147 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k
11.147 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k
11.147 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.147 * [taylor]: Taking taylor expansion of 1/2 in k
11.147 * [backup-simplify]: Simplify 1/2 into 1/2
11.147 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.147 * [taylor]: Taking taylor expansion of 1/2 in k
11.147 * [backup-simplify]: Simplify 1/2 into 1/2
11.147 * [taylor]: Taking taylor expansion of k in k
11.147 * [backup-simplify]: Simplify 0 into 0
11.147 * [backup-simplify]: Simplify 1 into 1
11.147 * [taylor]: Taking taylor expansion of (log (* n PI)) in k
11.147 * [taylor]: Taking taylor expansion of (* n PI) in k
11.147 * [taylor]: Taking taylor expansion of n in k
11.147 * [backup-simplify]: Simplify n into n
11.147 * [taylor]: Taking taylor expansion of PI in k
11.147 * [backup-simplify]: Simplify PI into PI
11.147 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.147 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI))
11.147 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.147 * [backup-simplify]: Simplify (- 0) into 0
11.148 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.148 * [backup-simplify]: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI)))
11.148 * [backup-simplify]: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2)
11.148 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k
11.148 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k
11.148 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k
11.148 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.148 * [taylor]: Taking taylor expansion of 1/2 in k
11.148 * [backup-simplify]: Simplify 1/2 into 1/2
11.148 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.148 * [taylor]: Taking taylor expansion of 1/2 in k
11.148 * [backup-simplify]: Simplify 1/2 into 1/2
11.148 * [taylor]: Taking taylor expansion of k in k
11.148 * [backup-simplify]: Simplify 0 into 0
11.148 * [backup-simplify]: Simplify 1 into 1
11.148 * [taylor]: Taking taylor expansion of (log 2) in k
11.148 * [taylor]: Taking taylor expansion of 2 in k
11.148 * [backup-simplify]: Simplify 2 into 2
11.148 * [backup-simplify]: Simplify (log 2) into (log 2)
11.153 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.154 * [backup-simplify]: Simplify (- 0) into 0
11.154 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.155 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
11.156 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
11.156 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
11.156 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.156 * [taylor]: Taking taylor expansion of k in k
11.156 * [backup-simplify]: Simplify 0 into 0
11.156 * [backup-simplify]: Simplify 1 into 1
11.156 * [backup-simplify]: Simplify (/ 1 1) into 1
11.156 * [backup-simplify]: Simplify (sqrt 0) into 0
11.157 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.158 * [backup-simplify]: Simplify (* (pow (* n PI) 1/2) (pow 2 1/2)) into (sqrt (* n (* PI 2)))
11.158 * [backup-simplify]: Simplify (* (sqrt (* n (* PI 2))) 0) into 0
11.158 * [taylor]: Taking taylor expansion of 0 in n
11.158 * [backup-simplify]: Simplify 0 into 0
11.158 * [backup-simplify]: Simplify 0 into 0
11.159 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
11.160 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
11.161 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.161 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.162 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log 2))) into (- (* 1/2 (log 2)))
11.167 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2)))
11.168 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
11.168 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* n PI) 1)))) 1) into 0
11.169 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
11.169 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.169 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.170 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* n PI)))) into (- (* 1/2 (log (* n PI))))
11.170 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 1) 1)))) into (* -1/2 (* (log (* n PI)) (sqrt (* n PI))))
11.172 * [backup-simplify]: Simplify (+ (* (pow (* n PI) 1/2) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (pow 2 1/2))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))
11.174 * [backup-simplify]: Simplify (+ (* (sqrt (* n (* PI 2))) +nan.0) (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
11.174 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
11.174 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
11.174 * [taylor]: Taking taylor expansion of +nan.0 in n
11.174 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.174 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
11.174 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.174 * [taylor]: Taking taylor expansion of 2 in n
11.174 * [backup-simplify]: Simplify 2 into 2
11.174 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.174 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.174 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.174 * [taylor]: Taking taylor expansion of (* n PI) in n
11.174 * [taylor]: Taking taylor expansion of n in n
11.174 * [backup-simplify]: Simplify 0 into 0
11.174 * [backup-simplify]: Simplify 1 into 1
11.175 * [taylor]: Taking taylor expansion of PI in n
11.175 * [backup-simplify]: Simplify PI into PI
11.175 * [backup-simplify]: Simplify (* 0 PI) into 0
11.176 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.176 * [backup-simplify]: Simplify (sqrt 0) into 0
11.177 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.178 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
11.178 * [backup-simplify]: Simplify (* +nan.0 0) into 0
11.179 * [backup-simplify]: Simplify (- 0) into 0
11.179 * [backup-simplify]: Simplify 0 into 0
11.179 * [backup-simplify]: Simplify 0 into 0
11.179 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
11.181 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
11.183 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
11.183 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
11.184 * [backup-simplify]: Simplify (- 0) into 0
11.184 * [backup-simplify]: Simplify (+ 0 0) into 0
11.185 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log 2)))) into 0
11.191 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2)))
11.191 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
11.192 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* n PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* n PI) 1)))) 2) into 0
11.193 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
11.193 * [backup-simplify]: Simplify (- 0) into 0
11.193 * [backup-simplify]: Simplify (+ 0 0) into 0
11.194 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* n PI))))) into 0
11.195 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI))))
11.198 * [backup-simplify]: Simplify (+ (* (pow (* n PI) 1/2) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) (pow 2 1/2)))) into (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI))))))
11.202 * [backup-simplify]: Simplify (+ (* (sqrt (* n (* PI 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) +nan.0) (* (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))))
11.202 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n
11.202 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n
11.202 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n
11.202 * [taylor]: Taking taylor expansion of +nan.0 in n
11.202 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.202 * [taylor]: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n
11.202 * [taylor]: Taking taylor expansion of (* (log 2) (sqrt 2)) in n
11.202 * [taylor]: Taking taylor expansion of (log 2) in n
11.203 * [taylor]: Taking taylor expansion of 2 in n
11.203 * [backup-simplify]: Simplify 2 into 2
11.203 * [backup-simplify]: Simplify (log 2) into (log 2)
11.203 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.203 * [taylor]: Taking taylor expansion of 2 in n
11.203 * [backup-simplify]: Simplify 2 into 2
11.203 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.203 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.204 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.204 * [taylor]: Taking taylor expansion of (* n PI) in n
11.204 * [taylor]: Taking taylor expansion of n in n
11.204 * [backup-simplify]: Simplify 0 into 0
11.204 * [backup-simplify]: Simplify 1 into 1
11.204 * [taylor]: Taking taylor expansion of PI in n
11.204 * [backup-simplify]: Simplify PI into PI
11.204 * [backup-simplify]: Simplify (* 0 PI) into 0
11.205 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.205 * [backup-simplify]: Simplify (sqrt 0) into 0
11.206 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.206 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n
11.206 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n
11.206 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) in n
11.206 * [taylor]: Taking taylor expansion of +nan.0 in n
11.206 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.206 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))) in n
11.206 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n
11.206 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.206 * [taylor]: Taking taylor expansion of 2 in n
11.206 * [backup-simplify]: Simplify 2 into 2
11.206 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.207 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.207 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
11.207 * [taylor]: Taking taylor expansion of (* n PI) in n
11.207 * [taylor]: Taking taylor expansion of n in n
11.207 * [backup-simplify]: Simplify 0 into 0
11.207 * [backup-simplify]: Simplify 1 into 1
11.207 * [taylor]: Taking taylor expansion of PI in n
11.207 * [backup-simplify]: Simplify PI into PI
11.207 * [backup-simplify]: Simplify (* 0 PI) into 0
11.208 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.208 * [backup-simplify]: Simplify (log PI) into (log PI)
11.209 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.209 * [taylor]: Taking taylor expansion of (* n PI) in n
11.209 * [taylor]: Taking taylor expansion of n in n
11.209 * [backup-simplify]: Simplify 0 into 0
11.209 * [backup-simplify]: Simplify 1 into 1
11.209 * [taylor]: Taking taylor expansion of PI in n
11.209 * [backup-simplify]: Simplify PI into PI
11.209 * [backup-simplify]: Simplify (* 0 PI) into 0
11.210 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.210 * [backup-simplify]: Simplify (sqrt 0) into 0
11.211 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.211 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
11.211 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
11.211 * [taylor]: Taking taylor expansion of +nan.0 in n
11.211 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.211 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
11.211 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.211 * [taylor]: Taking taylor expansion of 2 in n
11.211 * [backup-simplify]: Simplify 2 into 2
11.211 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.212 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.212 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.212 * [taylor]: Taking taylor expansion of (* n PI) in n
11.212 * [taylor]: Taking taylor expansion of n in n
11.212 * [backup-simplify]: Simplify 0 into 0
11.212 * [backup-simplify]: Simplify 1 into 1
11.212 * [taylor]: Taking taylor expansion of PI in n
11.212 * [backup-simplify]: Simplify PI into PI
11.212 * [backup-simplify]: Simplify (* 0 PI) into 0
11.213 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.213 * [backup-simplify]: Simplify (sqrt 0) into 0
11.214 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.215 * [backup-simplify]: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2))
11.215 * [backup-simplify]: Simplify (* (* (log 2) (sqrt 2)) 0) into 0
11.216 * [backup-simplify]: Simplify (* +nan.0 0) into 0
11.216 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.217 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n)))
11.218 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log PI) (log n))) 0) into 0
11.218 * [backup-simplify]: Simplify (* +nan.0 0) into 0
11.219 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
11.219 * [backup-simplify]: Simplify (* +nan.0 0) into 0
11.220 * [backup-simplify]: Simplify (- 0) into 0
11.220 * [backup-simplify]: Simplify (+ 0 0) into 0
11.220 * [backup-simplify]: Simplify (- 0) into 0
11.221 * [backup-simplify]: Simplify (+ 0 0) into 0
11.221 * [backup-simplify]: Simplify (- 0) into 0
11.221 * [backup-simplify]: Simplify 0 into 0
11.224 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
11.230 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
11.233 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
11.236 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
11.236 * [backup-simplify]: Simplify 0 into 0
11.237 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.241 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
11.245 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
11.246 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
11.246 * [backup-simplify]: Simplify (- 0) into 0
11.246 * [backup-simplify]: Simplify (+ 0 0) into 0
11.247 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log 2))))) into 0
11.261 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 3) 6)) (* (/ (pow (- (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log 2) 3) (sqrt 2)))
11.262 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.264 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* n PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* n PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* n PI) 1)))) 6) into 0
11.265 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
11.265 * [backup-simplify]: Simplify (- 0) into 0
11.265 * [backup-simplify]: Simplify (+ 0 0) into 0
11.266 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* n PI)))))) into 0
11.267 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* n PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log (* n PI)) 3) (sqrt (* n PI))))
11.274 * [backup-simplify]: Simplify (+ (* (pow (* n PI) 1/2) (* -1/48 (* (pow (log 2) 3) (sqrt 2)))) (+ (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1/48 (* (pow (log (* n PI)) 3) (sqrt (* n PI)))) (pow 2 1/2))))) into (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log (* n PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* n PI)) 3)) (sqrt (* n PI))))))))
11.289 * [backup-simplify]: Simplify (+ (* (sqrt (* n (* PI 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) +nan.0) (+ (* (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))))) +nan.0) (* (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log (* n PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* n PI)) 3)) (sqrt (* n PI)))))))) 0)))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))))))))
11.289 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))))))) in n
11.289 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))))))) in n
11.289 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n
11.289 * [taylor]: Taking taylor expansion of +nan.0 in n
11.289 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.289 * [taylor]: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n
11.289 * [taylor]: Taking taylor expansion of (* (log 2) (sqrt 2)) in n
11.289 * [taylor]: Taking taylor expansion of (log 2) in n
11.289 * [taylor]: Taking taylor expansion of 2 in n
11.289 * [backup-simplify]: Simplify 2 into 2
11.290 * [backup-simplify]: Simplify (log 2) into (log 2)
11.290 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.290 * [taylor]: Taking taylor expansion of 2 in n
11.290 * [backup-simplify]: Simplify 2 into 2
11.290 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.291 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.291 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.291 * [taylor]: Taking taylor expansion of (* n PI) in n
11.291 * [taylor]: Taking taylor expansion of n in n
11.291 * [backup-simplify]: Simplify 0 into 0
11.291 * [backup-simplify]: Simplify 1 into 1
11.291 * [taylor]: Taking taylor expansion of PI in n
11.291 * [backup-simplify]: Simplify PI into PI
11.292 * [backup-simplify]: Simplify (* 0 PI) into 0
11.293 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.294 * [backup-simplify]: Simplify (sqrt 0) into 0
11.295 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.295 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))))) in n
11.295 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))))) in n
11.295 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) in n
11.295 * [taylor]: Taking taylor expansion of +nan.0 in n
11.295 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.295 * [taylor]: Taking taylor expansion of (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI))) in n
11.296 * [taylor]: Taking taylor expansion of (* (pow (log 2) 2) (sqrt 2)) in n
11.296 * [taylor]: Taking taylor expansion of (pow (log 2) 2) in n
11.296 * [taylor]: Taking taylor expansion of (log 2) in n
11.296 * [taylor]: Taking taylor expansion of 2 in n
11.296 * [backup-simplify]: Simplify 2 into 2
11.296 * [backup-simplify]: Simplify (log 2) into (log 2)
11.296 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.296 * [taylor]: Taking taylor expansion of 2 in n
11.296 * [backup-simplify]: Simplify 2 into 2
11.297 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.297 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.297 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.297 * [taylor]: Taking taylor expansion of (* n PI) in n
11.297 * [taylor]: Taking taylor expansion of n in n
11.297 * [backup-simplify]: Simplify 0 into 0
11.297 * [backup-simplify]: Simplify 1 into 1
11.297 * [taylor]: Taking taylor expansion of PI in n
11.297 * [backup-simplify]: Simplify PI into PI
11.298 * [backup-simplify]: Simplify (* 0 PI) into 0
11.299 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.300 * [backup-simplify]: Simplify (sqrt 0) into 0
11.301 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.301 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))) in n
11.301 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))) in n
11.301 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) in n
11.301 * [taylor]: Taking taylor expansion of +nan.0 in n
11.301 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.301 * [taylor]: Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI))) in n
11.301 * [taylor]: Taking taylor expansion of (* (log 2) (* (sqrt 2) (log (* n PI)))) in n
11.301 * [taylor]: Taking taylor expansion of (log 2) in n
11.302 * [taylor]: Taking taylor expansion of 2 in n
11.302 * [backup-simplify]: Simplify 2 into 2
11.302 * [backup-simplify]: Simplify (log 2) into (log 2)
11.302 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n
11.302 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.302 * [taylor]: Taking taylor expansion of 2 in n
11.302 * [backup-simplify]: Simplify 2 into 2
11.302 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.303 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.303 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
11.303 * [taylor]: Taking taylor expansion of (* n PI) in n
11.303 * [taylor]: Taking taylor expansion of n in n
11.303 * [backup-simplify]: Simplify 0 into 0
11.303 * [backup-simplify]: Simplify 1 into 1
11.303 * [taylor]: Taking taylor expansion of PI in n
11.303 * [backup-simplify]: Simplify PI into PI
11.304 * [backup-simplify]: Simplify (* 0 PI) into 0
11.305 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.306 * [backup-simplify]: Simplify (log PI) into (log PI)
11.306 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.306 * [taylor]: Taking taylor expansion of (* n PI) in n
11.306 * [taylor]: Taking taylor expansion of n in n
11.306 * [backup-simplify]: Simplify 0 into 0
11.306 * [backup-simplify]: Simplify 1 into 1
11.306 * [taylor]: Taking taylor expansion of PI in n
11.306 * [backup-simplify]: Simplify PI into PI
11.307 * [backup-simplify]: Simplify (* 0 PI) into 0
11.308 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.309 * [backup-simplify]: Simplify (sqrt 0) into 0
11.310 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.310 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))) in n
11.310 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))) in n
11.310 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) in n
11.310 * [taylor]: Taking taylor expansion of +nan.0 in n
11.310 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.310 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI))) in n
11.310 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* n PI)) 2)) in n
11.310 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.310 * [taylor]: Taking taylor expansion of 2 in n
11.310 * [backup-simplify]: Simplify 2 into 2
11.311 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.311 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.311 * [taylor]: Taking taylor expansion of (pow (log (* n PI)) 2) in n
11.311 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
11.311 * [taylor]: Taking taylor expansion of (* n PI) in n
11.311 * [taylor]: Taking taylor expansion of n in n
11.311 * [backup-simplify]: Simplify 0 into 0
11.311 * [backup-simplify]: Simplify 1 into 1
11.311 * [taylor]: Taking taylor expansion of PI in n
11.311 * [backup-simplify]: Simplify PI into PI
11.312 * [backup-simplify]: Simplify (* 0 PI) into 0
11.314 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.314 * [backup-simplify]: Simplify (log PI) into (log PI)
11.315 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.315 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.315 * [taylor]: Taking taylor expansion of (* n PI) in n
11.315 * [taylor]: Taking taylor expansion of n in n
11.315 * [backup-simplify]: Simplify 0 into 0
11.315 * [backup-simplify]: Simplify 1 into 1
11.315 * [taylor]: Taking taylor expansion of PI in n
11.315 * [backup-simplify]: Simplify PI into PI
11.316 * [backup-simplify]: Simplify (* 0 PI) into 0
11.317 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.317 * [backup-simplify]: Simplify (sqrt 0) into 0
11.319 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.319 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))) in n
11.319 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) in n
11.319 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
11.319 * [taylor]: Taking taylor expansion of +nan.0 in n
11.319 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.319 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
11.319 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.319 * [taylor]: Taking taylor expansion of 2 in n
11.319 * [backup-simplify]: Simplify 2 into 2
11.319 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.320 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.320 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.320 * [taylor]: Taking taylor expansion of (* n PI) in n
11.320 * [taylor]: Taking taylor expansion of n in n
11.320 * [backup-simplify]: Simplify 0 into 0
11.320 * [backup-simplify]: Simplify 1 into 1
11.320 * [taylor]: Taking taylor expansion of PI in n
11.320 * [backup-simplify]: Simplify PI into PI
11.321 * [backup-simplify]: Simplify (* 0 PI) into 0
11.322 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.323 * [backup-simplify]: Simplify (sqrt 0) into 0
11.324 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.324 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))) in n
11.324 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) in n
11.324 * [taylor]: Taking taylor expansion of +nan.0 in n
11.324 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.324 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))) in n
11.324 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n
11.324 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.324 * [taylor]: Taking taylor expansion of 2 in n
11.324 * [backup-simplify]: Simplify 2 into 2
11.325 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.326 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.326 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
11.326 * [taylor]: Taking taylor expansion of (* n PI) in n
11.326 * [taylor]: Taking taylor expansion of n in n
11.326 * [backup-simplify]: Simplify 0 into 0
11.326 * [backup-simplify]: Simplify 1 into 1
11.326 * [taylor]: Taking taylor expansion of PI in n
11.326 * [backup-simplify]: Simplify PI into PI
11.326 * [backup-simplify]: Simplify (* 0 PI) into 0
11.328 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.328 * [backup-simplify]: Simplify (log PI) into (log PI)
11.328 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.328 * [taylor]: Taking taylor expansion of (* n PI) in n
11.328 * [taylor]: Taking taylor expansion of n in n
11.328 * [backup-simplify]: Simplify 0 into 0
11.328 * [backup-simplify]: Simplify 1 into 1
11.328 * [taylor]: Taking taylor expansion of PI in n
11.328 * [backup-simplify]: Simplify PI into PI
11.329 * [backup-simplify]: Simplify (* 0 PI) into 0
11.330 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.331 * [backup-simplify]: Simplify (sqrt 0) into 0
11.332 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.334 * [backup-simplify]: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2))
11.334 * [backup-simplify]: Simplify (* (* (log 2) (sqrt 2)) 0) into 0
11.335 * [backup-simplify]: Simplify (* +nan.0 0) into 0
11.336 * [backup-simplify]: Simplify (* (log 2) (log 2)) into (pow (log 2) 2)
11.338 * [backup-simplify]: Simplify (* (pow (log 2) 2) (sqrt 2)) into (* (pow (log 2) 2) (sqrt 2))
11.339 * [backup-simplify]: Simplify (* (* (pow (log 2) 2) (sqrt 2)) 0) into 0
11.340 * [backup-simplify]: Simplify (* +nan.0 0) into 0
11.341 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.342 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n)))
11.343 * [backup-simplify]: Simplify (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) into (* (log 2) (* (sqrt 2) (+ (log PI) (log n))))
11.344 * [backup-simplify]: Simplify (* (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) 0) into 0
11.345 * [backup-simplify]: Simplify (* +nan.0 0) into 0
11.346 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.347 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.348 * [backup-simplify]: Simplify (* (+ (log PI) (log n)) (+ (log PI) (log n))) into (pow (+ (log PI) (log n)) 2)
11.348 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) into (* (sqrt 2) (pow (+ (log PI) (log n)) 2))
11.349 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) 0) into 0
11.350 * [backup-simplify]: Simplify (* +nan.0 0) into 0
11.350 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
11.351 * [backup-simplify]: Simplify (* +nan.0 0) into 0
11.352 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.353 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n)))
11.354 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log PI) (log n))) 0) into 0
11.354 * [backup-simplify]: Simplify (* +nan.0 0) into 0
11.355 * [backup-simplify]: Simplify (- 0) into 0
11.355 * [backup-simplify]: Simplify (+ 0 0) into 0
11.356 * [backup-simplify]: Simplify (- 0) into 0
11.356 * [backup-simplify]: Simplify (+ 0 0) into 0
11.357 * [backup-simplify]: Simplify (- 0) into 0
11.357 * [backup-simplify]: Simplify (+ 0 0) into 0
11.357 * [backup-simplify]: Simplify (- 0) into 0
11.358 * [backup-simplify]: Simplify (+ 0 0) into 0
11.358 * [backup-simplify]: Simplify (- 0) into 0
11.359 * [backup-simplify]: Simplify (+ 0 0) into 0
11.359 * [backup-simplify]: Simplify (- 0) into 0
11.359 * [backup-simplify]: Simplify 0 into 0
11.361 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
11.362 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (sqrt 2))) into 0
11.366 * [backup-simplify]: Simplify (+ (* (* (log 2) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))
11.375 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))
11.376 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.378 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
11.378 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.379 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log PI) (log n)))) into 0
11.381 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log PI) (log n))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))
11.394 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))
11.397 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
11.403 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
11.407 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
11.414 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))
11.425 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))
11.438 * [backup-simplify]: Simplify (+ (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))
11.449 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))
11.460 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))
11.461 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.464 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
11.464 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
11.469 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
11.477 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
11.480 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
11.482 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
11.497 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))))
11.497 * [backup-simplify]: Simplify (/ (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) into (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k))
11.502 * [approximate]: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (k n) around 0
11.502 * [taylor]: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n
11.502 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
11.502 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in n
11.502 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in n
11.502 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in n
11.502 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.502 * [taylor]: Taking taylor expansion of 1/2 in n
11.502 * [backup-simplify]: Simplify 1/2 into 1/2
11.502 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.502 * [taylor]: Taking taylor expansion of 1/2 in n
11.502 * [backup-simplify]: Simplify 1/2 into 1/2
11.502 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.502 * [taylor]: Taking taylor expansion of k in n
11.502 * [backup-simplify]: Simplify k into k
11.502 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.502 * [taylor]: Taking taylor expansion of (log 2) in n
11.502 * [taylor]: Taking taylor expansion of 2 in n
11.502 * [backup-simplify]: Simplify 2 into 2
11.503 * [backup-simplify]: Simplify (log 2) into (log 2)
11.503 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.503 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.503 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.504 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
11.504 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
11.504 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.504 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
11.504 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
11.504 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.504 * [taylor]: Taking taylor expansion of 1/2 in n
11.504 * [backup-simplify]: Simplify 1/2 into 1/2
11.504 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.504 * [taylor]: Taking taylor expansion of 1/2 in n
11.504 * [backup-simplify]: Simplify 1/2 into 1/2
11.504 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.504 * [taylor]: Taking taylor expansion of k in n
11.504 * [backup-simplify]: Simplify k into k
11.504 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.504 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
11.504 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.504 * [taylor]: Taking taylor expansion of PI in n
11.504 * [backup-simplify]: Simplify PI into PI
11.504 * [taylor]: Taking taylor expansion of n in n
11.504 * [backup-simplify]: Simplify 0 into 0
11.504 * [backup-simplify]: Simplify 1 into 1
11.505 * [backup-simplify]: Simplify (/ PI 1) into PI
11.505 * [backup-simplify]: Simplify (log PI) into (log PI)
11.505 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.505 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.505 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.506 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.506 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
11.506 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
11.506 * [taylor]: Taking taylor expansion of (sqrt k) in n
11.506 * [taylor]: Taking taylor expansion of k in n
11.506 * [backup-simplify]: Simplify k into k
11.507 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
11.507 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
11.507 * [taylor]: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k
11.507 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in k
11.507 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k
11.507 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k
11.507 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k
11.507 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.507 * [taylor]: Taking taylor expansion of 1/2 in k
11.507 * [backup-simplify]: Simplify 1/2 into 1/2
11.507 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.507 * [taylor]: Taking taylor expansion of 1/2 in k
11.507 * [backup-simplify]: Simplify 1/2 into 1/2
11.507 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.507 * [taylor]: Taking taylor expansion of k in k
11.507 * [backup-simplify]: Simplify 0 into 0
11.507 * [backup-simplify]: Simplify 1 into 1
11.507 * [backup-simplify]: Simplify (/ 1 1) into 1
11.507 * [taylor]: Taking taylor expansion of (log 2) in k
11.507 * [taylor]: Taking taylor expansion of 2 in k
11.507 * [backup-simplify]: Simplify 2 into 2
11.507 * [backup-simplify]: Simplify (log 2) into (log 2)
11.508 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.508 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.508 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.509 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
11.509 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
11.509 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k
11.509 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k
11.509 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k
11.509 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.509 * [taylor]: Taking taylor expansion of 1/2 in k
11.509 * [backup-simplify]: Simplify 1/2 into 1/2
11.509 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.509 * [taylor]: Taking taylor expansion of 1/2 in k
11.509 * [backup-simplify]: Simplify 1/2 into 1/2
11.509 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.509 * [taylor]: Taking taylor expansion of k in k
11.509 * [backup-simplify]: Simplify 0 into 0
11.509 * [backup-simplify]: Simplify 1 into 1
11.510 * [backup-simplify]: Simplify (/ 1 1) into 1
11.510 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k
11.510 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.510 * [taylor]: Taking taylor expansion of PI in k
11.510 * [backup-simplify]: Simplify PI into PI
11.510 * [taylor]: Taking taylor expansion of n in k
11.510 * [backup-simplify]: Simplify n into n
11.510 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.510 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n))
11.510 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.510 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.510 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.511 * [backup-simplify]: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
11.511 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))
11.511 * [taylor]: Taking taylor expansion of (sqrt k) in k
11.511 * [taylor]: Taking taylor expansion of k in k
11.511 * [backup-simplify]: Simplify 0 into 0
11.511 * [backup-simplify]: Simplify 1 into 1
11.511 * [backup-simplify]: Simplify (sqrt 0) into 0
11.512 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.512 * [taylor]: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k
11.512 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in k
11.512 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k
11.512 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k
11.512 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k
11.512 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.512 * [taylor]: Taking taylor expansion of 1/2 in k
11.512 * [backup-simplify]: Simplify 1/2 into 1/2
11.512 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.512 * [taylor]: Taking taylor expansion of 1/2 in k
11.512 * [backup-simplify]: Simplify 1/2 into 1/2
11.512 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.512 * [taylor]: Taking taylor expansion of k in k
11.512 * [backup-simplify]: Simplify 0 into 0
11.512 * [backup-simplify]: Simplify 1 into 1
11.512 * [backup-simplify]: Simplify (/ 1 1) into 1
11.512 * [taylor]: Taking taylor expansion of (log 2) in k
11.512 * [taylor]: Taking taylor expansion of 2 in k
11.512 * [backup-simplify]: Simplify 2 into 2
11.513 * [backup-simplify]: Simplify (log 2) into (log 2)
11.513 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.513 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.514 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.514 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
11.514 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
11.514 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k
11.514 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k
11.514 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k
11.514 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.514 * [taylor]: Taking taylor expansion of 1/2 in k
11.515 * [backup-simplify]: Simplify 1/2 into 1/2
11.515 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.515 * [taylor]: Taking taylor expansion of 1/2 in k
11.515 * [backup-simplify]: Simplify 1/2 into 1/2
11.515 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.515 * [taylor]: Taking taylor expansion of k in k
11.515 * [backup-simplify]: Simplify 0 into 0
11.515 * [backup-simplify]: Simplify 1 into 1
11.515 * [backup-simplify]: Simplify (/ 1 1) into 1
11.515 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k
11.515 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.515 * [taylor]: Taking taylor expansion of PI in k
11.515 * [backup-simplify]: Simplify PI into PI
11.515 * [taylor]: Taking taylor expansion of n in k
11.515 * [backup-simplify]: Simplify n into n
11.515 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.515 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n))
11.515 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.516 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.516 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.516 * [backup-simplify]: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
11.516 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))
11.516 * [taylor]: Taking taylor expansion of (sqrt k) in k
11.516 * [taylor]: Taking taylor expansion of k in k
11.516 * [backup-simplify]: Simplify 0 into 0
11.516 * [backup-simplify]: Simplify 1 into 1
11.516 * [backup-simplify]: Simplify (sqrt 0) into 0
11.517 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.518 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))
11.518 * [backup-simplify]: Simplify (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0
11.518 * [taylor]: Taking taylor expansion of 0 in n
11.518 * [backup-simplify]: Simplify 0 into 0
11.518 * [backup-simplify]: Simplify 0 into 0
11.518 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0
11.519 * [backup-simplify]: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))
11.519 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n
11.519 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n
11.519 * [taylor]: Taking taylor expansion of +nan.0 in n
11.519 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.519 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
11.519 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
11.519 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.519 * [taylor]: Taking taylor expansion of (log 2) in n
11.519 * [taylor]: Taking taylor expansion of 2 in n
11.519 * [backup-simplify]: Simplify 2 into 2
11.520 * [backup-simplify]: Simplify (log 2) into (log 2)
11.520 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.520 * [taylor]: Taking taylor expansion of 1/2 in n
11.520 * [backup-simplify]: Simplify 1/2 into 1/2
11.520 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.520 * [taylor]: Taking taylor expansion of 1/2 in n
11.520 * [backup-simplify]: Simplify 1/2 into 1/2
11.520 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.520 * [taylor]: Taking taylor expansion of k in n
11.520 * [backup-simplify]: Simplify k into k
11.520 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.520 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.520 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.520 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.520 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
11.521 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
11.521 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.521 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
11.521 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
11.521 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.521 * [taylor]: Taking taylor expansion of 1/2 in n
11.521 * [backup-simplify]: Simplify 1/2 into 1/2
11.521 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.521 * [taylor]: Taking taylor expansion of 1/2 in n
11.521 * [backup-simplify]: Simplify 1/2 into 1/2
11.521 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.521 * [taylor]: Taking taylor expansion of k in n
11.521 * [backup-simplify]: Simplify k into k
11.521 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.521 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
11.521 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.521 * [taylor]: Taking taylor expansion of PI in n
11.521 * [backup-simplify]: Simplify PI into PI
11.521 * [taylor]: Taking taylor expansion of n in n
11.521 * [backup-simplify]: Simplify 0 into 0
11.521 * [backup-simplify]: Simplify 1 into 1
11.521 * [backup-simplify]: Simplify (/ PI 1) into PI
11.522 * [backup-simplify]: Simplify (log PI) into (log PI)
11.522 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.522 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.522 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.522 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.523 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
11.523 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
11.524 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))
11.524 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
11.526 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
11.527 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
11.527 * [backup-simplify]: Simplify 0 into 0
11.530 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
11.531 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0
11.532 * [backup-simplify]: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))
11.532 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n
11.532 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n
11.532 * [taylor]: Taking taylor expansion of +nan.0 in n
11.533 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.533 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
11.533 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
11.533 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.533 * [taylor]: Taking taylor expansion of (log 2) in n
11.533 * [taylor]: Taking taylor expansion of 2 in n
11.533 * [backup-simplify]: Simplify 2 into 2
11.533 * [backup-simplify]: Simplify (log 2) into (log 2)
11.533 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.533 * [taylor]: Taking taylor expansion of 1/2 in n
11.533 * [backup-simplify]: Simplify 1/2 into 1/2
11.533 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.533 * [taylor]: Taking taylor expansion of 1/2 in n
11.533 * [backup-simplify]: Simplify 1/2 into 1/2
11.533 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.533 * [taylor]: Taking taylor expansion of k in n
11.533 * [backup-simplify]: Simplify k into k
11.533 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.534 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.534 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.534 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.534 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
11.535 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
11.535 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.535 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
11.535 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
11.535 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.535 * [taylor]: Taking taylor expansion of 1/2 in n
11.535 * [backup-simplify]: Simplify 1/2 into 1/2
11.535 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.535 * [taylor]: Taking taylor expansion of 1/2 in n
11.535 * [backup-simplify]: Simplify 1/2 into 1/2
11.535 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.535 * [taylor]: Taking taylor expansion of k in n
11.535 * [backup-simplify]: Simplify k into k
11.535 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.535 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
11.535 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.535 * [taylor]: Taking taylor expansion of PI in n
11.535 * [backup-simplify]: Simplify PI into PI
11.535 * [taylor]: Taking taylor expansion of n in n
11.535 * [backup-simplify]: Simplify 0 into 0
11.536 * [backup-simplify]: Simplify 1 into 1
11.536 * [backup-simplify]: Simplify (/ PI 1) into PI
11.537 * [backup-simplify]: Simplify (log PI) into (log PI)
11.537 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.537 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.537 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.538 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.539 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
11.539 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
11.540 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))
11.541 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
11.542 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
11.544 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
11.545 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.546 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
11.546 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.547 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.547 * [backup-simplify]: Simplify (- 0) into 0
11.548 * [backup-simplify]: Simplify (+ 0 0) into 0
11.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.549 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0
11.550 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.550 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.551 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.551 * [backup-simplify]: Simplify (- 0) into 0
11.552 * [backup-simplify]: Simplify (+ 0 0) into 0
11.553 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
11.554 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
11.555 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.556 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into 0
11.557 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
11.558 * [backup-simplify]: Simplify (- 0) into 0
11.558 * [backup-simplify]: Simplify 0 into 0
11.558 * [backup-simplify]: Simplify 0 into 0
11.562 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
11.563 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
11.565 * [backup-simplify]: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))
11.565 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n
11.565 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n
11.565 * [taylor]: Taking taylor expansion of +nan.0 in n
11.565 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.565 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
11.565 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
11.565 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.565 * [taylor]: Taking taylor expansion of (log 2) in n
11.565 * [taylor]: Taking taylor expansion of 2 in n
11.565 * [backup-simplify]: Simplify 2 into 2
11.566 * [backup-simplify]: Simplify (log 2) into (log 2)
11.566 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.566 * [taylor]: Taking taylor expansion of 1/2 in n
11.566 * [backup-simplify]: Simplify 1/2 into 1/2
11.566 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.566 * [taylor]: Taking taylor expansion of 1/2 in n
11.566 * [backup-simplify]: Simplify 1/2 into 1/2
11.566 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.566 * [taylor]: Taking taylor expansion of k in n
11.566 * [backup-simplify]: Simplify k into k
11.566 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.566 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.566 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.566 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.567 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
11.567 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
11.567 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.567 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
11.567 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
11.567 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.567 * [taylor]: Taking taylor expansion of 1/2 in n
11.567 * [backup-simplify]: Simplify 1/2 into 1/2
11.567 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.567 * [taylor]: Taking taylor expansion of 1/2 in n
11.567 * [backup-simplify]: Simplify 1/2 into 1/2
11.567 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.567 * [taylor]: Taking taylor expansion of k in n
11.567 * [backup-simplify]: Simplify k into k
11.568 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.568 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
11.568 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.568 * [taylor]: Taking taylor expansion of PI in n
11.568 * [backup-simplify]: Simplify PI into PI
11.568 * [taylor]: Taking taylor expansion of n in n
11.568 * [backup-simplify]: Simplify 0 into 0
11.568 * [backup-simplify]: Simplify 1 into 1
11.568 * [backup-simplify]: Simplify (/ PI 1) into PI
11.569 * [backup-simplify]: Simplify (log PI) into (log PI)
11.569 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.569 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.569 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.569 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.570 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
11.570 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
11.571 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))
11.571 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
11.572 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
11.573 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
11.575 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 3))))))))
11.576 * [backup-simplify]: Simplify (/ (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) into (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k)))
11.576 * [approximate]: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (k n) around 0
11.576 * [taylor]: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n
11.576 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
11.576 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.576 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
11.576 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
11.576 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.576 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.576 * [taylor]: Taking taylor expansion of 1/2 in n
11.576 * [backup-simplify]: Simplify 1/2 into 1/2
11.576 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.576 * [taylor]: Taking taylor expansion of k in n
11.576 * [backup-simplify]: Simplify k into k
11.576 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.576 * [taylor]: Taking taylor expansion of 1/2 in n
11.576 * [backup-simplify]: Simplify 1/2 into 1/2
11.576 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
11.576 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
11.576 * [taylor]: Taking taylor expansion of -1 in n
11.576 * [backup-simplify]: Simplify -1 into -1
11.576 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.576 * [taylor]: Taking taylor expansion of PI in n
11.576 * [backup-simplify]: Simplify PI into PI
11.576 * [taylor]: Taking taylor expansion of n in n
11.576 * [backup-simplify]: Simplify 0 into 0
11.576 * [backup-simplify]: Simplify 1 into 1
11.577 * [backup-simplify]: Simplify (/ PI 1) into PI
11.577 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
11.578 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
11.578 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.578 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.579 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.579 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
11.580 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
11.580 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.580 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in n
11.580 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in n
11.580 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.580 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.580 * [taylor]: Taking taylor expansion of 1/2 in n
11.580 * [backup-simplify]: Simplify 1/2 into 1/2
11.580 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.580 * [taylor]: Taking taylor expansion of k in n
11.580 * [backup-simplify]: Simplify k into k
11.580 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.580 * [taylor]: Taking taylor expansion of 1/2 in n
11.580 * [backup-simplify]: Simplify 1/2 into 1/2
11.580 * [taylor]: Taking taylor expansion of (log 2) in n
11.580 * [taylor]: Taking taylor expansion of 2 in n
11.580 * [backup-simplify]: Simplify 2 into 2
11.581 * [backup-simplify]: Simplify (log 2) into (log 2)
11.581 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.581 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.581 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
11.581 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
11.581 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
11.581 * [taylor]: Taking taylor expansion of (/ -1 k) in n
11.581 * [taylor]: Taking taylor expansion of -1 in n
11.581 * [backup-simplify]: Simplify -1 into -1
11.581 * [taylor]: Taking taylor expansion of k in n
11.581 * [backup-simplify]: Simplify k into k
11.581 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
11.582 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
11.582 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
11.582 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
11.583 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
11.584 * [backup-simplify]: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (sqrt (/ -1 k)))
11.584 * [taylor]: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k
11.584 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
11.584 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.584 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k
11.584 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k
11.584 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.584 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.584 * [taylor]: Taking taylor expansion of 1/2 in k
11.584 * [backup-simplify]: Simplify 1/2 into 1/2
11.584 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.584 * [taylor]: Taking taylor expansion of k in k
11.584 * [backup-simplify]: Simplify 0 into 0
11.584 * [backup-simplify]: Simplify 1 into 1
11.584 * [backup-simplify]: Simplify (/ 1 1) into 1
11.584 * [taylor]: Taking taylor expansion of 1/2 in k
11.584 * [backup-simplify]: Simplify 1/2 into 1/2
11.584 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k
11.584 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k
11.584 * [taylor]: Taking taylor expansion of -1 in k
11.584 * [backup-simplify]: Simplify -1 into -1
11.584 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.584 * [taylor]: Taking taylor expansion of PI in k
11.584 * [backup-simplify]: Simplify PI into PI
11.584 * [taylor]: Taking taylor expansion of n in k
11.584 * [backup-simplify]: Simplify n into n
11.585 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.585 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n))
11.585 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n)))
11.585 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.585 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.585 * [backup-simplify]: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
11.585 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
11.585 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.585 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k
11.585 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k
11.585 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.585 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.585 * [taylor]: Taking taylor expansion of 1/2 in k
11.585 * [backup-simplify]: Simplify 1/2 into 1/2
11.585 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.586 * [taylor]: Taking taylor expansion of k in k
11.586 * [backup-simplify]: Simplify 0 into 0
11.586 * [backup-simplify]: Simplify 1 into 1
11.586 * [backup-simplify]: Simplify (/ 1 1) into 1
11.586 * [taylor]: Taking taylor expansion of 1/2 in k
11.586 * [backup-simplify]: Simplify 1/2 into 1/2
11.586 * [taylor]: Taking taylor expansion of (log 2) in k
11.586 * [taylor]: Taking taylor expansion of 2 in k
11.586 * [backup-simplify]: Simplify 2 into 2
11.586 * [backup-simplify]: Simplify (log 2) into (log 2)
11.586 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.587 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.587 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
11.588 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
11.588 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
11.588 * [taylor]: Taking taylor expansion of (/ -1 k) in k
11.588 * [taylor]: Taking taylor expansion of -1 in k
11.588 * [backup-simplify]: Simplify -1 into -1
11.588 * [taylor]: Taking taylor expansion of k in k
11.588 * [backup-simplify]: Simplify 0 into 0
11.588 * [backup-simplify]: Simplify 1 into 1
11.588 * [backup-simplify]: Simplify (/ -1 1) into -1
11.588 * [backup-simplify]: Simplify (sqrt 0) into 0
11.589 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
11.590 * [backup-simplify]: Simplify (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))
11.590 * [backup-simplify]: Simplify (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))
11.590 * [taylor]: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k
11.590 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
11.590 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.590 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k
11.590 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k
11.590 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.590 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.590 * [taylor]: Taking taylor expansion of 1/2 in k
11.590 * [backup-simplify]: Simplify 1/2 into 1/2
11.590 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.590 * [taylor]: Taking taylor expansion of k in k
11.590 * [backup-simplify]: Simplify 0 into 0
11.590 * [backup-simplify]: Simplify 1 into 1
11.591 * [backup-simplify]: Simplify (/ 1 1) into 1
11.591 * [taylor]: Taking taylor expansion of 1/2 in k
11.591 * [backup-simplify]: Simplify 1/2 into 1/2
11.591 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k
11.591 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k
11.591 * [taylor]: Taking taylor expansion of -1 in k
11.591 * [backup-simplify]: Simplify -1 into -1
11.591 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.591 * [taylor]: Taking taylor expansion of PI in k
11.591 * [backup-simplify]: Simplify PI into PI
11.591 * [taylor]: Taking taylor expansion of n in k
11.591 * [backup-simplify]: Simplify n into n
11.591 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.591 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n))
11.591 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n)))
11.591 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.591 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.591 * [backup-simplify]: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
11.592 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
11.592 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.592 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k
11.592 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k
11.592 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.592 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.592 * [taylor]: Taking taylor expansion of 1/2 in k
11.592 * [backup-simplify]: Simplify 1/2 into 1/2
11.592 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.592 * [taylor]: Taking taylor expansion of k in k
11.592 * [backup-simplify]: Simplify 0 into 0
11.592 * [backup-simplify]: Simplify 1 into 1
11.592 * [backup-simplify]: Simplify (/ 1 1) into 1
11.592 * [taylor]: Taking taylor expansion of 1/2 in k
11.592 * [backup-simplify]: Simplify 1/2 into 1/2
11.592 * [taylor]: Taking taylor expansion of (log 2) in k
11.592 * [taylor]: Taking taylor expansion of 2 in k
11.592 * [backup-simplify]: Simplify 2 into 2
11.592 * [backup-simplify]: Simplify (log 2) into (log 2)
11.593 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.593 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.594 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
11.594 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
11.594 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
11.594 * [taylor]: Taking taylor expansion of (/ -1 k) in k
11.594 * [taylor]: Taking taylor expansion of -1 in k
11.594 * [backup-simplify]: Simplify -1 into -1
11.594 * [taylor]: Taking taylor expansion of k in k
11.594 * [backup-simplify]: Simplify 0 into 0
11.594 * [backup-simplify]: Simplify 1 into 1
11.594 * [backup-simplify]: Simplify (/ -1 1) into -1
11.594 * [backup-simplify]: Simplify (sqrt 0) into 0
11.595 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
11.596 * [backup-simplify]: Simplify (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))
11.596 * [backup-simplify]: Simplify (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))
11.596 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
11.596 * [taylor]: Taking taylor expansion of +nan.0 in n
11.596 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.596 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
11.596 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.596 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
11.596 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
11.596 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.596 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.596 * [taylor]: Taking taylor expansion of 1/2 in n
11.596 * [backup-simplify]: Simplify 1/2 into 1/2
11.596 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.596 * [taylor]: Taking taylor expansion of k in n
11.596 * [backup-simplify]: Simplify k into k
11.596 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.597 * [taylor]: Taking taylor expansion of 1/2 in n
11.597 * [backup-simplify]: Simplify 1/2 into 1/2
11.597 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
11.597 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
11.597 * [taylor]: Taking taylor expansion of -1 in n
11.597 * [backup-simplify]: Simplify -1 into -1
11.597 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.597 * [taylor]: Taking taylor expansion of PI in n
11.597 * [backup-simplify]: Simplify PI into PI
11.597 * [taylor]: Taking taylor expansion of n in n
11.597 * [backup-simplify]: Simplify 0 into 0
11.597 * [backup-simplify]: Simplify 1 into 1
11.597 * [backup-simplify]: Simplify (/ PI 1) into PI
11.597 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
11.598 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
11.598 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.598 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.599 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.600 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
11.601 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
11.601 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
11.601 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.601 * [taylor]: Taking taylor expansion of (log 2) in n
11.601 * [taylor]: Taking taylor expansion of 2 in n
11.601 * [backup-simplify]: Simplify 2 into 2
11.601 * [backup-simplify]: Simplify (log 2) into (log 2)
11.601 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.601 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.601 * [taylor]: Taking taylor expansion of 1/2 in n
11.601 * [backup-simplify]: Simplify 1/2 into 1/2
11.601 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.601 * [taylor]: Taking taylor expansion of k in n
11.602 * [backup-simplify]: Simplify k into k
11.602 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.602 * [taylor]: Taking taylor expansion of 1/2 in n
11.602 * [backup-simplify]: Simplify 1/2 into 1/2
11.602 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.602 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.602 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
11.603 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
11.605 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
11.607 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
11.608 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
11.609 * [backup-simplify]: Simplify (+ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
11.610 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
11.613 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
11.615 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))))
11.615 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n
11.615 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
11.615 * [taylor]: Taking taylor expansion of +nan.0 in n
11.615 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.615 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
11.615 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.615 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
11.615 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
11.615 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.615 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.615 * [taylor]: Taking taylor expansion of 1/2 in n
11.615 * [backup-simplify]: Simplify 1/2 into 1/2
11.615 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.615 * [taylor]: Taking taylor expansion of k in n
11.615 * [backup-simplify]: Simplify k into k
11.615 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.615 * [taylor]: Taking taylor expansion of 1/2 in n
11.615 * [backup-simplify]: Simplify 1/2 into 1/2
11.615 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
11.615 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
11.615 * [taylor]: Taking taylor expansion of -1 in n
11.616 * [backup-simplify]: Simplify -1 into -1
11.616 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.616 * [taylor]: Taking taylor expansion of PI in n
11.616 * [backup-simplify]: Simplify PI into PI
11.616 * [taylor]: Taking taylor expansion of n in n
11.616 * [backup-simplify]: Simplify 0 into 0
11.616 * [backup-simplify]: Simplify 1 into 1
11.616 * [backup-simplify]: Simplify (/ PI 1) into PI
11.617 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
11.623 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
11.624 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.624 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.626 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.627 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
11.628 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
11.628 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
11.628 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.628 * [taylor]: Taking taylor expansion of (log 2) in n
11.628 * [taylor]: Taking taylor expansion of 2 in n
11.628 * [backup-simplify]: Simplify 2 into 2
11.629 * [backup-simplify]: Simplify (log 2) into (log 2)
11.629 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.629 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.629 * [taylor]: Taking taylor expansion of 1/2 in n
11.629 * [backup-simplify]: Simplify 1/2 into 1/2
11.629 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.629 * [taylor]: Taking taylor expansion of k in n
11.629 * [backup-simplify]: Simplify k into k
11.629 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.629 * [taylor]: Taking taylor expansion of 1/2 in n
11.629 * [backup-simplify]: Simplify 1/2 into 1/2
11.629 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.629 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.630 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
11.630 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
11.632 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
11.634 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
11.636 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))))
11.638 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))))
11.639 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.639 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.640 * [backup-simplify]: Simplify (+ 0 0) into 0
11.641 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
11.642 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
11.643 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0
11.644 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.645 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0
11.647 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0
11.647 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.648 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.648 * [backup-simplify]: Simplify (+ 0 0) into 0
11.650 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.651 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0
11.653 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
11.654 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
11.657 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into 0
11.657 * [backup-simplify]: Simplify 0 into 0
11.658 * [backup-simplify]: Simplify (+ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0
11.659 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.663 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
11.666 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))))
11.666 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n
11.666 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
11.666 * [taylor]: Taking taylor expansion of +nan.0 in n
11.666 * [backup-simplify]: Simplify +nan.0 into +nan.0
11.666 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
11.666 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.666 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
11.666 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
11.666 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.666 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.666 * [taylor]: Taking taylor expansion of 1/2 in n
11.666 * [backup-simplify]: Simplify 1/2 into 1/2
11.666 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.667 * [taylor]: Taking taylor expansion of k in n
11.667 * [backup-simplify]: Simplify k into k
11.667 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.667 * [taylor]: Taking taylor expansion of 1/2 in n
11.667 * [backup-simplify]: Simplify 1/2 into 1/2
11.667 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
11.667 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
11.667 * [taylor]: Taking taylor expansion of -1 in n
11.667 * [backup-simplify]: Simplify -1 into -1
11.667 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.667 * [taylor]: Taking taylor expansion of PI in n
11.667 * [backup-simplify]: Simplify PI into PI
11.667 * [taylor]: Taking taylor expansion of n in n
11.667 * [backup-simplify]: Simplify 0 into 0
11.667 * [backup-simplify]: Simplify 1 into 1
11.667 * [backup-simplify]: Simplify (/ PI 1) into PI
11.668 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
11.669 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
11.669 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.669 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.671 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.672 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
11.673 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
11.673 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
11.673 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.673 * [taylor]: Taking taylor expansion of (log 2) in n
11.673 * [taylor]: Taking taylor expansion of 2 in n
11.673 * [backup-simplify]: Simplify 2 into 2
11.674 * [backup-simplify]: Simplify (log 2) into (log 2)
11.674 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.674 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.674 * [taylor]: Taking taylor expansion of 1/2 in n
11.674 * [backup-simplify]: Simplify 1/2 into 1/2
11.674 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.674 * [taylor]: Taking taylor expansion of k in n
11.674 * [backup-simplify]: Simplify k into k
11.674 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.674 * [taylor]: Taking taylor expansion of 1/2 in n
11.674 * [backup-simplify]: Simplify 1/2 into 1/2
11.674 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.674 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.675 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
11.675 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
11.677 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
11.679 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
11.681 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))))
11.682 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))))
11.688 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))))))))
11.689 * * * * [progress]: [ 4 / 4 ] generating series at (2 1)
11.689 * [backup-simplify]: Simplify (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) into (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k))))
11.689 * [approximate]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in (k n) around 0
11.689 * [taylor]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in n
11.689 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n
11.689 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n
11.689 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n
11.689 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
11.689 * [taylor]: Taking taylor expansion of 1/2 in n
11.689 * [backup-simplify]: Simplify 1/2 into 1/2
11.689 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
11.689 * [taylor]: Taking taylor expansion of 1/2 in n
11.689 * [backup-simplify]: Simplify 1/2 into 1/2
11.689 * [taylor]: Taking taylor expansion of k in n
11.689 * [backup-simplify]: Simplify k into k
11.689 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
11.689 * [taylor]: Taking taylor expansion of (* n PI) in n
11.689 * [taylor]: Taking taylor expansion of n in n
11.689 * [backup-simplify]: Simplify 0 into 0
11.689 * [backup-simplify]: Simplify 1 into 1
11.690 * [taylor]: Taking taylor expansion of PI in n
11.690 * [backup-simplify]: Simplify PI into PI
11.690 * [backup-simplify]: Simplify (* 0 PI) into 0
11.692 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.692 * [backup-simplify]: Simplify (log PI) into (log PI)
11.692 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
11.692 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
11.692 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
11.693 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.694 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
11.694 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
11.694 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in n
11.694 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in n
11.694 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in n
11.694 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
11.694 * [taylor]: Taking taylor expansion of 1/2 in n
11.694 * [backup-simplify]: Simplify 1/2 into 1/2
11.694 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
11.694 * [taylor]: Taking taylor expansion of 1/2 in n
11.694 * [backup-simplify]: Simplify 1/2 into 1/2
11.695 * [taylor]: Taking taylor expansion of k in n
11.695 * [backup-simplify]: Simplify k into k
11.695 * [taylor]: Taking taylor expansion of (log 2) in n
11.695 * [taylor]: Taking taylor expansion of 2 in n
11.695 * [backup-simplify]: Simplify 2 into 2
11.695 * [backup-simplify]: Simplify (log 2) into (log 2)
11.695 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
11.695 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
11.695 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
11.696 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k)))
11.696 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k))))
11.696 * [taylor]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in k
11.696 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k
11.696 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k
11.696 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k
11.696 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.696 * [taylor]: Taking taylor expansion of 1/2 in k
11.696 * [backup-simplify]: Simplify 1/2 into 1/2
11.696 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.696 * [taylor]: Taking taylor expansion of 1/2 in k
11.697 * [backup-simplify]: Simplify 1/2 into 1/2
11.697 * [taylor]: Taking taylor expansion of k in k
11.697 * [backup-simplify]: Simplify 0 into 0
11.697 * [backup-simplify]: Simplify 1 into 1
11.697 * [taylor]: Taking taylor expansion of (log (* n PI)) in k
11.697 * [taylor]: Taking taylor expansion of (* n PI) in k
11.697 * [taylor]: Taking taylor expansion of n in k
11.697 * [backup-simplify]: Simplify n into n
11.697 * [taylor]: Taking taylor expansion of PI in k
11.697 * [backup-simplify]: Simplify PI into PI
11.697 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.697 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI))
11.697 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.698 * [backup-simplify]: Simplify (- 0) into 0
11.698 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.698 * [backup-simplify]: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI)))
11.698 * [backup-simplify]: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2)
11.698 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k
11.698 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k
11.698 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k
11.698 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.698 * [taylor]: Taking taylor expansion of 1/2 in k
11.699 * [backup-simplify]: Simplify 1/2 into 1/2
11.699 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.699 * [taylor]: Taking taylor expansion of 1/2 in k
11.699 * [backup-simplify]: Simplify 1/2 into 1/2
11.699 * [taylor]: Taking taylor expansion of k in k
11.699 * [backup-simplify]: Simplify 0 into 0
11.699 * [backup-simplify]: Simplify 1 into 1
11.699 * [taylor]: Taking taylor expansion of (log 2) in k
11.699 * [taylor]: Taking taylor expansion of 2 in k
11.699 * [backup-simplify]: Simplify 2 into 2
11.699 * [backup-simplify]: Simplify (log 2) into (log 2)
11.700 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.700 * [backup-simplify]: Simplify (- 0) into 0
11.701 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.702 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
11.703 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
11.703 * [taylor]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in k
11.703 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k
11.703 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k
11.703 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k
11.703 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.703 * [taylor]: Taking taylor expansion of 1/2 in k
11.704 * [backup-simplify]: Simplify 1/2 into 1/2
11.704 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.704 * [taylor]: Taking taylor expansion of 1/2 in k
11.704 * [backup-simplify]: Simplify 1/2 into 1/2
11.704 * [taylor]: Taking taylor expansion of k in k
11.704 * [backup-simplify]: Simplify 0 into 0
11.704 * [backup-simplify]: Simplify 1 into 1
11.704 * [taylor]: Taking taylor expansion of (log (* n PI)) in k
11.704 * [taylor]: Taking taylor expansion of (* n PI) in k
11.704 * [taylor]: Taking taylor expansion of n in k
11.704 * [backup-simplify]: Simplify n into n
11.704 * [taylor]: Taking taylor expansion of PI in k
11.704 * [backup-simplify]: Simplify PI into PI
11.704 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.704 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI))
11.704 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.705 * [backup-simplify]: Simplify (- 0) into 0
11.705 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.705 * [backup-simplify]: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI)))
11.705 * [backup-simplify]: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2)
11.705 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k
11.705 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k
11.705 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k
11.706 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.706 * [taylor]: Taking taylor expansion of 1/2 in k
11.706 * [backup-simplify]: Simplify 1/2 into 1/2
11.706 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.706 * [taylor]: Taking taylor expansion of 1/2 in k
11.706 * [backup-simplify]: Simplify 1/2 into 1/2
11.706 * [taylor]: Taking taylor expansion of k in k
11.706 * [backup-simplify]: Simplify 0 into 0
11.706 * [backup-simplify]: Simplify 1 into 1
11.706 * [taylor]: Taking taylor expansion of (log 2) in k
11.706 * [taylor]: Taking taylor expansion of 2 in k
11.706 * [backup-simplify]: Simplify 2 into 2
11.706 * [backup-simplify]: Simplify (log 2) into (log 2)
11.707 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.707 * [backup-simplify]: Simplify (- 0) into 0
11.707 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.708 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
11.709 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
11.710 * [backup-simplify]: Simplify (* (pow (* n PI) 1/2) (pow 2 1/2)) into (sqrt (* n (* PI 2)))
11.710 * [taylor]: Taking taylor expansion of (sqrt (* n (* PI 2))) in n
11.710 * [taylor]: Taking taylor expansion of (* n (* PI 2)) in n
11.710 * [taylor]: Taking taylor expansion of n in n
11.710 * [backup-simplify]: Simplify 0 into 0
11.710 * [backup-simplify]: Simplify 1 into 1
11.710 * [taylor]: Taking taylor expansion of (* PI 2) in n
11.710 * [taylor]: Taking taylor expansion of PI in n
11.710 * [backup-simplify]: Simplify PI into PI
11.710 * [taylor]: Taking taylor expansion of 2 in n
11.710 * [backup-simplify]: Simplify 2 into 2
11.710 * [backup-simplify]: Simplify (* PI 2) into (* 2 PI)
11.711 * [backup-simplify]: Simplify (* 0 (* 2 PI)) into 0
11.711 * [backup-simplify]: Simplify (+ (* PI 0) (* 0 2)) into 0
11.712 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
11.713 * [backup-simplify]: Simplify (sqrt 0) into 0
11.714 * [backup-simplify]: Simplify (/ (* 2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI)
11.714 * [backup-simplify]: Simplify 0 into 0
11.715 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
11.715 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
11.716 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.716 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.717 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log 2))) into (- (* 1/2 (log 2)))
11.722 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2)))
11.722 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
11.723 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* n PI) 1)))) 1) into 0
11.723 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
11.724 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.724 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.724 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* n PI)))) into (- (* 1/2 (log (* n PI))))
11.724 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 1) 1)))) into (* -1/2 (* (log (* n PI)) (sqrt (* n PI))))
11.726 * [backup-simplify]: Simplify (+ (* (pow (* n PI) 1/2) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (pow 2 1/2))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))
11.726 * [taylor]: Taking taylor expansion of (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) in n
11.726 * [taylor]: Taking taylor expansion of (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))) in n
11.726 * [taylor]: Taking taylor expansion of (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n
11.726 * [taylor]: Taking taylor expansion of 1/2 in n
11.726 * [backup-simplify]: Simplify 1/2 into 1/2
11.726 * [taylor]: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n
11.726 * [taylor]: Taking taylor expansion of (* (log 2) (sqrt 2)) in n
11.726 * [taylor]: Taking taylor expansion of (log 2) in n
11.726 * [taylor]: Taking taylor expansion of 2 in n
11.726 * [backup-simplify]: Simplify 2 into 2
11.727 * [backup-simplify]: Simplify (log 2) into (log 2)
11.727 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.727 * [taylor]: Taking taylor expansion of 2 in n
11.727 * [backup-simplify]: Simplify 2 into 2
11.727 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.727 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.727 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.727 * [taylor]: Taking taylor expansion of (* n PI) in n
11.727 * [taylor]: Taking taylor expansion of n in n
11.727 * [backup-simplify]: Simplify 0 into 0
11.727 * [backup-simplify]: Simplify 1 into 1
11.727 * [taylor]: Taking taylor expansion of PI in n
11.727 * [backup-simplify]: Simplify PI into PI
11.728 * [backup-simplify]: Simplify (* 0 PI) into 0
11.729 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.729 * [backup-simplify]: Simplify (sqrt 0) into 0
11.730 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.730 * [taylor]: Taking taylor expansion of (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) in n
11.730 * [taylor]: Taking taylor expansion of 1/2 in n
11.730 * [backup-simplify]: Simplify 1/2 into 1/2
11.730 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))) in n
11.730 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n
11.730 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.730 * [taylor]: Taking taylor expansion of 2 in n
11.730 * [backup-simplify]: Simplify 2 into 2
11.730 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.730 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.730 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
11.731 * [taylor]: Taking taylor expansion of (* n PI) in n
11.731 * [taylor]: Taking taylor expansion of n in n
11.731 * [backup-simplify]: Simplify 0 into 0
11.731 * [backup-simplify]: Simplify 1 into 1
11.731 * [taylor]: Taking taylor expansion of PI in n
11.731 * [backup-simplify]: Simplify PI into PI
11.731 * [backup-simplify]: Simplify (* 0 PI) into 0
11.732 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.732 * [backup-simplify]: Simplify (log PI) into (log PI)
11.732 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.732 * [taylor]: Taking taylor expansion of (* n PI) in n
11.732 * [taylor]: Taking taylor expansion of n in n
11.732 * [backup-simplify]: Simplify 0 into 0
11.732 * [backup-simplify]: Simplify 1 into 1
11.732 * [taylor]: Taking taylor expansion of PI in n
11.732 * [backup-simplify]: Simplify PI into PI
11.733 * [backup-simplify]: Simplify (* 0 PI) into 0
11.734 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.734 * [backup-simplify]: Simplify (sqrt 0) into 0
11.735 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.736 * [backup-simplify]: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2))
11.736 * [backup-simplify]: Simplify (* (* (log 2) (sqrt 2)) 0) into 0
11.736 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.737 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.737 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n)))
11.738 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log PI) (log n))) 0) into 0
11.738 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.739 * [backup-simplify]: Simplify (+ 0 0) into 0
11.739 * [backup-simplify]: Simplify (- 0) into 0
11.739 * [backup-simplify]: Simplify 0 into 0
11.739 * [backup-simplify]: Simplify (* +nan.0 PI) into (* +nan.0 PI)
11.741 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
11.741 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
11.742 * [backup-simplify]: Simplify (- 0) into 0
11.742 * [backup-simplify]: Simplify (+ 0 0) into 0
11.743 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log 2)))) into 0
11.753 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2)))
11.754 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
11.755 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* n PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* n PI) 1)))) 2) into 0
11.756 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
11.756 * [backup-simplify]: Simplify (- 0) into 0
11.756 * [backup-simplify]: Simplify (+ 0 0) into 0
11.757 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* n PI))))) into 0
11.757 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI))))
11.761 * [backup-simplify]: Simplify (+ (* (pow (* n PI) 1/2) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) (pow 2 1/2)))) into (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI))))))
11.761 * [taylor]: Taking taylor expansion of (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))))) in n
11.761 * [taylor]: Taking taylor expansion of (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) in n
11.761 * [taylor]: Taking taylor expansion of 1/8 in n
11.761 * [backup-simplify]: Simplify 1/8 into 1/8
11.761 * [taylor]: Taking taylor expansion of (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI))) in n
11.761 * [taylor]: Taking taylor expansion of (* (pow (log 2) 2) (sqrt 2)) in n
11.761 * [taylor]: Taking taylor expansion of (pow (log 2) 2) in n
11.761 * [taylor]: Taking taylor expansion of (log 2) in n
11.761 * [taylor]: Taking taylor expansion of 2 in n
11.761 * [backup-simplify]: Simplify 2 into 2
11.761 * [backup-simplify]: Simplify (log 2) into (log 2)
11.761 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.761 * [taylor]: Taking taylor expansion of 2 in n
11.761 * [backup-simplify]: Simplify 2 into 2
11.762 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.762 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.762 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.762 * [taylor]: Taking taylor expansion of (* n PI) in n
11.762 * [taylor]: Taking taylor expansion of n in n
11.762 * [backup-simplify]: Simplify 0 into 0
11.762 * [backup-simplify]: Simplify 1 into 1
11.762 * [taylor]: Taking taylor expansion of PI in n
11.762 * [backup-simplify]: Simplify PI into PI
11.762 * [backup-simplify]: Simplify (* 0 PI) into 0
11.763 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.764 * [backup-simplify]: Simplify (sqrt 0) into 0
11.765 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.765 * [taylor]: Taking taylor expansion of (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI))))) in n
11.765 * [taylor]: Taking taylor expansion of (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) in n
11.765 * [taylor]: Taking taylor expansion of 1/4 in n
11.765 * [backup-simplify]: Simplify 1/4 into 1/4
11.765 * [taylor]: Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI))) in n
11.765 * [taylor]: Taking taylor expansion of (* (log 2) (* (sqrt 2) (log (* n PI)))) in n
11.765 * [taylor]: Taking taylor expansion of (log 2) in n
11.765 * [taylor]: Taking taylor expansion of 2 in n
11.765 * [backup-simplify]: Simplify 2 into 2
11.765 * [backup-simplify]: Simplify (log 2) into (log 2)
11.766 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n
11.766 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.766 * [taylor]: Taking taylor expansion of 2 in n
11.766 * [backup-simplify]: Simplify 2 into 2
11.766 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.767 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.767 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
11.767 * [taylor]: Taking taylor expansion of (* n PI) in n
11.767 * [taylor]: Taking taylor expansion of n in n
11.767 * [backup-simplify]: Simplify 0 into 0
11.767 * [backup-simplify]: Simplify 1 into 1
11.767 * [taylor]: Taking taylor expansion of PI in n
11.767 * [backup-simplify]: Simplify PI into PI
11.767 * [backup-simplify]: Simplify (* 0 PI) into 0
11.769 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.769 * [backup-simplify]: Simplify (log PI) into (log PI)
11.769 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.769 * [taylor]: Taking taylor expansion of (* n PI) in n
11.769 * [taylor]: Taking taylor expansion of n in n
11.770 * [backup-simplify]: Simplify 0 into 0
11.770 * [backup-simplify]: Simplify 1 into 1
11.770 * [taylor]: Taking taylor expansion of PI in n
11.770 * [backup-simplify]: Simplify PI into PI
11.770 * [backup-simplify]: Simplify (* 0 PI) into 0
11.771 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.772 * [backup-simplify]: Simplify (sqrt 0) into 0
11.773 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.773 * [taylor]: Taking taylor expansion of (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) in n
11.773 * [taylor]: Taking taylor expansion of 1/8 in n
11.773 * [backup-simplify]: Simplify 1/8 into 1/8
11.773 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI))) in n
11.773 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* n PI)) 2)) in n
11.773 * [taylor]: Taking taylor expansion of (sqrt 2) in n
11.773 * [taylor]: Taking taylor expansion of 2 in n
11.773 * [backup-simplify]: Simplify 2 into 2
11.774 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
11.775 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
11.775 * [taylor]: Taking taylor expansion of (pow (log (* n PI)) 2) in n
11.775 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
11.775 * [taylor]: Taking taylor expansion of (* n PI) in n
11.775 * [taylor]: Taking taylor expansion of n in n
11.775 * [backup-simplify]: Simplify 0 into 0
11.775 * [backup-simplify]: Simplify 1 into 1
11.775 * [taylor]: Taking taylor expansion of PI in n
11.775 * [backup-simplify]: Simplify PI into PI
11.775 * [backup-simplify]: Simplify (* 0 PI) into 0
11.777 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.777 * [backup-simplify]: Simplify (log PI) into (log PI)
11.778 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.778 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
11.778 * [taylor]: Taking taylor expansion of (* n PI) in n
11.778 * [taylor]: Taking taylor expansion of n in n
11.778 * [backup-simplify]: Simplify 0 into 0
11.778 * [backup-simplify]: Simplify 1 into 1
11.778 * [taylor]: Taking taylor expansion of PI in n
11.778 * [backup-simplify]: Simplify PI into PI
11.779 * [backup-simplify]: Simplify (* 0 PI) into 0
11.781 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.781 * [backup-simplify]: Simplify (sqrt 0) into 0
11.782 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
11.784 * [backup-simplify]: Simplify (* (log 2) (log 2)) into (pow (log 2) 2)
11.785 * [backup-simplify]: Simplify (* (pow (log 2) 2) (sqrt 2)) into (* (pow (log 2) 2) (sqrt 2))
11.786 * [backup-simplify]: Simplify (* (* (pow (log 2) 2) (sqrt 2)) 0) into 0
11.787 * [backup-simplify]: Simplify (* 1/8 0) into 0
11.788 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.789 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n)))
11.790 * [backup-simplify]: Simplify (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) into (* (log 2) (* (sqrt 2) (+ (log PI) (log n))))
11.792 * [backup-simplify]: Simplify (* (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) 0) into 0
11.792 * [backup-simplify]: Simplify (* 1/4 0) into 0
11.793 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.794 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.794 * [backup-simplify]: Simplify (* (+ (log PI) (log n)) (+ (log PI) (log n))) into (pow (+ (log PI) (log n)) 2)
11.795 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) into (* (sqrt 2) (pow (+ (log PI) (log n)) 2))
11.796 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) 0) into 0
11.797 * [backup-simplify]: Simplify (* 1/8 0) into 0
11.797 * [backup-simplify]: Simplify (+ 0 0) into 0
11.797 * [backup-simplify]: Simplify (+ 0 0) into 0
11.797 * [backup-simplify]: Simplify 0 into 0
11.799 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
11.800 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (sqrt 2))) into 0
11.804 * [backup-simplify]: Simplify (+ (* (* (log 2) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))
11.813 * [backup-simplify]: Simplify (+ (* 1/2 (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))
11.814 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.815 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
11.816 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
11.817 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log PI) (log n)))) into 0
11.819 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log PI) (log n))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))
11.825 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))
11.834 * [backup-simplify]: Simplify (+ (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))))
11.845 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))))
11.852 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))))
11.853 * [backup-simplify]: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
11.854 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
11.856 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
11.857 * [backup-simplify]: Simplify (* +nan.0 (pow PI 2)) into (* +nan.0 (pow PI 2))
11.871 * [backup-simplify]: Simplify (+ (* (* +nan.0 (pow PI 2)) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))))) (* n k)) (* (* +nan.0 PI) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (pow n 2) (pow PI 2))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* n PI)))))))))))
11.871 * [backup-simplify]: Simplify (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2)))) into (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))
11.871 * [approximate]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0
11.871 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
11.871 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in n
11.871 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in n
11.871 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in n
11.871 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.871 * [taylor]: Taking taylor expansion of 1/2 in n
11.871 * [backup-simplify]: Simplify 1/2 into 1/2
11.871 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.871 * [taylor]: Taking taylor expansion of 1/2 in n
11.871 * [backup-simplify]: Simplify 1/2 into 1/2
11.871 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.871 * [taylor]: Taking taylor expansion of k in n
11.871 * [backup-simplify]: Simplify k into k
11.871 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.871 * [taylor]: Taking taylor expansion of (log 2) in n
11.871 * [taylor]: Taking taylor expansion of 2 in n
11.871 * [backup-simplify]: Simplify 2 into 2
11.872 * [backup-simplify]: Simplify (log 2) into (log 2)
11.872 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.872 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.872 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.872 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
11.873 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
11.873 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.873 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
11.873 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
11.873 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.873 * [taylor]: Taking taylor expansion of 1/2 in n
11.873 * [backup-simplify]: Simplify 1/2 into 1/2
11.873 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.873 * [taylor]: Taking taylor expansion of 1/2 in n
11.873 * [backup-simplify]: Simplify 1/2 into 1/2
11.873 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.873 * [taylor]: Taking taylor expansion of k in n
11.873 * [backup-simplify]: Simplify k into k
11.873 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.873 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
11.873 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.873 * [taylor]: Taking taylor expansion of PI in n
11.873 * [backup-simplify]: Simplify PI into PI
11.873 * [taylor]: Taking taylor expansion of n in n
11.873 * [backup-simplify]: Simplify 0 into 0
11.873 * [backup-simplify]: Simplify 1 into 1
11.874 * [backup-simplify]: Simplify (/ PI 1) into PI
11.874 * [backup-simplify]: Simplify (log PI) into (log PI)
11.874 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.874 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.874 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.875 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.876 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
11.876 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
11.876 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in k
11.876 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k
11.876 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k
11.876 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k
11.876 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.876 * [taylor]: Taking taylor expansion of 1/2 in k
11.876 * [backup-simplify]: Simplify 1/2 into 1/2
11.876 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.876 * [taylor]: Taking taylor expansion of 1/2 in k
11.876 * [backup-simplify]: Simplify 1/2 into 1/2
11.876 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.877 * [taylor]: Taking taylor expansion of k in k
11.877 * [backup-simplify]: Simplify 0 into 0
11.877 * [backup-simplify]: Simplify 1 into 1
11.877 * [backup-simplify]: Simplify (/ 1 1) into 1
11.877 * [taylor]: Taking taylor expansion of (log 2) in k
11.877 * [taylor]: Taking taylor expansion of 2 in k
11.877 * [backup-simplify]: Simplify 2 into 2
11.877 * [backup-simplify]: Simplify (log 2) into (log 2)
11.878 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.878 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.879 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.879 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
11.880 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
11.880 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k
11.880 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k
11.880 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k
11.880 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.880 * [taylor]: Taking taylor expansion of 1/2 in k
11.880 * [backup-simplify]: Simplify 1/2 into 1/2
11.880 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.880 * [taylor]: Taking taylor expansion of 1/2 in k
11.880 * [backup-simplify]: Simplify 1/2 into 1/2
11.880 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.880 * [taylor]: Taking taylor expansion of k in k
11.880 * [backup-simplify]: Simplify 0 into 0
11.880 * [backup-simplify]: Simplify 1 into 1
11.880 * [backup-simplify]: Simplify (/ 1 1) into 1
11.881 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k
11.881 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.881 * [taylor]: Taking taylor expansion of PI in k
11.881 * [backup-simplify]: Simplify PI into PI
11.881 * [taylor]: Taking taylor expansion of n in k
11.881 * [backup-simplify]: Simplify n into n
11.881 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.881 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n))
11.881 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.882 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.882 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.882 * [backup-simplify]: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
11.882 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))
11.882 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in k
11.882 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k
11.882 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k
11.882 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k
11.882 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.882 * [taylor]: Taking taylor expansion of 1/2 in k
11.882 * [backup-simplify]: Simplify 1/2 into 1/2
11.882 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.882 * [taylor]: Taking taylor expansion of 1/2 in k
11.882 * [backup-simplify]: Simplify 1/2 into 1/2
11.882 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.882 * [taylor]: Taking taylor expansion of k in k
11.883 * [backup-simplify]: Simplify 0 into 0
11.883 * [backup-simplify]: Simplify 1 into 1
11.883 * [backup-simplify]: Simplify (/ 1 1) into 1
11.883 * [taylor]: Taking taylor expansion of (log 2) in k
11.883 * [taylor]: Taking taylor expansion of 2 in k
11.883 * [backup-simplify]: Simplify 2 into 2
11.883 * [backup-simplify]: Simplify (log 2) into (log 2)
11.884 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.884 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.884 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.885 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
11.886 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
11.886 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k
11.886 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k
11.886 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k
11.886 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.886 * [taylor]: Taking taylor expansion of 1/2 in k
11.886 * [backup-simplify]: Simplify 1/2 into 1/2
11.886 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.886 * [taylor]: Taking taylor expansion of 1/2 in k
11.886 * [backup-simplify]: Simplify 1/2 into 1/2
11.886 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.886 * [taylor]: Taking taylor expansion of k in k
11.886 * [backup-simplify]: Simplify 0 into 0
11.886 * [backup-simplify]: Simplify 1 into 1
11.886 * [backup-simplify]: Simplify (/ 1 1) into 1
11.887 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k
11.887 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.887 * [taylor]: Taking taylor expansion of PI in k
11.887 * [backup-simplify]: Simplify PI into PI
11.887 * [taylor]: Taking taylor expansion of n in k
11.887 * [backup-simplify]: Simplify n into n
11.887 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.887 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n))
11.887 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.888 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.888 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.888 * [backup-simplify]: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
11.888 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))
11.889 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))
11.889 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
11.889 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
11.889 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.889 * [taylor]: Taking taylor expansion of (log 2) in n
11.889 * [taylor]: Taking taylor expansion of 2 in n
11.890 * [backup-simplify]: Simplify 2 into 2
11.890 * [backup-simplify]: Simplify (log 2) into (log 2)
11.890 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.890 * [taylor]: Taking taylor expansion of 1/2 in n
11.890 * [backup-simplify]: Simplify 1/2 into 1/2
11.890 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.890 * [taylor]: Taking taylor expansion of 1/2 in n
11.890 * [backup-simplify]: Simplify 1/2 into 1/2
11.890 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.890 * [taylor]: Taking taylor expansion of k in n
11.890 * [backup-simplify]: Simplify k into k
11.890 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.890 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.890 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.891 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.891 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
11.892 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
11.892 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.892 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
11.892 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
11.892 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.892 * [taylor]: Taking taylor expansion of 1/2 in n
11.892 * [backup-simplify]: Simplify 1/2 into 1/2
11.892 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.892 * [taylor]: Taking taylor expansion of 1/2 in n
11.892 * [backup-simplify]: Simplify 1/2 into 1/2
11.892 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.892 * [taylor]: Taking taylor expansion of k in n
11.892 * [backup-simplify]: Simplify k into k
11.892 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.892 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
11.892 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.892 * [taylor]: Taking taylor expansion of PI in n
11.892 * [backup-simplify]: Simplify PI into PI
11.892 * [taylor]: Taking taylor expansion of n in n
11.892 * [backup-simplify]: Simplify 0 into 0
11.892 * [backup-simplify]: Simplify 1 into 1
11.893 * [backup-simplify]: Simplify (/ PI 1) into PI
11.893 * [backup-simplify]: Simplify (log PI) into (log PI)
11.893 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.893 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.893 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.894 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.895 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
11.895 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
11.897 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))
11.898 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))
11.898 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0
11.899 * [taylor]: Taking taylor expansion of 0 in n
11.899 * [backup-simplify]: Simplify 0 into 0
11.899 * [backup-simplify]: Simplify 0 into 0
11.900 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.901 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
11.902 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.902 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.902 * [backup-simplify]: Simplify (- 0) into 0
11.903 * [backup-simplify]: Simplify (+ 0 0) into 0
11.904 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.904 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0
11.906 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.906 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.906 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.907 * [backup-simplify]: Simplify (- 0) into 0
11.907 * [backup-simplify]: Simplify (+ 0 0) into 0
11.909 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
11.909 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
11.911 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.912 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into 0
11.912 * [backup-simplify]: Simplify 0 into 0
11.913 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0
11.913 * [taylor]: Taking taylor expansion of 0 in n
11.913 * [backup-simplify]: Simplify 0 into 0
11.913 * [backup-simplify]: Simplify 0 into 0
11.913 * [backup-simplify]: Simplify 0 into 0
11.914 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.917 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
11.918 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.918 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.919 * [backup-simplify]: Simplify (- 0) into 0
11.919 * [backup-simplify]: Simplify (+ 0 0) into 0
11.920 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
11.921 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0
11.923 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.923 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.924 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.925 * [backup-simplify]: Simplify (- 0) into 0
11.925 * [backup-simplify]: Simplify (+ 0 0) into 0
11.926 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
11.927 * [backup-simplify]: Simplify (+ (* (log 2) 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
11.928 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.929 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
11.929 * [backup-simplify]: Simplify 0 into 0
11.930 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
11.930 * [taylor]: Taking taylor expansion of 0 in n
11.930 * [backup-simplify]: Simplify 0 into 0
11.930 * [backup-simplify]: Simplify 0 into 0
11.931 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))) into (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))
11.931 * [backup-simplify]: Simplify (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2)))) into (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)))
11.931 * [approximate]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0
11.931 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
11.931 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.931 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
11.931 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
11.931 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.931 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.931 * [taylor]: Taking taylor expansion of 1/2 in n
11.931 * [backup-simplify]: Simplify 1/2 into 1/2
11.931 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.931 * [taylor]: Taking taylor expansion of k in n
11.931 * [backup-simplify]: Simplify k into k
11.931 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.931 * [taylor]: Taking taylor expansion of 1/2 in n
11.931 * [backup-simplify]: Simplify 1/2 into 1/2
11.931 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
11.931 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
11.931 * [taylor]: Taking taylor expansion of -1 in n
11.931 * [backup-simplify]: Simplify -1 into -1
11.931 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.931 * [taylor]: Taking taylor expansion of PI in n
11.931 * [backup-simplify]: Simplify PI into PI
11.931 * [taylor]: Taking taylor expansion of n in n
11.931 * [backup-simplify]: Simplify 0 into 0
11.931 * [backup-simplify]: Simplify 1 into 1
11.932 * [backup-simplify]: Simplify (/ PI 1) into PI
11.932 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
11.932 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
11.933 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.933 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.933 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.934 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
11.935 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
11.935 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.935 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in n
11.935 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in n
11.935 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.935 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.935 * [taylor]: Taking taylor expansion of 1/2 in n
11.935 * [backup-simplify]: Simplify 1/2 into 1/2
11.935 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.935 * [taylor]: Taking taylor expansion of k in n
11.935 * [backup-simplify]: Simplify k into k
11.935 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.935 * [taylor]: Taking taylor expansion of 1/2 in n
11.935 * [backup-simplify]: Simplify 1/2 into 1/2
11.935 * [taylor]: Taking taylor expansion of (log 2) in n
11.935 * [taylor]: Taking taylor expansion of 2 in n
11.935 * [backup-simplify]: Simplify 2 into 2
11.936 * [backup-simplify]: Simplify (log 2) into (log 2)
11.936 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.936 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.936 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
11.936 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
11.936 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
11.936 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.936 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k
11.936 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k
11.936 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.936 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.936 * [taylor]: Taking taylor expansion of 1/2 in k
11.936 * [backup-simplify]: Simplify 1/2 into 1/2
11.936 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.936 * [taylor]: Taking taylor expansion of k in k
11.936 * [backup-simplify]: Simplify 0 into 0
11.936 * [backup-simplify]: Simplify 1 into 1
11.937 * [backup-simplify]: Simplify (/ 1 1) into 1
11.937 * [taylor]: Taking taylor expansion of 1/2 in k
11.937 * [backup-simplify]: Simplify 1/2 into 1/2
11.937 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k
11.937 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k
11.937 * [taylor]: Taking taylor expansion of -1 in k
11.937 * [backup-simplify]: Simplify -1 into -1
11.937 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.937 * [taylor]: Taking taylor expansion of PI in k
11.937 * [backup-simplify]: Simplify PI into PI
11.937 * [taylor]: Taking taylor expansion of n in k
11.937 * [backup-simplify]: Simplify n into n
11.937 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.937 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n))
11.937 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n)))
11.937 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.938 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.938 * [backup-simplify]: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
11.938 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
11.938 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.938 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k
11.938 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k
11.938 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.938 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.938 * [taylor]: Taking taylor expansion of 1/2 in k
11.938 * [backup-simplify]: Simplify 1/2 into 1/2
11.938 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.938 * [taylor]: Taking taylor expansion of k in k
11.938 * [backup-simplify]: Simplify 0 into 0
11.938 * [backup-simplify]: Simplify 1 into 1
11.938 * [backup-simplify]: Simplify (/ 1 1) into 1
11.938 * [taylor]: Taking taylor expansion of 1/2 in k
11.938 * [backup-simplify]: Simplify 1/2 into 1/2
11.938 * [taylor]: Taking taylor expansion of (log 2) in k
11.938 * [taylor]: Taking taylor expansion of 2 in k
11.938 * [backup-simplify]: Simplify 2 into 2
11.939 * [backup-simplify]: Simplify (log 2) into (log 2)
11.939 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.939 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.940 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
11.940 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
11.940 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
11.940 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.940 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k
11.940 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k
11.940 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.940 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.940 * [taylor]: Taking taylor expansion of 1/2 in k
11.940 * [backup-simplify]: Simplify 1/2 into 1/2
11.940 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.940 * [taylor]: Taking taylor expansion of k in k
11.940 * [backup-simplify]: Simplify 0 into 0
11.940 * [backup-simplify]: Simplify 1 into 1
11.940 * [backup-simplify]: Simplify (/ 1 1) into 1
11.940 * [taylor]: Taking taylor expansion of 1/2 in k
11.940 * [backup-simplify]: Simplify 1/2 into 1/2
11.941 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k
11.941 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k
11.941 * [taylor]: Taking taylor expansion of -1 in k
11.941 * [backup-simplify]: Simplify -1 into -1
11.941 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.941 * [taylor]: Taking taylor expansion of PI in k
11.941 * [backup-simplify]: Simplify PI into PI
11.941 * [taylor]: Taking taylor expansion of n in k
11.941 * [backup-simplify]: Simplify n into n
11.941 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.941 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n))
11.941 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n)))
11.941 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.941 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.941 * [backup-simplify]: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
11.941 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
11.942 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.942 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k
11.942 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k
11.942 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.942 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.942 * [taylor]: Taking taylor expansion of 1/2 in k
11.942 * [backup-simplify]: Simplify 1/2 into 1/2
11.942 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.942 * [taylor]: Taking taylor expansion of k in k
11.942 * [backup-simplify]: Simplify 0 into 0
11.942 * [backup-simplify]: Simplify 1 into 1
11.942 * [backup-simplify]: Simplify (/ 1 1) into 1
11.942 * [taylor]: Taking taylor expansion of 1/2 in k
11.942 * [backup-simplify]: Simplify 1/2 into 1/2
11.942 * [taylor]: Taking taylor expansion of (log 2) in k
11.942 * [taylor]: Taking taylor expansion of 2 in k
11.942 * [backup-simplify]: Simplify 2 into 2
11.942 * [backup-simplify]: Simplify (log 2) into (log 2)
11.943 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.943 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.943 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
11.944 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
11.944 * [backup-simplify]: Simplify (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))
11.944 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
11.944 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.944 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
11.944 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
11.944 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.944 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.944 * [taylor]: Taking taylor expansion of 1/2 in n
11.944 * [backup-simplify]: Simplify 1/2 into 1/2
11.944 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.944 * [taylor]: Taking taylor expansion of k in n
11.944 * [backup-simplify]: Simplify k into k
11.944 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.944 * [taylor]: Taking taylor expansion of 1/2 in n
11.944 * [backup-simplify]: Simplify 1/2 into 1/2
11.944 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
11.944 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
11.944 * [taylor]: Taking taylor expansion of -1 in n
11.945 * [backup-simplify]: Simplify -1 into -1
11.945 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.945 * [taylor]: Taking taylor expansion of PI in n
11.945 * [backup-simplify]: Simplify PI into PI
11.945 * [taylor]: Taking taylor expansion of n in n
11.945 * [backup-simplify]: Simplify 0 into 0
11.945 * [backup-simplify]: Simplify 1 into 1
11.945 * [backup-simplify]: Simplify (/ PI 1) into PI
11.945 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
11.946 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
11.946 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.946 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.947 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.948 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
11.948 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
11.949 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
11.949 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.949 * [taylor]: Taking taylor expansion of (log 2) in n
11.949 * [taylor]: Taking taylor expansion of 2 in n
11.949 * [backup-simplify]: Simplify 2 into 2
11.949 * [backup-simplify]: Simplify (log 2) into (log 2)
11.949 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.949 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.949 * [taylor]: Taking taylor expansion of 1/2 in n
11.949 * [backup-simplify]: Simplify 1/2 into 1/2
11.949 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.949 * [taylor]: Taking taylor expansion of k in n
11.949 * [backup-simplify]: Simplify k into k
11.950 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.950 * [taylor]: Taking taylor expansion of 1/2 in n
11.950 * [backup-simplify]: Simplify 1/2 into 1/2
11.950 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.950 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.950 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
11.951 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
11.952 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
11.954 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
11.955 * [backup-simplify]: Simplify (+ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
11.955 * [taylor]: Taking taylor expansion of 0 in n
11.955 * [backup-simplify]: Simplify 0 into 0
11.955 * [backup-simplify]: Simplify 0 into 0
11.955 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.956 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.956 * [backup-simplify]: Simplify (+ 0 0) into 0
11.958 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
11.958 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
11.960 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0
11.961 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.961 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0
11.963 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0
11.963 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.964 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.964 * [backup-simplify]: Simplify (+ 0 0) into 0
11.966 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.967 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0
11.969 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
11.971 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
11.971 * [backup-simplify]: Simplify 0 into 0
11.972 * [backup-simplify]: Simplify (+ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0
11.972 * [taylor]: Taking taylor expansion of 0 in n
11.972 * [backup-simplify]: Simplify 0 into 0
11.972 * [backup-simplify]: Simplify 0 into 0
11.972 * [backup-simplify]: Simplify 0 into 0
11.972 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.973 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.973 * [backup-simplify]: Simplify (+ 0 0) into 0
11.976 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
11.978 * [backup-simplify]: Simplify (+ (* (log 2) 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
11.979 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.980 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.981 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0
11.985 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0
11.985 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.986 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.986 * [backup-simplify]: Simplify (+ 0 0) into 0
11.988 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
11.989 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0
11.992 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.000 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 0) (+ (* 0 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0
12.001 * [backup-simplify]: Simplify 0 into 0
12.002 * [backup-simplify]: Simplify (+ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))))) into 0
12.002 * [taylor]: Taking taylor expansion of 0 in n
12.002 * [backup-simplify]: Simplify 0 into 0
12.002 * [backup-simplify]: Simplify 0 into 0
12.004 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))) into (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))
12.004 * * * [progress]: simplifying candidates
12.004 * * * * [progress]: [ 1 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (exp (* (+ (log n) (log PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
12.004 * * * * [progress]: [ 2 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (exp (* (log (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
12.005 * * * * [progress]: [ 3 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (exp (* (log (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
12.005 * * * * [progress]: [ 4 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (* 1 (- 1/2 (/ k 2))))) (sqrt k)))>
12.005 * * * * [progress]: [ 5 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (* 1 (- 1/2 (/ k 2))))) (sqrt k)))>
12.005 * * * * [progress]: [ 6 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (pow (* n PI) (/ k 2)))) (sqrt k)))>
12.005 * * * * [progress]: [ 7 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (pow (* n PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))) (sqrt k)))>
12.005 * * * * [progress]: [ 8 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (pow (* n PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))) (sqrt k)))>
12.005 * * * * [progress]: [ 9 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (pow (* n PI) 1) (- 1/2 (/ k 2)))) (sqrt k)))>
12.005 * * * * [progress]: [ 10 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (pow (* n PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2))))) (sqrt k)))>
12.005 * * * * [progress]: [ 11 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (pow (* n PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))))) (sqrt k)))>
12.005 * * * * [progress]: [ 12 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (pow (* n PI) 1) (- 1/2 (/ k 2)))) (sqrt k)))>
12.005 * * * * [progress]: [ 13 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow (* n PI) 1/2) (pow (* n PI) (- (/ k 2))))) (sqrt k)))>
12.005 * * * * [progress]: [ 14 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow (* n PI) 1/2) (pow (* n PI) (- (/ k 2))))) (sqrt k)))>
12.005 * * * * [progress]: [ 15 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))) (sqrt k)))>
12.005 * * * * [progress]: [ 16 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (pow (* n PI) (- 1/2 (/ k 2))) 1)) (sqrt k)))>
12.006 * * * * [progress]: [ 17 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (exp (log (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.006 * * * * [progress]: [ 18 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (log (exp (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.006 * * * * [progress]: [ 19 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (cbrt (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.006 * * * * [progress]: [ 20 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (cbrt (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.006 * * * * [progress]: [ 21 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.006 * * * * [progress]: [ 22 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* 1 (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.006 * * * * [progress]: [ 23 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
12.006 * * * * [progress]: [ 24 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (posit16->real (real->posit16 (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.006 * * * * [progress]: [ 25 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (pow (* n PI) 1) (- 1/2 (/ k 2)))) (sqrt k)))>
12.006 * * * * [progress]: [ 26 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (pow (* n PI) 1) (- 1/2 (/ k 2)))) (sqrt k)))>
12.006 * * * * [progress]: [ 27 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (exp (+ (log n) (log PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
12.006 * * * * [progress]: [ 28 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (exp (log (* n PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
12.006 * * * * [progress]: [ 29 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (log (exp (* n PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
12.006 * * * * [progress]: [ 30 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (cbrt (* (* (* n n) n) (* (* PI PI) PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
12.006 * * * * [progress]: [ 31 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
12.006 * * * * [progress]: [ 32 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (cbrt (* (* (* n PI) (* n PI)) (* n PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
12.007 * * * * [progress]: [ 33 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* (sqrt (* n PI)) (sqrt (* n PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
12.007 * * * * [progress]: [ 34 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* 1 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
12.007 * * * * [progress]: [ 35 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
12.007 * * * * [progress]: [ 36 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* (* n (* (cbrt PI) (cbrt PI))) (cbrt PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
12.007 * * * * [progress]: [ 37 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* (* n (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
12.007 * * * * [progress]: [ 38 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* (* n 1) PI) (- 1/2 (/ k 2)))) (sqrt k)))>
12.007 * * * * [progress]: [ 39 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
12.007 * * * * [progress]: [ 40 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* (sqrt n) (* (sqrt n) PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
12.007 * * * * [progress]: [ 41 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* 1 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
12.007 * * * * [progress]: [ 42 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (posit16->real (real->posit16 (* n PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
12.007 * * * * [progress]: [ 43 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2)))) (sqrt k)))>
12.007 * * * * [progress]: [ 44 / 145 ] simplifiying candidate #<alt (λ (k n) (pow (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1))>
12.007 * * * * [progress]: [ 45 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (+ (* (log 2) (- 1/2 (/ k 2))) (* (+ (log n) (log PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
12.007 * * * * [progress]: [ 46 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
12.007 * * * * [progress]: [ 47 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
12.008 * * * * [progress]: [ 48 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (+ (* (log 2) (- 1/2 (/ k 2))) (log (pow (* n PI) (- 1/2 (/ k 2))))) (log (sqrt k)))))>
12.008 * * * * [progress]: [ 49 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (+ (* (log 2) (- 1/2 (/ k 2))) (* (+ (log n) (log PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
12.008 * * * * [progress]: [ 50 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
12.008 * * * * [progress]: [ 51 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
12.008 * * * * [progress]: [ 52 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (+ (* (log 2) (- 1/2 (/ k 2))) (log (pow (* n PI) (- 1/2 (/ k 2))))) (log (sqrt k)))))>
12.008 * * * * [progress]: [ 53 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (+ (log (pow 2 (- 1/2 (/ k 2)))) (* (+ (log n) (log PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
12.008 * * * * [progress]: [ 54 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (+ (log (pow 2 (- 1/2 (/ k 2)))) (* (log (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
12.008 * * * * [progress]: [ 55 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (+ (log (pow 2 (- 1/2 (/ k 2)))) (* (log (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
12.008 * * * * [progress]: [ 56 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (+ (log (pow 2 (- 1/2 (/ k 2)))) (log (pow (* n PI) (- 1/2 (/ k 2))))) (log (sqrt k)))))>
12.008 * * * * [progress]: [ 57 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (log (sqrt k)))))>
12.008 * * * * [progress]: [ 58 / 145 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.008 * * * * [progress]: [ 59 / 145 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.008 * * * * [progress]: [ 60 / 145 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
12.008 * * * * [progress]: [ 61 / 145 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
12.008 * * * * [progress]: [ 62 / 145 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))) (cbrt (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))) (cbrt (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.008 * * * * [progress]: [ 63 / 145 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.008 * * * * [progress]: [ 64 / 145 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.009 * * * * [progress]: [ 65 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (- (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (- (sqrt k))))>
12.009 * * * * [progress]: [ 66 / 145 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
12.009 * * * * [progress]: [ 67 / 145 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
12.009 * * * * [progress]: [ 68 / 145 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
12.009 * * * * [progress]: [ 69 / 145 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
12.009 * * * * [progress]: [ 70 / 145 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
12.009 * * * * [progress]: [ 71 / 145 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
12.009 * * * * [progress]: [ 72 / 145 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))>
12.009 * * * * [progress]: [ 73 / 145 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (/ 1 (sqrt k))))>
12.009 * * * * [progress]: [ 74 / 145 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))))>
12.009 * * * * [progress]: [ 75 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
12.009 * * * * [progress]: [ 76 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
12.009 * * * * [progress]: [ 77 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
12.009 * * * * [progress]: [ 78 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt 1)) (sqrt k)))>
12.009 * * * * [progress]: [ 79 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
12.009 * * * * [progress]: [ 80 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) 1) (sqrt k)))>
12.009 * * * * [progress]: [ 81 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (pow 2 (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2))))))>
12.009 * * * * [progress]: [ 82 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 1/2) (pow (* n PI) 1/2)) (* (sqrt k) (* (pow 2 (/ k 2)) (pow (* n PI) (/ k 2))))))>
12.009 * * * * [progress]: [ 83 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) 1/2)) (* (sqrt k) (pow (* n PI) (/ k 2)))))>
12.009 * * * * [progress]: [ 84 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 1/2) (pow (* n PI) (- 1/2 (/ k 2)))) (* (sqrt k) (pow 2 (/ k 2)))))>
12.009 * * * * [progress]: [ 85 / 145 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.009 * * * * [progress]: [ 86 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
12.009 * * * * [progress]: [ 87 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) 1) (sqrt k)))>
12.009 * * * * [progress]: [ 88 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log 2) (- 1/2 (/ k 2))) (* (+ (log n) (log PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
12.010 * * * * [progress]: [ 89 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
12.010 * * * * [progress]: [ 90 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
12.010 * * * * [progress]: [ 91 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log 2) (- 1/2 (/ k 2))) (log (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.010 * * * * [progress]: [ 92 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log 2) (- 1/2 (/ k 2))) (* (+ (log n) (log PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
12.010 * * * * [progress]: [ 93 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
12.010 * * * * [progress]: [ 94 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
12.010 * * * * [progress]: [ 95 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log 2) (- 1/2 (/ k 2))) (log (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.010 * * * * [progress]: [ 96 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (* (+ (log n) (log PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
12.010 * * * * [progress]: [ 97 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (* (log (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
12.010 * * * * [progress]: [ 98 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (* (log (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
12.010 * * * * [progress]: [ 99 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (log (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.010 * * * * [progress]: [ 100 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.010 * * * * [progress]: [ 101 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.010 * * * * [progress]: [ 102 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.010 * * * * [progress]: [ 103 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (cbrt (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))) (cbrt (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.010 * * * * [progress]: [ 104 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.010 * * * * [progress]: [ 105 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.010 * * * * [progress]: [ 106 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow 2 1/2) (pow (* n PI) 1/2)) (* (pow 2 (/ k 2)) (pow (* n PI) (/ k 2)))) (sqrt k)))>
12.010 * * * * [progress]: [ 107 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.010 * * * * [progress]: [ 108 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.010 * * * * [progress]: [ 109 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (sqrt 2) (- 1/2 (/ k 2))) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2))) (* (pow (sqrt 2) (- 1/2 (/ k 2))) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
12.010 * * * * [progress]: [ 110 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.010 * * * * [progress]: [ 111 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2))) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
12.010 * * * * [progress]: [ 112 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.010 * * * * [progress]: [ 113 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow 2 (/ (- 1/2 (/ k 2)) 2)) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2))) (* (pow 2 (/ (- 1/2 (/ k 2)) 2)) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k)))>
12.011 * * * * [progress]: [ 114 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) 1/2)) (pow (* n PI) (- (/ k 2)))) (sqrt k)))>
12.011 * * * * [progress]: [ 115 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) 1/2)) (pow (* n PI) (- (/ k 2)))) (sqrt k)))>
12.011 * * * * [progress]: [ 116 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow 2 (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (sqrt k)))>
12.011 * * * * [progress]: [ 117 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow 2 (- 1/2 (/ k 2))) (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2)))))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.011 * * * * [progress]: [ 118 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow 2 (- 1/2 (/ k 2))) (sqrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.011 * * * * [progress]: [ 119 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow 2 (- 1/2 (/ k 2))) 1) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>
12.011 * * * * [progress]: [ 120 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2))) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
12.011 * * * * [progress]: [ 121 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 1/2) (* (pow 2 (- (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.011 * * * * [progress]: [ 122 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 1/2) (* (pow 2 (- (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.011 * * * * [progress]: [ 123 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (cbrt 2) (cbrt 2)) (- 1/2 (/ k 2))) (* (pow (cbrt 2) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.011 * * * * [progress]: [ 124 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (sqrt 2) (- 1/2 (/ k 2))) (* (pow (sqrt 2) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.011 * * * * [progress]: [ 125 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 1 (- 1/2 (/ k 2))) (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.011 * * * * [progress]: [ 126 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.011 * * * * [progress]: [ 127 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.011 * * * * [progress]: [ 128 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.011 * * * * [progress]: [ 129 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (/ (- 1/2 (/ k 2)) 2)) (* (pow 2 (/ (- 1/2 (/ k 2)) 2)) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))>
12.011 * * * * [progress]: [ 130 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) 1/2)) (pow (* n PI) (/ k 2))) (sqrt k)))>
12.011 * * * * [progress]: [ 131 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow 2 1/2) (pow (* n PI) (- 1/2 (/ k 2)))) (pow 2 (/ k 2))) (sqrt k)))>
12.011 * * * * [progress]: [ 132 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))) (sqrt k)))>
12.011 * * * * [progress]: [ 133 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k)))>
12.011 * * * * [progress]: [ 134 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k)))))) (sqrt k)))>
12.011 * * * * [progress]: [ 135 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n)))))) (sqrt k)))>
12.011 * * * * [progress]: [ 136 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))) (sqrt k)))>
12.012 * * * * [progress]: [ 137 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>
12.012 * * * * [progress]: [ 138 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>
12.012 * * * * [progress]: [ 139 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>
12.012 * * * * [progress]: [ 140 / 145 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))))>
12.012 * * * * [progress]: [ 141 / 145 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 3)))))))))>
12.012 * * * * [progress]: [ 142 / 145 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))))))))))>
12.012 * * * * [progress]: [ 143 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (pow n 2) (pow PI 2))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* n PI))))))))))) (sqrt k)))>
12.012 * * * * [progress]: [ 144 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (sqrt k)))>
12.012 * * * * [progress]: [ 145 / 145 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (sqrt k)))>
12.013 * [simplify]: Simplifying:
  (* (+ (log n) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* n PI)) (- 1/2 (/ k 2)))
  (* (log (* n PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n PI) 1/2)
  (pow (* n PI) (/ k 2))
  (pow (* n PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* n PI) 1)
  (pow (* n PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n PI) 1)
  (pow (* n PI) 1/2)
  (pow (* n PI) (- (/ k 2)))
  (pow (* n PI) 1/2)
  (pow (* n PI) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* n PI) (- 1/2 (/ k 2))))
  (exp (pow (* n PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n PI) (- 1/2 (/ k 2))))
  (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* n PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* n PI) (- 1/2 (/ k 2))))
  (pow (* n PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n PI) (- 1/2 (/ k 2))))
  (* n PI)
  (+ (log n) (log PI))
  (log (* n PI))
  (exp (* n PI))
  (* (* (* n n) n) (* (* PI PI) PI))
  (* (cbrt (* n PI)) (cbrt (* n PI)))
  (cbrt (* n PI))
  (* (* (* n PI) (* n PI)) (* n PI))
  (sqrt (* n PI))
  (sqrt (* n PI))
  (* (sqrt n) (sqrt PI))
  (* (sqrt n) (sqrt PI))
  (* n (* (cbrt PI) (cbrt PI)))
  (* n (sqrt PI))
  (* n 1)
  (* (cbrt n) PI)
  (* (sqrt n) PI)
  (* n PI)
  (real->posit16 (* n PI))
  (- (+ (* (log 2) (- 1/2 (/ k 2))) (* (+ (log n) (log PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (- (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (- (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (- (+ (* (log 2) (- 1/2 (/ k 2))) (log (pow (* n PI) (- 1/2 (/ k 2))))) (log (sqrt k)))
  (- (+ (* (log 2) (- 1/2 (/ k 2))) (* (+ (log n) (log PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (- (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (- (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (- (+ (* (log 2) (- 1/2 (/ k 2))) (log (pow (* n PI) (- 1/2 (/ k 2))))) (log (sqrt k)))
  (- (+ (log (pow 2 (- 1/2 (/ k 2)))) (* (+ (log n) (log PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (- (+ (log (pow 2 (- 1/2 (/ k 2)))) (* (log (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (- (+ (log (pow 2 (- 1/2 (/ k 2)))) (* (log (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (- (+ (log (pow 2 (- 1/2 (/ k 2)))) (log (pow (* n PI) (- 1/2 (/ k 2))))) (log (sqrt k)))
  (- (log (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (log (sqrt k)))
  (log (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))
  (exp (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))
  (/ (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (/ (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))) (cbrt (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))
  (cbrt (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))
  (* (* (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))
  (sqrt (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))
  (sqrt (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))
  (- (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))
  (- (sqrt k))
  (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow 2 (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow 2 (- 1/2 (/ k 2))) 1)
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))
  (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt 1))
  (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) 1)
  (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2))))
  (* (sqrt k) (* (pow 2 (/ k 2)) (pow (* n PI) (/ k 2))))
  (* (sqrt k) (pow (* n PI) (/ k 2)))
  (* (sqrt k) (pow 2 (/ k 2)))
  (real->posit16 (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))
  (* 2 (* n PI))
  (+ (* (log 2) (- 1/2 (/ k 2))) (* (+ (log n) (log PI)) (- 1/2 (/ k 2))))
  (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2))))
  (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2))))
  (+ (* (log 2) (- 1/2 (/ k 2))) (log (pow (* n PI) (- 1/2 (/ k 2)))))
  (+ (* (log 2) (- 1/2 (/ k 2))) (* (+ (log n) (log PI)) (- 1/2 (/ k 2))))
  (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2))))
  (+ (* (log 2) (- 1/2 (/ k 2))) (* (log (* n PI)) (- 1/2 (/ k 2))))
  (+ (* (log 2) (- 1/2 (/ k 2))) (log (pow (* n PI) (- 1/2 (/ k 2)))))
  (+ (log (pow 2 (- 1/2 (/ k 2)))) (* (+ (log n) (log PI)) (- 1/2 (/ k 2))))
  (+ (log (pow 2 (- 1/2 (/ k 2)))) (* (log (* n PI)) (- 1/2 (/ k 2))))
  (+ (log (pow 2 (- 1/2 (/ k 2)))) (* (log (* n PI)) (- 1/2 (/ k 2))))
  (+ (log (pow 2 (- 1/2 (/ k 2)))) (log (pow (* n PI) (- 1/2 (/ k 2)))))
  (log (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))
  (exp (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))
  (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))))
  (* (cbrt (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (cbrt (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))))
  (cbrt (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))
  (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))
  (sqrt (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))
  (sqrt (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))
  (* (pow 2 1/2) (pow (* n PI) 1/2))
  (* (pow 2 (/ k 2)) (pow (* n PI) (/ k 2)))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))
  (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))
  (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))
  (* (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))
  (* (pow 2 (/ (- 1/2 (/ k 2)) 2)) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (pow 2 (/ (- 1/2 (/ k 2)) 2)) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) 1/2))
  (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) 1/2))
  (* (pow 2 (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))
  (* (pow 2 (- 1/2 (/ k 2))) (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))))
  (* (pow 2 (- 1/2 (/ k 2))) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))
  (* (pow 2 (- 1/2 (/ k 2))) 1)
  (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (pow 2 (- (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))
  (* (pow 2 (- (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))
  (* (pow (cbrt 2) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))
  (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2))))
  (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2))))
  (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))
  (* (pow 2 (/ (- 1/2 (/ k 2)) 2)) (pow (* n PI) (- 1/2 (/ k 2))))
  (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) 1/2))
  (* (pow 2 1/2) (pow (* n PI) (- 1/2 (/ k 2))))
  (real->posit16 (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))
  (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n)))))
  (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))
  (* n PI)
  (* n PI)
  (* n PI)
  (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))))
  (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))))))))
  (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (pow n 2) (pow PI 2))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* n PI)))))))))))
  (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))
  (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))
12.016 * * [simplify]: iteration 0: 290 enodes
12.102 * * [simplify]: iteration 1: 814 enodes
12.518 * * [simplify]: iteration 2: 2935 enodes
13.794 * * [simplify]: iteration complete: 5000 enodes
13.794 * * [simplify]: Extracting #0: cost 95 inf + 0
13.797 * * [simplify]: Extracting #1: cost 734 inf + 1
13.804 * * [simplify]: Extracting #2: cost 1257 inf + 3135
13.830 * * [simplify]: Extracting #3: cost 1384 inf + 84033
13.912 * * [simplify]: Extracting #4: cost 904 inf + 298383
14.042 * * [simplify]: Extracting #5: cost 279 inf + 577013
14.202 * * [simplify]: Extracting #6: cost 67 inf + 683393
14.337 * * [simplify]: Extracting #7: cost 5 inf + 710542
14.487 * * [simplify]: Extracting #8: cost 0 inf + 711367
14.628 * [simplify]: Simplified to:
  (* (log (* n PI)) (- 1/2 (* k 1/2)))
  (* (log (* n PI)) (- 1/2 (* k 1/2)))
  (* (log (* n PI)) (- 1/2 (* k 1/2)))
  (- 1/2 (* k 1/2))
  (- 1/2 (* k 1/2))
  (sqrt (* n PI))
  (pow (* n PI) (/ k 2))
  (pow (* n PI) (* (cbrt (- 1/2 (* k 1/2))) (cbrt (- 1/2 (* k 1/2)))))
  (pow (* n PI) (sqrt (- 1/2 (* k 1/2))))
  (* n PI)
  (pow (* n PI) (+ (sqrt (/ k 2)) (sqrt 1/2)))
  (pow (* n PI) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* n PI)
  (sqrt (* n PI))
  (pow (* n PI) (* k -1/2))
  (sqrt (* n PI))
  (pow (* n PI) (* k -1/2))
  (pow n (- 1/2 (* k 1/2)))
  (pow PI (- 1/2 (* k 1/2)))
  (* (log (* n PI)) (- 1/2 (* k 1/2)))
  (exp (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))))
  (* (cbrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))) (cbrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))))
  (cbrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))))
  (* (* (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))) (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))) (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))))
  (sqrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))))
  (sqrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))))
  (pow (* n PI) (- 1/4 (/ k 4)))
  (pow (* n PI) (- 1/4 (/ k 4)))
  (real->posit16 (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))))
  (* n PI)
  (log (* n PI))
  (log (* n PI))
  (exp (* n PI))
  (* (* n PI) (* (* n PI) (* n PI)))
  (* (cbrt (* n PI)) (cbrt (* n PI)))
  (cbrt (* n PI))
  (* (* n PI) (* (* n PI) (* n PI)))
  (sqrt (* n PI))
  (sqrt (* n PI))
  (* (sqrt PI) (sqrt n))
  (* (sqrt PI) (sqrt n))
  (* (* n (cbrt PI)) (cbrt PI))
  (* (sqrt PI) n)
  n
  (* PI (cbrt n))
  (* PI (sqrt n))
  (* n PI)
  (real->posit16 (* n PI))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (- (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
  (exp (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (sqrt k)))
  (/ (* (* (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))) (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))) (* (sqrt k) k))
  (/ (* (* (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))) (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))) (* (sqrt k) k))
  (* (cbrt (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (sqrt k))) (cbrt (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (sqrt k))))
  (cbrt (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (sqrt k)))
  (* (* (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (sqrt k)) (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (sqrt k))) (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (sqrt k)))
  (sqrt (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (sqrt k)))
  (sqrt (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (sqrt k)))
  (- (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))))
  (- (sqrt k))
  (/ (exp (* (- 1/2 (* k 1/2)) (log 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))) (cbrt (sqrt k)))
  (/ (exp (* (- 1/2 (* k 1/2)) (log 2))) (fabs (cbrt k)))
  (/ (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))) (sqrt (cbrt k)))
  (/ (exp (* (- 1/2 (* k 1/2)) (log 2))) (sqrt (sqrt k)))
  (/ (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))) (sqrt (sqrt k)))
  (exp (* (- 1/2 (* k 1/2)) (log 2)))
  (/ (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))) (sqrt k))
  (/ (exp (* (- 1/2 (* k 1/2)) (log 2))) (sqrt (sqrt k)))
  (/ (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))) (sqrt (sqrt k)))
  (exp (* (- 1/2 (* k 1/2)) (log 2)))
  (/ (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))))
  (/ (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (fabs (cbrt k)))
  (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (sqrt (sqrt k)))
  (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))
  (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (sqrt (sqrt k)))
  (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))
  (/ (sqrt k) (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))))
  (* (* (pow (* n PI) (/ k 2)) (sqrt k)) (pow 2 (/ k 2)))
  (* (pow (* n PI) (/ k 2)) (sqrt k))
  (* (pow 2 (/ k 2)) (sqrt k))
  (real->posit16 (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (sqrt k)))
  (* n (* PI 2))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))
  (exp (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))))
  (* (* (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))) (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))))
  (* (cbrt (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))) (cbrt (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))))
  (cbrt (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))))
  (* (* (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))) (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))))
  (sqrt (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))))
  (sqrt (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))))
  (* (sqrt 2) (sqrt (* n PI)))
  (* (pow 2 (/ k 2)) (pow (* n PI) (/ k 2)))
  (* (sqrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))) (pow (sqrt 2) (- 1/2 (* k 1/2))))
  (* (sqrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))) (pow (sqrt 2) (- 1/2 (* k 1/2))))
  (* (pow (* n PI) (/ (- 1/2 (* k 1/2)) 2)) (pow (sqrt 2) (- 1/2 (* k 1/2))))
  (* (pow (* n PI) (/ (- 1/2 (* k 1/2)) 2)) (pow (sqrt 2) (- 1/2 (* k 1/2))))
  (* (sqrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))) (sqrt (exp (* (- 1/2 (* k 1/2)) (log 2)))))
  (* (sqrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))) (sqrt (exp (* (- 1/2 (* k 1/2)) (log 2)))))
  (* (pow (* n PI) (/ (- 1/2 (* k 1/2)) 2)) (sqrt (exp (* (- 1/2 (* k 1/2)) (log 2)))))
  (* (pow (* n PI) (/ (- 1/2 (* k 1/2)) 2)) (sqrt (exp (* (- 1/2 (* k 1/2)) (log 2)))))
  (* (sqrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))) (pow 2 (/ (- 1/2 (* k 1/2)) 2)))
  (* (sqrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))) (pow 2 (/ (- 1/2 (* k 1/2)) 2)))
  (* (pow (* n PI) (- 1/4 (/ k 4))) (pow 2 (- 1/4 (/ k 4))))
  (* (pow (* n PI) (- 1/4 (/ k 4))) (pow 2 (- 1/4 (/ k 4))))
  (* (sqrt (* n PI)) (exp (* (- 1/2 (* k 1/2)) (log 2))))
  (* (sqrt (* n PI)) (exp (* (- 1/2 (* k 1/2)) (log 2))))
  (* (exp (* (- 1/2 (* k 1/2)) (log 2))) (pow n (- 1/2 (* k 1/2))))
  (* (* (cbrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))) (exp (* (- 1/2 (* k 1/2)) (log 2)))) (cbrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))))
  (* (exp (* (- 1/2 (* k 1/2)) (log 2))) (sqrt (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))))
  (exp (* (- 1/2 (* k 1/2)) (log 2)))
  (* (exp (* (- 1/2 (* k 1/2)) (log 2))) (pow (* n PI) (/ (- 1/2 (* k 1/2)) 2)))
  (* (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))) (pow 2 (- (* k 1/2))))
  (* (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))) (pow 2 (- (* k 1/2))))
  (* (pow (cbrt 2) (- 1/2 (* k 1/2))) (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))))
  (* (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))) (pow (sqrt 2) (- 1/2 (* k 1/2))))
  (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))
  (* (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))) (cbrt (exp (* (- 1/2 (* k 1/2)) (log 2)))))
  (* (sqrt (exp (* (- 1/2 (* k 1/2)) (log 2)))) (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))))
  (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))
  (* (pow 2 (/ (- 1/2 (* k 1/2)) 2)) (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))))
  (* (sqrt (* n PI)) (exp (* (- 1/2 (* k 1/2)) (log 2))))
  (* (sqrt 2) (exp (* (log (* n PI)) (- 1/2 (* k 1/2)))))
  (real->posit16 (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))))
  (+ (+ (+ (sqrt (* n PI)) (* (* (* 1/8 (sqrt (* n PI))) (* k k)) (* (log n) (log n)))) (- (* (* (sqrt (* n PI)) (log PI)) (* (* (* k k) (log n)) 1/4)) (* 1/2 (* (sqrt (* n PI)) (+ (* k (log n)) (* k (log PI))))))) (* (* (* k (log PI)) (* k (log PI))) (* 1/8 (sqrt (* n PI)))))
  (exp (* (log (* n PI)) (- 1/2 (* k 1/2))))
  (pow (/ (- PI) (/ -1 n)) (- 1/2 (* k 1/2)))
  (* n PI)
  (* n PI)
  (* n PI)
  (+ (* +nan.0 (* (- (sqrt 2)) (* n (* k PI)))) (- (- (* (* +nan.0 (sqrt 2)) (* n PI)) (* (* (* +nan.0 (log 2)) (sqrt 2)) (* n (* k PI)))) (+ (* (- (* +nan.0 (sqrt 2))) (* (* k (log n)) (* PI n))) (* +nan.0 (- (* (sqrt 2) (* (* (* k (log PI)) PI) n)) (* (sqrt 2) (* (* n PI) (* n PI))))))))
  (+ (* (- +nan.0) (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) k)) (* +nan.0 (- (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (* k k)) (/ (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2)))) (* k (* k k))))))
  (- (/ (* (exp (* (- 1/2 (* k 1/2)) (+ (- (log (- PI)) (log (/ -1 n))) (log 2)))) (- +nan.0)) (* k k)) (- (/ (* (exp (* (- 1/2 (* k 1/2)) (+ (- (log (- PI)) (log (/ -1 n))) (log 2)))) (- +nan.0)) k) (* (exp (* (- 1/2 (* k 1/2)) (+ (- (log (- PI)) (log (/ -1 n))) (log 2)))) (- +nan.0))))
  (- (- (* (* (sqrt 2) n) (* (* (* k (log PI)) PI) +nan.0)) (+ (- (* (* (* +nan.0 (log 2)) (sqrt 2)) (* n (* k PI))) (* +nan.0 (* (* n PI) (* n PI)))) (* +nan.0 (- (* (* (sqrt 2) n) (* (* k (log n)) PI)) (* n PI))))))
  (exp (* (- 1/2 (* k 1/2)) (+ (log (* n PI)) (log 2))))
  (exp (* (- 1/2 (* k 1/2)) (+ (- (log (- PI)) (log (/ -1 n))) (log 2))))
14.646 * * * [progress]: adding candidates to table
15.397 * * [progress]: iteration 4 / 4
15.397 * * * [progress]: picking best candidate
15.438 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
15.438 * * * [progress]: localizing error
15.472 * * * [progress]: generating rewritten candidates
15.472 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1)
15.480 * * * * [progress]: [ 2 / 4 ] rewriting at (2)
15.524 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1)
15.535 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2)
15.549 * * * [progress]: generating series expansions
15.549 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1)
15.550 * [backup-simplify]: Simplify (pow (* n PI) (- 1/2 (/ k 2))) into (pow (* n PI) (- 1/2 (* 1/2 k)))
15.550 * [approximate]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in (n k) around 0
15.550 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k
15.550 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k
15.550 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k
15.550 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
15.550 * [taylor]: Taking taylor expansion of 1/2 in k
15.550 * [backup-simplify]: Simplify 1/2 into 1/2
15.550 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
15.550 * [taylor]: Taking taylor expansion of 1/2 in k
15.550 * [backup-simplify]: Simplify 1/2 into 1/2
15.550 * [taylor]: Taking taylor expansion of k in k
15.550 * [backup-simplify]: Simplify 0 into 0
15.550 * [backup-simplify]: Simplify 1 into 1
15.550 * [taylor]: Taking taylor expansion of (log (* n PI)) in k
15.550 * [taylor]: Taking taylor expansion of (* n PI) in k
15.550 * [taylor]: Taking taylor expansion of n in k
15.550 * [backup-simplify]: Simplify n into n
15.550 * [taylor]: Taking taylor expansion of PI in k
15.550 * [backup-simplify]: Simplify PI into PI
15.550 * [backup-simplify]: Simplify (* n PI) into (* n PI)
15.550 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI))
15.551 * [backup-simplify]: Simplify (* 1/2 0) into 0
15.551 * [backup-simplify]: Simplify (- 0) into 0
15.551 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
15.551 * [backup-simplify]: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI)))
15.551 * [backup-simplify]: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2)
15.551 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n
15.551 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n
15.551 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n
15.551 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
15.551 * [taylor]: Taking taylor expansion of 1/2 in n
15.551 * [backup-simplify]: Simplify 1/2 into 1/2
15.551 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
15.551 * [taylor]: Taking taylor expansion of 1/2 in n
15.551 * [backup-simplify]: Simplify 1/2 into 1/2
15.551 * [taylor]: Taking taylor expansion of k in n
15.551 * [backup-simplify]: Simplify k into k
15.551 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
15.551 * [taylor]: Taking taylor expansion of (* n PI) in n
15.551 * [taylor]: Taking taylor expansion of n in n
15.551 * [backup-simplify]: Simplify 0 into 0
15.551 * [backup-simplify]: Simplify 1 into 1
15.551 * [taylor]: Taking taylor expansion of PI in n
15.552 * [backup-simplify]: Simplify PI into PI
15.552 * [backup-simplify]: Simplify (* 0 PI) into 0
15.553 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.553 * [backup-simplify]: Simplify (log PI) into (log PI)
15.553 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
15.553 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
15.553 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
15.554 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
15.554 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
15.554 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
15.555 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n
15.555 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n
15.555 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n
15.555 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
15.555 * [taylor]: Taking taylor expansion of 1/2 in n
15.555 * [backup-simplify]: Simplify 1/2 into 1/2
15.555 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
15.555 * [taylor]: Taking taylor expansion of 1/2 in n
15.555 * [backup-simplify]: Simplify 1/2 into 1/2
15.555 * [taylor]: Taking taylor expansion of k in n
15.555 * [backup-simplify]: Simplify k into k
15.555 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
15.555 * [taylor]: Taking taylor expansion of (* n PI) in n
15.555 * [taylor]: Taking taylor expansion of n in n
15.555 * [backup-simplify]: Simplify 0 into 0
15.555 * [backup-simplify]: Simplify 1 into 1
15.555 * [taylor]: Taking taylor expansion of PI in n
15.555 * [backup-simplify]: Simplify PI into PI
15.555 * [backup-simplify]: Simplify (* 0 PI) into 0
15.556 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.556 * [backup-simplify]: Simplify (log PI) into (log PI)
15.556 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
15.556 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
15.557 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
15.557 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
15.558 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
15.559 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
15.559 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) in k
15.559 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) in k
15.559 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
15.559 * [taylor]: Taking taylor expansion of 1/2 in k
15.559 * [backup-simplify]: Simplify 1/2 into 1/2
15.559 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
15.559 * [taylor]: Taking taylor expansion of 1/2 in k
15.559 * [backup-simplify]: Simplify 1/2 into 1/2
15.559 * [taylor]: Taking taylor expansion of k in k
15.559 * [backup-simplify]: Simplify 0 into 0
15.559 * [backup-simplify]: Simplify 1 into 1
15.559 * [taylor]: Taking taylor expansion of (+ (log PI) (log n)) in k
15.559 * [taylor]: Taking taylor expansion of (log PI) in k
15.559 * [taylor]: Taking taylor expansion of PI in k
15.559 * [backup-simplify]: Simplify PI into PI
15.560 * [backup-simplify]: Simplify (log PI) into (log PI)
15.560 * [taylor]: Taking taylor expansion of (log n) in k
15.560 * [taylor]: Taking taylor expansion of n in k
15.560 * [backup-simplify]: Simplify n into n
15.560 * [backup-simplify]: Simplify (log n) into (log n)
15.560 * [backup-simplify]: Simplify (* 1/2 0) into 0
15.561 * [backup-simplify]: Simplify (- 0) into 0
15.561 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
15.562 * [backup-simplify]: Simplify (+ (log PI) (log n)) into (+ (log PI) (log n))
15.563 * [backup-simplify]: Simplify (* 1/2 (+ (log PI) (log n))) into (* 1/2 (+ (log PI) (log n)))
15.563 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n))))
15.564 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n))))
15.565 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
15.567 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
15.567 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
15.568 * [backup-simplify]: Simplify (- 0) into 0
15.568 * [backup-simplify]: Simplify (+ 0 0) into 0
15.569 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
15.569 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log PI) (log n)))) into 0
15.571 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
15.571 * [taylor]: Taking taylor expansion of 0 in k
15.571 * [backup-simplify]: Simplify 0 into 0
15.571 * [backup-simplify]: Simplify 0 into 0
15.572 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
15.573 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
15.574 * [backup-simplify]: Simplify (+ 0 0) into 0
15.574 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
15.575 * [backup-simplify]: Simplify (- 1/2) into -1/2
15.575 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
15.576 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log PI) (log n)))) into (- (+ (* 1/2 (log PI)) (* 1/2 (log n))))
15.578 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n)))))
15.580 * [backup-simplify]: Simplify (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n)))))
15.581 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
15.584 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
15.585 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
15.586 * [backup-simplify]: Simplify (- 0) into 0
15.586 * [backup-simplify]: Simplify (+ 0 0) into 0
15.587 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
15.588 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log PI) (log n))))) into 0
15.590 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
15.590 * [taylor]: Taking taylor expansion of 0 in k
15.590 * [backup-simplify]: Simplify 0 into 0
15.590 * [backup-simplify]: Simplify 0 into 0
15.590 * [backup-simplify]: Simplify 0 into 0
15.593 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
15.595 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
15.595 * [backup-simplify]: Simplify (+ 0 0) into 0
15.596 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
15.596 * [backup-simplify]: Simplify (- 0) into 0
15.597 * [backup-simplify]: Simplify (+ 0 0) into 0
15.598 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log PI) (log n))))) into 0
15.600 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n))))))
15.603 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n))))))
15.608 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log PI) (log n)))))) into (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k)))))
15.608 * [backup-simplify]: Simplify (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))
15.609 * [approximate]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
15.609 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k
15.609 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k
15.609 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k
15.609 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
15.609 * [taylor]: Taking taylor expansion of 1/2 in k
15.609 * [backup-simplify]: Simplify 1/2 into 1/2
15.609 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
15.609 * [taylor]: Taking taylor expansion of 1/2 in k
15.609 * [backup-simplify]: Simplify 1/2 into 1/2
15.609 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.609 * [taylor]: Taking taylor expansion of k in k
15.609 * [backup-simplify]: Simplify 0 into 0
15.609 * [backup-simplify]: Simplify 1 into 1
15.609 * [backup-simplify]: Simplify (/ 1 1) into 1
15.609 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k
15.609 * [taylor]: Taking taylor expansion of (/ PI n) in k
15.609 * [taylor]: Taking taylor expansion of PI in k
15.609 * [backup-simplify]: Simplify PI into PI
15.609 * [taylor]: Taking taylor expansion of n in k
15.609 * [backup-simplify]: Simplify n into n
15.609 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
15.610 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n))
15.610 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.610 * [backup-simplify]: Simplify (- 1/2) into -1/2
15.611 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
15.611 * [backup-simplify]: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
15.611 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))
15.611 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
15.611 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
15.611 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
15.611 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
15.611 * [taylor]: Taking taylor expansion of 1/2 in n
15.611 * [backup-simplify]: Simplify 1/2 into 1/2
15.611 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
15.611 * [taylor]: Taking taylor expansion of 1/2 in n
15.611 * [backup-simplify]: Simplify 1/2 into 1/2
15.611 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.611 * [taylor]: Taking taylor expansion of k in n
15.611 * [backup-simplify]: Simplify k into k
15.611 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.611 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
15.611 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.611 * [taylor]: Taking taylor expansion of PI in n
15.611 * [backup-simplify]: Simplify PI into PI
15.611 * [taylor]: Taking taylor expansion of n in n
15.612 * [backup-simplify]: Simplify 0 into 0
15.612 * [backup-simplify]: Simplify 1 into 1
15.612 * [backup-simplify]: Simplify (/ PI 1) into PI
15.612 * [backup-simplify]: Simplify (log PI) into (log PI)
15.613 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
15.613 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
15.613 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
15.614 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
15.614 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
15.615 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
15.615 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
15.615 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
15.615 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
15.615 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
15.615 * [taylor]: Taking taylor expansion of 1/2 in n
15.615 * [backup-simplify]: Simplify 1/2 into 1/2
15.615 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
15.615 * [taylor]: Taking taylor expansion of 1/2 in n
15.615 * [backup-simplify]: Simplify 1/2 into 1/2
15.615 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.615 * [taylor]: Taking taylor expansion of k in n
15.615 * [backup-simplify]: Simplify k into k
15.615 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.615 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
15.615 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.615 * [taylor]: Taking taylor expansion of PI in n
15.615 * [backup-simplify]: Simplify PI into PI
15.615 * [taylor]: Taking taylor expansion of n in n
15.615 * [backup-simplify]: Simplify 0 into 0
15.615 * [backup-simplify]: Simplify 1 into 1
15.616 * [backup-simplify]: Simplify (/ PI 1) into PI
15.616 * [backup-simplify]: Simplify (log PI) into (log PI)
15.616 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
15.616 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
15.616 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
15.617 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
15.618 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
15.618 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
15.618 * [taylor]: Taking taylor expansion of (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
15.618 * [taylor]: Taking taylor expansion of (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
15.618 * [taylor]: Taking taylor expansion of (- (log PI) (log n)) in k
15.619 * [taylor]: Taking taylor expansion of (log PI) in k
15.619 * [taylor]: Taking taylor expansion of PI in k
15.619 * [backup-simplify]: Simplify PI into PI
15.619 * [backup-simplify]: Simplify (log PI) into (log PI)
15.619 * [taylor]: Taking taylor expansion of (log n) in k
15.619 * [taylor]: Taking taylor expansion of n in k
15.619 * [backup-simplify]: Simplify n into n
15.619 * [backup-simplify]: Simplify (log n) into (log n)
15.619 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
15.619 * [taylor]: Taking taylor expansion of 1/2 in k
15.619 * [backup-simplify]: Simplify 1/2 into 1/2
15.619 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
15.619 * [taylor]: Taking taylor expansion of 1/2 in k
15.619 * [backup-simplify]: Simplify 1/2 into 1/2
15.619 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.619 * [taylor]: Taking taylor expansion of k in k
15.619 * [backup-simplify]: Simplify 0 into 0
15.619 * [backup-simplify]: Simplify 1 into 1
15.620 * [backup-simplify]: Simplify (/ 1 1) into 1
15.620 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
15.620 * [backup-simplify]: Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n))
15.621 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.621 * [backup-simplify]: Simplify (- 1/2) into -1/2
15.621 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
15.622 * [backup-simplify]: Simplify (* (- (log PI) (log n)) -1/2) into (* -1/2 (- (log PI) (log n)))
15.623 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
15.623 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
15.624 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
15.626 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
15.626 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
15.626 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
15.627 * [backup-simplify]: Simplify (- 0) into 0
15.627 * [backup-simplify]: Simplify (+ 0 0) into 0
15.628 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
15.628 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0
15.630 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
15.630 * [taylor]: Taking taylor expansion of 0 in k
15.630 * [backup-simplify]: Simplify 0 into 0
15.630 * [backup-simplify]: Simplify 0 into 0
15.630 * [backup-simplify]: Simplify 0 into 0
15.631 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.634 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
15.635 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
15.636 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
15.636 * [backup-simplify]: Simplify (- 0) into 0
15.636 * [backup-simplify]: Simplify (+ 0 0) into 0
15.637 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
15.638 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0
15.646 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
15.646 * [taylor]: Taking taylor expansion of 0 in k
15.646 * [backup-simplify]: Simplify 0 into 0
15.646 * [backup-simplify]: Simplify 0 into 0
15.646 * [backup-simplify]: Simplify 0 into 0
15.646 * [backup-simplify]: Simplify 0 into 0
15.647 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.653 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
15.653 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
15.655 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
15.655 * [backup-simplify]: Simplify (- 0) into 0
15.655 * [backup-simplify]: Simplify (+ 0 0) into 0
15.656 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
15.657 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0
15.660 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
15.660 * [taylor]: Taking taylor expansion of 0 in k
15.660 * [backup-simplify]: Simplify 0 into 0
15.660 * [backup-simplify]: Simplify 0 into 0
15.660 * [backup-simplify]: Simplify (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n)))))
15.661 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
15.661 * [approximate]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
15.661 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
15.661 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k
15.661 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k
15.661 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
15.661 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
15.661 * [taylor]: Taking taylor expansion of 1/2 in k
15.661 * [backup-simplify]: Simplify 1/2 into 1/2
15.661 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.661 * [taylor]: Taking taylor expansion of k in k
15.661 * [backup-simplify]: Simplify 0 into 0
15.661 * [backup-simplify]: Simplify 1 into 1
15.661 * [backup-simplify]: Simplify (/ 1 1) into 1
15.661 * [taylor]: Taking taylor expansion of 1/2 in k
15.661 * [backup-simplify]: Simplify 1/2 into 1/2
15.662 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k
15.662 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k
15.662 * [taylor]: Taking taylor expansion of -1 in k
15.662 * [backup-simplify]: Simplify -1 into -1
15.662 * [taylor]: Taking taylor expansion of (/ PI n) in k
15.662 * [taylor]: Taking taylor expansion of PI in k
15.662 * [backup-simplify]: Simplify PI into PI
15.662 * [taylor]: Taking taylor expansion of n in k
15.662 * [backup-simplify]: Simplify n into n
15.662 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
15.662 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n))
15.662 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n)))
15.662 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.663 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
15.663 * [backup-simplify]: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
15.663 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
15.663 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
15.663 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
15.663 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
15.663 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
15.663 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
15.663 * [taylor]: Taking taylor expansion of 1/2 in n
15.664 * [backup-simplify]: Simplify 1/2 into 1/2
15.664 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.664 * [taylor]: Taking taylor expansion of k in n
15.664 * [backup-simplify]: Simplify k into k
15.664 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.664 * [taylor]: Taking taylor expansion of 1/2 in n
15.664 * [backup-simplify]: Simplify 1/2 into 1/2
15.664 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
15.664 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
15.664 * [taylor]: Taking taylor expansion of -1 in n
15.664 * [backup-simplify]: Simplify -1 into -1
15.664 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.664 * [taylor]: Taking taylor expansion of PI in n
15.664 * [backup-simplify]: Simplify PI into PI
15.664 * [taylor]: Taking taylor expansion of n in n
15.664 * [backup-simplify]: Simplify 0 into 0
15.664 * [backup-simplify]: Simplify 1 into 1
15.664 * [backup-simplify]: Simplify (/ PI 1) into PI
15.665 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
15.665 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
15.665 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
15.665 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
15.666 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
15.667 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
15.668 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
15.668 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
15.668 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
15.668 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
15.668 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
15.668 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
15.668 * [taylor]: Taking taylor expansion of 1/2 in n
15.668 * [backup-simplify]: Simplify 1/2 into 1/2
15.668 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.668 * [taylor]: Taking taylor expansion of k in n
15.668 * [backup-simplify]: Simplify k into k
15.668 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.668 * [taylor]: Taking taylor expansion of 1/2 in n
15.668 * [backup-simplify]: Simplify 1/2 into 1/2
15.668 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
15.668 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
15.668 * [taylor]: Taking taylor expansion of -1 in n
15.668 * [backup-simplify]: Simplify -1 into -1
15.668 * [taylor]: Taking taylor expansion of (/ PI n) in n
15.668 * [taylor]: Taking taylor expansion of PI in n
15.668 * [backup-simplify]: Simplify PI into PI
15.668 * [taylor]: Taking taylor expansion of n in n
15.668 * [backup-simplify]: Simplify 0 into 0
15.668 * [backup-simplify]: Simplify 1 into 1
15.668 * [backup-simplify]: Simplify (/ PI 1) into PI
15.669 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
15.669 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
15.669 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
15.670 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
15.670 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
15.671 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
15.672 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
15.672 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) in k
15.672 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) in k
15.672 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
15.672 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
15.672 * [taylor]: Taking taylor expansion of 1/2 in k
15.672 * [backup-simplify]: Simplify 1/2 into 1/2
15.672 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.672 * [taylor]: Taking taylor expansion of k in k
15.672 * [backup-simplify]: Simplify 0 into 0
15.672 * [backup-simplify]: Simplify 1 into 1
15.672 * [backup-simplify]: Simplify (/ 1 1) into 1
15.672 * [taylor]: Taking taylor expansion of 1/2 in k
15.672 * [backup-simplify]: Simplify 1/2 into 1/2
15.672 * [taylor]: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k
15.672 * [taylor]: Taking taylor expansion of (log (* -1 PI)) in k
15.672 * [taylor]: Taking taylor expansion of (* -1 PI) in k
15.672 * [taylor]: Taking taylor expansion of -1 in k
15.672 * [backup-simplify]: Simplify -1 into -1
15.672 * [taylor]: Taking taylor expansion of PI in k
15.672 * [backup-simplify]: Simplify PI into PI
15.673 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
15.674 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
15.674 * [taylor]: Taking taylor expansion of (log n) in k
15.674 * [taylor]: Taking taylor expansion of n in k
15.674 * [backup-simplify]: Simplify n into n
15.674 * [backup-simplify]: Simplify (log n) into (log n)
15.674 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
15.674 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
15.674 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
15.675 * [backup-simplify]: Simplify (+ (log (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n))
15.676 * [backup-simplify]: Simplify (* 1/2 (- (log (* -1 PI)) (log n))) into (* 1/2 (- (log (* -1 PI)) (log n)))
15.676 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
15.677 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
15.678 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
15.678 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0
15.679 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0
15.679 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
15.680 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
15.680 * [backup-simplify]: Simplify (+ 0 0) into 0
15.681 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
15.681 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0
15.683 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
15.683 * [taylor]: Taking taylor expansion of 0 in k
15.683 * [backup-simplify]: Simplify 0 into 0
15.683 * [backup-simplify]: Simplify 0 into 0
15.683 * [backup-simplify]: Simplify 0 into 0
15.683 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.684 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0
15.686 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0
15.686 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
15.686 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
15.687 * [backup-simplify]: Simplify (+ 0 0) into 0
15.687 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
15.688 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0
15.690 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
15.690 * [taylor]: Taking taylor expansion of 0 in k
15.690 * [backup-simplify]: Simplify 0 into 0
15.690 * [backup-simplify]: Simplify 0 into 0
15.690 * [backup-simplify]: Simplify 0 into 0
15.690 * [backup-simplify]: Simplify 0 into 0
15.691 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.691 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
15.695 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -1 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -1 PI) 1)))) 6) into 0
15.695 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
15.696 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
15.696 * [backup-simplify]: Simplify (+ 0 0) into 0
15.697 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
15.699 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n)))))) into 0
15.702 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
15.702 * [taylor]: Taking taylor expansion of 0 in k
15.702 * [backup-simplify]: Simplify 0 into 0
15.702 * [backup-simplify]: Simplify 0 into 0
15.703 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))) into (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))
15.703 * * * * [progress]: [ 2 / 4 ] generating series at (2)
15.704 * [backup-simplify]: Simplify (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) into (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k)))
15.704 * [approximate]: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (k n) around 0
15.704 * [taylor]: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n
15.704 * [taylor]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in n
15.704 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n
15.704 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n
15.704 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n
15.704 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
15.704 * [taylor]: Taking taylor expansion of 1/2 in n
15.704 * [backup-simplify]: Simplify 1/2 into 1/2
15.704 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
15.704 * [taylor]: Taking taylor expansion of 1/2 in n
15.704 * [backup-simplify]: Simplify 1/2 into 1/2
15.704 * [taylor]: Taking taylor expansion of k in n
15.704 * [backup-simplify]: Simplify k into k
15.704 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
15.704 * [taylor]: Taking taylor expansion of (* n PI) in n
15.704 * [taylor]: Taking taylor expansion of n in n
15.704 * [backup-simplify]: Simplify 0 into 0
15.704 * [backup-simplify]: Simplify 1 into 1
15.704 * [taylor]: Taking taylor expansion of PI in n
15.704 * [backup-simplify]: Simplify PI into PI
15.705 * [backup-simplify]: Simplify (* 0 PI) into 0
15.706 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.707 * [backup-simplify]: Simplify (log PI) into (log PI)
15.707 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
15.707 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
15.707 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
15.708 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
15.708 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
15.709 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
15.709 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in n
15.709 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in n
15.709 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in n
15.709 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
15.709 * [taylor]: Taking taylor expansion of 1/2 in n
15.709 * [backup-simplify]: Simplify 1/2 into 1/2
15.709 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
15.709 * [taylor]: Taking taylor expansion of 1/2 in n
15.709 * [backup-simplify]: Simplify 1/2 into 1/2
15.709 * [taylor]: Taking taylor expansion of k in n
15.709 * [backup-simplify]: Simplify k into k
15.709 * [taylor]: Taking taylor expansion of (log 2) in n
15.709 * [taylor]: Taking taylor expansion of 2 in n
15.709 * [backup-simplify]: Simplify 2 into 2
15.710 * [backup-simplify]: Simplify (log 2) into (log 2)
15.710 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
15.710 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
15.710 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
15.710 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k)))
15.711 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k))))
15.711 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
15.711 * [taylor]: Taking taylor expansion of (/ 1 k) in n
15.711 * [taylor]: Taking taylor expansion of k in n
15.711 * [backup-simplify]: Simplify k into k
15.711 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
15.711 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
15.711 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
15.711 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
15.711 * [taylor]: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k
15.711 * [taylor]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in k
15.711 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k
15.711 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k
15.711 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k
15.711 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
15.711 * [taylor]: Taking taylor expansion of 1/2 in k
15.711 * [backup-simplify]: Simplify 1/2 into 1/2
15.711 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
15.712 * [taylor]: Taking taylor expansion of 1/2 in k
15.712 * [backup-simplify]: Simplify 1/2 into 1/2
15.712 * [taylor]: Taking taylor expansion of k in k
15.712 * [backup-simplify]: Simplify 0 into 0
15.712 * [backup-simplify]: Simplify 1 into 1
15.712 * [taylor]: Taking taylor expansion of (log (* n PI)) in k
15.712 * [taylor]: Taking taylor expansion of (* n PI) in k
15.712 * [taylor]: Taking taylor expansion of n in k
15.712 * [backup-simplify]: Simplify n into n
15.712 * [taylor]: Taking taylor expansion of PI in k
15.712 * [backup-simplify]: Simplify PI into PI
15.712 * [backup-simplify]: Simplify (* n PI) into (* n PI)
15.712 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI))
15.712 * [backup-simplify]: Simplify (* 1/2 0) into 0
15.713 * [backup-simplify]: Simplify (- 0) into 0
15.713 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
15.713 * [backup-simplify]: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI)))
15.713 * [backup-simplify]: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2)
15.713 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k
15.713 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k
15.714 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k
15.714 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
15.714 * [taylor]: Taking taylor expansion of 1/2 in k
15.714 * [backup-simplify]: Simplify 1/2 into 1/2
15.714 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
15.714 * [taylor]: Taking taylor expansion of 1/2 in k
15.714 * [backup-simplify]: Simplify 1/2 into 1/2
15.714 * [taylor]: Taking taylor expansion of k in k
15.714 * [backup-simplify]: Simplify 0 into 0
15.714 * [backup-simplify]: Simplify 1 into 1
15.714 * [taylor]: Taking taylor expansion of (log 2) in k
15.714 * [taylor]: Taking taylor expansion of 2 in k
15.714 * [backup-simplify]: Simplify 2 into 2
15.714 * [backup-simplify]: Simplify (log 2) into (log 2)
15.715 * [backup-simplify]: Simplify (* 1/2 0) into 0
15.715 * [backup-simplify]: Simplify (- 0) into 0
15.716 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
15.717 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
15.718 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
15.718 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
15.718 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.718 * [taylor]: Taking taylor expansion of k in k
15.718 * [backup-simplify]: Simplify 0 into 0
15.718 * [backup-simplify]: Simplify 1 into 1
15.719 * [backup-simplify]: Simplify (/ 1 1) into 1
15.719 * [backup-simplify]: Simplify (sqrt 0) into 0
15.720 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.721 * [taylor]: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k
15.721 * [taylor]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in k
15.721 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k
15.721 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k
15.721 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k
15.721 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
15.721 * [taylor]: Taking taylor expansion of 1/2 in k
15.721 * [backup-simplify]: Simplify 1/2 into 1/2
15.721 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
15.721 * [taylor]: Taking taylor expansion of 1/2 in k
15.721 * [backup-simplify]: Simplify 1/2 into 1/2
15.721 * [taylor]: Taking taylor expansion of k in k
15.721 * [backup-simplify]: Simplify 0 into 0
15.721 * [backup-simplify]: Simplify 1 into 1
15.721 * [taylor]: Taking taylor expansion of (log (* n PI)) in k
15.721 * [taylor]: Taking taylor expansion of (* n PI) in k
15.721 * [taylor]: Taking taylor expansion of n in k
15.721 * [backup-simplify]: Simplify n into n
15.721 * [taylor]: Taking taylor expansion of PI in k
15.721 * [backup-simplify]: Simplify PI into PI
15.721 * [backup-simplify]: Simplify (* n PI) into (* n PI)
15.721 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI))
15.722 * [backup-simplify]: Simplify (* 1/2 0) into 0
15.722 * [backup-simplify]: Simplify (- 0) into 0
15.722 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
15.722 * [backup-simplify]: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI)))
15.723 * [backup-simplify]: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2)
15.723 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k
15.723 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k
15.723 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k
15.723 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
15.723 * [taylor]: Taking taylor expansion of 1/2 in k
15.723 * [backup-simplify]: Simplify 1/2 into 1/2
15.723 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
15.723 * [taylor]: Taking taylor expansion of 1/2 in k
15.723 * [backup-simplify]: Simplify 1/2 into 1/2
15.723 * [taylor]: Taking taylor expansion of k in k
15.723 * [backup-simplify]: Simplify 0 into 0
15.723 * [backup-simplify]: Simplify 1 into 1
15.723 * [taylor]: Taking taylor expansion of (log 2) in k
15.723 * [taylor]: Taking taylor expansion of 2 in k
15.723 * [backup-simplify]: Simplify 2 into 2
15.723 * [backup-simplify]: Simplify (log 2) into (log 2)
15.724 * [backup-simplify]: Simplify (* 1/2 0) into 0
15.724 * [backup-simplify]: Simplify (- 0) into 0
15.725 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
15.725 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
15.727 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
15.727 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
15.727 * [taylor]: Taking taylor expansion of (/ 1 k) in k
15.727 * [taylor]: Taking taylor expansion of k in k
15.727 * [backup-simplify]: Simplify 0 into 0
15.727 * [backup-simplify]: Simplify 1 into 1
15.728 * [backup-simplify]: Simplify (/ 1 1) into 1
15.728 * [backup-simplify]: Simplify (sqrt 0) into 0
15.729 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
15.730 * [backup-simplify]: Simplify (* (pow (* n PI) 1/2) (pow 2 1/2)) into (sqrt (* n (* PI 2)))
15.730 * [backup-simplify]: Simplify (* (sqrt (* n (* PI 2))) 0) into 0
15.730 * [taylor]: Taking taylor expansion of 0 in n
15.730 * [backup-simplify]: Simplify 0 into 0
15.730 * [backup-simplify]: Simplify 0 into 0
15.732 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
15.733 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
15.733 * [backup-simplify]: Simplify (- 1/2) into -1/2
15.734 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
15.736 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log 2))) into (- (* 1/2 (log 2)))
15.745 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2)))
15.746 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
15.747 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* n PI) 1)))) 1) into 0
15.747 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
15.748 * [backup-simplify]: Simplify (- 1/2) into -1/2
15.748 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
15.749 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* n PI)))) into (- (* 1/2 (log (* n PI))))
15.749 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 1) 1)))) into (* -1/2 (* (log (* n PI)) (sqrt (* n PI))))
15.752 * [backup-simplify]: Simplify (+ (* (pow (* n PI) 1/2) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (pow 2 1/2))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))
15.755 * [backup-simplify]: Simplify (+ (* (sqrt (* n (* PI 2))) +nan.0) (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
15.755 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
15.755 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
15.755 * [taylor]: Taking taylor expansion of +nan.0 in n
15.755 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.755 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
15.756 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.756 * [taylor]: Taking taylor expansion of 2 in n
15.756 * [backup-simplify]: Simplify 2 into 2
15.756 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.757 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.757 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.757 * [taylor]: Taking taylor expansion of (* n PI) in n
15.757 * [taylor]: Taking taylor expansion of n in n
15.757 * [backup-simplify]: Simplify 0 into 0
15.757 * [backup-simplify]: Simplify 1 into 1
15.757 * [taylor]: Taking taylor expansion of PI in n
15.757 * [backup-simplify]: Simplify PI into PI
15.757 * [backup-simplify]: Simplify (* 0 PI) into 0
15.759 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.759 * [backup-simplify]: Simplify (sqrt 0) into 0
15.761 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.761 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
15.762 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.762 * [backup-simplify]: Simplify (- 0) into 0
15.762 * [backup-simplify]: Simplify 0 into 0
15.762 * [backup-simplify]: Simplify 0 into 0
15.763 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
15.766 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
15.772 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
15.773 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
15.773 * [backup-simplify]: Simplify (- 0) into 0
15.774 * [backup-simplify]: Simplify (+ 0 0) into 0
15.775 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log 2)))) into 0
15.785 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2)))
15.786 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
15.788 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* n PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* n PI) 1)))) 2) into 0
15.788 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
15.789 * [backup-simplify]: Simplify (- 0) into 0
15.789 * [backup-simplify]: Simplify (+ 0 0) into 0
15.790 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* n PI))))) into 0
15.790 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI))))
15.794 * [backup-simplify]: Simplify (+ (* (pow (* n PI) 1/2) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) (pow 2 1/2)))) into (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI))))))
15.798 * [backup-simplify]: Simplify (+ (* (sqrt (* n (* PI 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) +nan.0) (* (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))))
15.798 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n
15.798 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n
15.798 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n
15.798 * [taylor]: Taking taylor expansion of +nan.0 in n
15.798 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.798 * [taylor]: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n
15.798 * [taylor]: Taking taylor expansion of (* (log 2) (sqrt 2)) in n
15.798 * [taylor]: Taking taylor expansion of (log 2) in n
15.798 * [taylor]: Taking taylor expansion of 2 in n
15.798 * [backup-simplify]: Simplify 2 into 2
15.798 * [backup-simplify]: Simplify (log 2) into (log 2)
15.798 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.798 * [taylor]: Taking taylor expansion of 2 in n
15.798 * [backup-simplify]: Simplify 2 into 2
15.799 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.799 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.799 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.799 * [taylor]: Taking taylor expansion of (* n PI) in n
15.799 * [taylor]: Taking taylor expansion of n in n
15.799 * [backup-simplify]: Simplify 0 into 0
15.799 * [backup-simplify]: Simplify 1 into 1
15.799 * [taylor]: Taking taylor expansion of PI in n
15.799 * [backup-simplify]: Simplify PI into PI
15.799 * [backup-simplify]: Simplify (* 0 PI) into 0
15.800 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.800 * [backup-simplify]: Simplify (sqrt 0) into 0
15.801 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.801 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n
15.801 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n
15.801 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) in n
15.801 * [taylor]: Taking taylor expansion of +nan.0 in n
15.801 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.801 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))) in n
15.801 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n
15.802 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.802 * [taylor]: Taking taylor expansion of 2 in n
15.802 * [backup-simplify]: Simplify 2 into 2
15.802 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.802 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.802 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
15.802 * [taylor]: Taking taylor expansion of (* n PI) in n
15.802 * [taylor]: Taking taylor expansion of n in n
15.802 * [backup-simplify]: Simplify 0 into 0
15.802 * [backup-simplify]: Simplify 1 into 1
15.802 * [taylor]: Taking taylor expansion of PI in n
15.802 * [backup-simplify]: Simplify PI into PI
15.803 * [backup-simplify]: Simplify (* 0 PI) into 0
15.803 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.804 * [backup-simplify]: Simplify (log PI) into (log PI)
15.804 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.804 * [taylor]: Taking taylor expansion of (* n PI) in n
15.804 * [taylor]: Taking taylor expansion of n in n
15.804 * [backup-simplify]: Simplify 0 into 0
15.804 * [backup-simplify]: Simplify 1 into 1
15.804 * [taylor]: Taking taylor expansion of PI in n
15.804 * [backup-simplify]: Simplify PI into PI
15.804 * [backup-simplify]: Simplify (* 0 PI) into 0
15.805 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.805 * [backup-simplify]: Simplify (sqrt 0) into 0
15.806 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.806 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
15.806 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
15.806 * [taylor]: Taking taylor expansion of +nan.0 in n
15.806 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.806 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
15.806 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.806 * [taylor]: Taking taylor expansion of 2 in n
15.806 * [backup-simplify]: Simplify 2 into 2
15.806 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.807 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.807 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.807 * [taylor]: Taking taylor expansion of (* n PI) in n
15.807 * [taylor]: Taking taylor expansion of n in n
15.807 * [backup-simplify]: Simplify 0 into 0
15.807 * [backup-simplify]: Simplify 1 into 1
15.807 * [taylor]: Taking taylor expansion of PI in n
15.807 * [backup-simplify]: Simplify PI into PI
15.807 * [backup-simplify]: Simplify (* 0 PI) into 0
15.808 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.808 * [backup-simplify]: Simplify (sqrt 0) into 0
15.809 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.810 * [backup-simplify]: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2))
15.810 * [backup-simplify]: Simplify (* (* (log 2) (sqrt 2)) 0) into 0
15.811 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.811 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
15.812 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n)))
15.812 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log PI) (log n))) 0) into 0
15.812 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.813 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
15.813 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.813 * [backup-simplify]: Simplify (- 0) into 0
15.814 * [backup-simplify]: Simplify (+ 0 0) into 0
15.814 * [backup-simplify]: Simplify (- 0) into 0
15.814 * [backup-simplify]: Simplify (+ 0 0) into 0
15.814 * [backup-simplify]: Simplify (- 0) into 0
15.814 * [backup-simplify]: Simplify 0 into 0
15.816 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
15.819 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
15.822 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
15.824 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
15.824 * [backup-simplify]: Simplify 0 into 0
15.825 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
15.829 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
15.834 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
15.836 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
15.836 * [backup-simplify]: Simplify (- 0) into 0
15.836 * [backup-simplify]: Simplify (+ 0 0) into 0
15.837 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log 2))))) into 0
15.845 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 3) 6)) (* (/ (pow (- (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log 2) 3) (sqrt 2)))
15.846 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
15.848 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* n PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* n PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* n PI) 1)))) 6) into 0
15.849 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
15.849 * [backup-simplify]: Simplify (- 0) into 0
15.849 * [backup-simplify]: Simplify (+ 0 0) into 0
15.850 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* n PI)))))) into 0
15.851 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* n PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log (* n PI)) 3) (sqrt (* n PI))))
15.856 * [backup-simplify]: Simplify (+ (* (pow (* n PI) 1/2) (* -1/48 (* (pow (log 2) 3) (sqrt 2)))) (+ (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1/48 (* (pow (log (* n PI)) 3) (sqrt (* n PI)))) (pow 2 1/2))))) into (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log (* n PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* n PI)) 3)) (sqrt (* n PI))))))))
15.866 * [backup-simplify]: Simplify (+ (* (sqrt (* n (* PI 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) +nan.0) (+ (* (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))))) +nan.0) (* (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log (* n PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* n PI)) 3)) (sqrt (* n PI)))))))) 0)))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))))))))
15.867 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))))))) in n
15.867 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))))))) in n
15.867 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n
15.867 * [taylor]: Taking taylor expansion of +nan.0 in n
15.867 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.867 * [taylor]: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n
15.867 * [taylor]: Taking taylor expansion of (* (log 2) (sqrt 2)) in n
15.867 * [taylor]: Taking taylor expansion of (log 2) in n
15.867 * [taylor]: Taking taylor expansion of 2 in n
15.867 * [backup-simplify]: Simplify 2 into 2
15.867 * [backup-simplify]: Simplify (log 2) into (log 2)
15.867 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.867 * [taylor]: Taking taylor expansion of 2 in n
15.867 * [backup-simplify]: Simplify 2 into 2
15.867 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.868 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.868 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.868 * [taylor]: Taking taylor expansion of (* n PI) in n
15.868 * [taylor]: Taking taylor expansion of n in n
15.868 * [backup-simplify]: Simplify 0 into 0
15.868 * [backup-simplify]: Simplify 1 into 1
15.868 * [taylor]: Taking taylor expansion of PI in n
15.868 * [backup-simplify]: Simplify PI into PI
15.868 * [backup-simplify]: Simplify (* 0 PI) into 0
15.870 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.870 * [backup-simplify]: Simplify (sqrt 0) into 0
15.871 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.871 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))))) in n
15.871 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))))) in n
15.871 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) in n
15.871 * [taylor]: Taking taylor expansion of +nan.0 in n
15.871 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.872 * [taylor]: Taking taylor expansion of (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI))) in n
15.872 * [taylor]: Taking taylor expansion of (* (pow (log 2) 2) (sqrt 2)) in n
15.872 * [taylor]: Taking taylor expansion of (pow (log 2) 2) in n
15.872 * [taylor]: Taking taylor expansion of (log 2) in n
15.872 * [taylor]: Taking taylor expansion of 2 in n
15.872 * [backup-simplify]: Simplify 2 into 2
15.872 * [backup-simplify]: Simplify (log 2) into (log 2)
15.872 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.872 * [taylor]: Taking taylor expansion of 2 in n
15.872 * [backup-simplify]: Simplify 2 into 2
15.872 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.873 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.873 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.873 * [taylor]: Taking taylor expansion of (* n PI) in n
15.873 * [taylor]: Taking taylor expansion of n in n
15.873 * [backup-simplify]: Simplify 0 into 0
15.873 * [backup-simplify]: Simplify 1 into 1
15.873 * [taylor]: Taking taylor expansion of PI in n
15.873 * [backup-simplify]: Simplify PI into PI
15.874 * [backup-simplify]: Simplify (* 0 PI) into 0
15.875 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.875 * [backup-simplify]: Simplify (sqrt 0) into 0
15.877 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.877 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))) in n
15.877 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))) in n
15.877 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) in n
15.877 * [taylor]: Taking taylor expansion of +nan.0 in n
15.877 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.877 * [taylor]: Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI))) in n
15.877 * [taylor]: Taking taylor expansion of (* (log 2) (* (sqrt 2) (log (* n PI)))) in n
15.877 * [taylor]: Taking taylor expansion of (log 2) in n
15.877 * [taylor]: Taking taylor expansion of 2 in n
15.877 * [backup-simplify]: Simplify 2 into 2
15.877 * [backup-simplify]: Simplify (log 2) into (log 2)
15.877 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n
15.877 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.877 * [taylor]: Taking taylor expansion of 2 in n
15.877 * [backup-simplify]: Simplify 2 into 2
15.878 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.878 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.878 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
15.878 * [taylor]: Taking taylor expansion of (* n PI) in n
15.878 * [taylor]: Taking taylor expansion of n in n
15.878 * [backup-simplify]: Simplify 0 into 0
15.878 * [backup-simplify]: Simplify 1 into 1
15.878 * [taylor]: Taking taylor expansion of PI in n
15.879 * [backup-simplify]: Simplify PI into PI
15.879 * [backup-simplify]: Simplify (* 0 PI) into 0
15.880 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.881 * [backup-simplify]: Simplify (log PI) into (log PI)
15.881 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.881 * [taylor]: Taking taylor expansion of (* n PI) in n
15.881 * [taylor]: Taking taylor expansion of n in n
15.881 * [backup-simplify]: Simplify 0 into 0
15.881 * [backup-simplify]: Simplify 1 into 1
15.881 * [taylor]: Taking taylor expansion of PI in n
15.881 * [backup-simplify]: Simplify PI into PI
15.881 * [backup-simplify]: Simplify (* 0 PI) into 0
15.883 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.883 * [backup-simplify]: Simplify (sqrt 0) into 0
15.884 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.884 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))) in n
15.884 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))) in n
15.885 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) in n
15.885 * [taylor]: Taking taylor expansion of +nan.0 in n
15.885 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.885 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI))) in n
15.885 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* n PI)) 2)) in n
15.885 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.885 * [taylor]: Taking taylor expansion of 2 in n
15.885 * [backup-simplify]: Simplify 2 into 2
15.885 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.886 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.886 * [taylor]: Taking taylor expansion of (pow (log (* n PI)) 2) in n
15.886 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
15.886 * [taylor]: Taking taylor expansion of (* n PI) in n
15.886 * [taylor]: Taking taylor expansion of n in n
15.886 * [backup-simplify]: Simplify 0 into 0
15.886 * [backup-simplify]: Simplify 1 into 1
15.886 * [taylor]: Taking taylor expansion of PI in n
15.886 * [backup-simplify]: Simplify PI into PI
15.886 * [backup-simplify]: Simplify (* 0 PI) into 0
15.888 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.888 * [backup-simplify]: Simplify (log PI) into (log PI)
15.889 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
15.889 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.889 * [taylor]: Taking taylor expansion of (* n PI) in n
15.889 * [taylor]: Taking taylor expansion of n in n
15.889 * [backup-simplify]: Simplify 0 into 0
15.889 * [backup-simplify]: Simplify 1 into 1
15.889 * [taylor]: Taking taylor expansion of PI in n
15.889 * [backup-simplify]: Simplify PI into PI
15.889 * [backup-simplify]: Simplify (* 0 PI) into 0
15.891 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.891 * [backup-simplify]: Simplify (sqrt 0) into 0
15.893 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.893 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))) in n
15.893 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) in n
15.893 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
15.893 * [taylor]: Taking taylor expansion of +nan.0 in n
15.893 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.893 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
15.893 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.893 * [taylor]: Taking taylor expansion of 2 in n
15.893 * [backup-simplify]: Simplify 2 into 2
15.893 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.894 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.894 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.894 * [taylor]: Taking taylor expansion of (* n PI) in n
15.894 * [taylor]: Taking taylor expansion of n in n
15.894 * [backup-simplify]: Simplify 0 into 0
15.894 * [backup-simplify]: Simplify 1 into 1
15.894 * [taylor]: Taking taylor expansion of PI in n
15.894 * [backup-simplify]: Simplify PI into PI
15.895 * [backup-simplify]: Simplify (* 0 PI) into 0
15.896 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.897 * [backup-simplify]: Simplify (sqrt 0) into 0
15.898 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.898 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))) in n
15.898 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) in n
15.898 * [taylor]: Taking taylor expansion of +nan.0 in n
15.898 * [backup-simplify]: Simplify +nan.0 into +nan.0
15.898 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))) in n
15.898 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n
15.898 * [taylor]: Taking taylor expansion of (sqrt 2) in n
15.898 * [taylor]: Taking taylor expansion of 2 in n
15.898 * [backup-simplify]: Simplify 2 into 2
15.899 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
15.899 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
15.899 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
15.899 * [taylor]: Taking taylor expansion of (* n PI) in n
15.899 * [taylor]: Taking taylor expansion of n in n
15.899 * [backup-simplify]: Simplify 0 into 0
15.900 * [backup-simplify]: Simplify 1 into 1
15.900 * [taylor]: Taking taylor expansion of PI in n
15.900 * [backup-simplify]: Simplify PI into PI
15.900 * [backup-simplify]: Simplify (* 0 PI) into 0
15.901 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.901 * [backup-simplify]: Simplify (log PI) into (log PI)
15.901 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
15.901 * [taylor]: Taking taylor expansion of (* n PI) in n
15.901 * [taylor]: Taking taylor expansion of n in n
15.901 * [backup-simplify]: Simplify 0 into 0
15.901 * [backup-simplify]: Simplify 1 into 1
15.901 * [taylor]: Taking taylor expansion of PI in n
15.901 * [backup-simplify]: Simplify PI into PI
15.902 * [backup-simplify]: Simplify (* 0 PI) into 0
15.903 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
15.903 * [backup-simplify]: Simplify (sqrt 0) into 0
15.904 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
15.905 * [backup-simplify]: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2))
15.905 * [backup-simplify]: Simplify (* (* (log 2) (sqrt 2)) 0) into 0
15.906 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.907 * [backup-simplify]: Simplify (* (log 2) (log 2)) into (pow (log 2) 2)
15.908 * [backup-simplify]: Simplify (* (pow (log 2) 2) (sqrt 2)) into (* (pow (log 2) 2) (sqrt 2))
15.908 * [backup-simplify]: Simplify (* (* (pow (log 2) 2) (sqrt 2)) 0) into 0
15.909 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.909 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
15.910 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n)))
15.911 * [backup-simplify]: Simplify (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) into (* (log 2) (* (sqrt 2) (+ (log PI) (log n))))
15.912 * [backup-simplify]: Simplify (* (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) 0) into 0
15.912 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.913 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
15.913 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
15.914 * [backup-simplify]: Simplify (* (+ (log PI) (log n)) (+ (log PI) (log n))) into (pow (+ (log PI) (log n)) 2)
15.914 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) into (* (sqrt 2) (pow (+ (log PI) (log n)) 2))
15.915 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) 0) into 0
15.915 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.916 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
15.916 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.917 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
15.917 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n)))
15.918 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log PI) (log n))) 0) into 0
15.918 * [backup-simplify]: Simplify (* +nan.0 0) into 0
15.918 * [backup-simplify]: Simplify (- 0) into 0
15.918 * [backup-simplify]: Simplify (+ 0 0) into 0
15.919 * [backup-simplify]: Simplify (- 0) into 0
15.919 * [backup-simplify]: Simplify (+ 0 0) into 0
15.919 * [backup-simplify]: Simplify (- 0) into 0
15.919 * [backup-simplify]: Simplify (+ 0 0) into 0
15.920 * [backup-simplify]: Simplify (- 0) into 0
15.920 * [backup-simplify]: Simplify (+ 0 0) into 0
15.920 * [backup-simplify]: Simplify (- 0) into 0
15.920 * [backup-simplify]: Simplify (+ 0 0) into 0
15.921 * [backup-simplify]: Simplify (- 0) into 0
15.921 * [backup-simplify]: Simplify 0 into 0
15.921 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
15.922 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (sqrt 2))) into 0
15.925 * [backup-simplify]: Simplify (+ (* (* (log 2) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))
15.929 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))
15.930 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
15.932 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
15.933 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
15.934 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log PI) (log n)))) into 0
15.935 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log PI) (log n))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))
15.941 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))
15.944 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
15.949 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
15.953 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
15.960 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))
15.970 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))
15.987 * [backup-simplify]: Simplify (+ (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))
16.007 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))
16.026 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))
16.027 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.031 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
16.032 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
16.037 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
16.044 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
16.049 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
16.052 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
16.076 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))))
16.076 * [backup-simplify]: Simplify (* (/ (pow 2 (- 1/2 (/ (/ 1 k) 2))) 1) (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) into (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k))
16.076 * [approximate]: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (k n) around 0
16.076 * [taylor]: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n
16.076 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
16.076 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in n
16.076 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in n
16.076 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in n
16.076 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.076 * [taylor]: Taking taylor expansion of 1/2 in n
16.076 * [backup-simplify]: Simplify 1/2 into 1/2
16.077 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.077 * [taylor]: Taking taylor expansion of 1/2 in n
16.077 * [backup-simplify]: Simplify 1/2 into 1/2
16.077 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.077 * [taylor]: Taking taylor expansion of k in n
16.077 * [backup-simplify]: Simplify k into k
16.077 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.077 * [taylor]: Taking taylor expansion of (log 2) in n
16.077 * [taylor]: Taking taylor expansion of 2 in n
16.077 * [backup-simplify]: Simplify 2 into 2
16.077 * [backup-simplify]: Simplify (log 2) into (log 2)
16.077 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.077 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.077 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.077 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
16.078 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
16.078 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
16.078 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
16.078 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
16.078 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.078 * [taylor]: Taking taylor expansion of 1/2 in n
16.078 * [backup-simplify]: Simplify 1/2 into 1/2
16.078 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.078 * [taylor]: Taking taylor expansion of 1/2 in n
16.078 * [backup-simplify]: Simplify 1/2 into 1/2
16.078 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.078 * [taylor]: Taking taylor expansion of k in n
16.078 * [backup-simplify]: Simplify k into k
16.078 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.078 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
16.078 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.078 * [taylor]: Taking taylor expansion of PI in n
16.078 * [backup-simplify]: Simplify PI into PI
16.078 * [taylor]: Taking taylor expansion of n in n
16.078 * [backup-simplify]: Simplify 0 into 0
16.078 * [backup-simplify]: Simplify 1 into 1
16.078 * [backup-simplify]: Simplify (/ PI 1) into PI
16.079 * [backup-simplify]: Simplify (log PI) into (log PI)
16.079 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.079 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.079 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.079 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
16.080 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
16.080 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
16.080 * [taylor]: Taking taylor expansion of (sqrt k) in n
16.080 * [taylor]: Taking taylor expansion of k in n
16.080 * [backup-simplify]: Simplify k into k
16.080 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
16.080 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
16.080 * [taylor]: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k
16.080 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in k
16.080 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k
16.080 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k
16.080 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k
16.080 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
16.080 * [taylor]: Taking taylor expansion of 1/2 in k
16.080 * [backup-simplify]: Simplify 1/2 into 1/2
16.080 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.080 * [taylor]: Taking taylor expansion of 1/2 in k
16.080 * [backup-simplify]: Simplify 1/2 into 1/2
16.080 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.080 * [taylor]: Taking taylor expansion of k in k
16.080 * [backup-simplify]: Simplify 0 into 0
16.080 * [backup-simplify]: Simplify 1 into 1
16.081 * [backup-simplify]: Simplify (/ 1 1) into 1
16.081 * [taylor]: Taking taylor expansion of (log 2) in k
16.081 * [taylor]: Taking taylor expansion of 2 in k
16.081 * [backup-simplify]: Simplify 2 into 2
16.081 * [backup-simplify]: Simplify (log 2) into (log 2)
16.081 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.082 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.082 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.082 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
16.083 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
16.083 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k
16.083 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k
16.083 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k
16.083 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
16.083 * [taylor]: Taking taylor expansion of 1/2 in k
16.083 * [backup-simplify]: Simplify 1/2 into 1/2
16.083 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.083 * [taylor]: Taking taylor expansion of 1/2 in k
16.083 * [backup-simplify]: Simplify 1/2 into 1/2
16.083 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.083 * [taylor]: Taking taylor expansion of k in k
16.083 * [backup-simplify]: Simplify 0 into 0
16.083 * [backup-simplify]: Simplify 1 into 1
16.083 * [backup-simplify]: Simplify (/ 1 1) into 1
16.083 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k
16.083 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.083 * [taylor]: Taking taylor expansion of PI in k
16.083 * [backup-simplify]: Simplify PI into PI
16.083 * [taylor]: Taking taylor expansion of n in k
16.083 * [backup-simplify]: Simplify n into n
16.083 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.083 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n))
16.084 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.084 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.084 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.084 * [backup-simplify]: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
16.084 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))
16.084 * [taylor]: Taking taylor expansion of (sqrt k) in k
16.084 * [taylor]: Taking taylor expansion of k in k
16.084 * [backup-simplify]: Simplify 0 into 0
16.084 * [backup-simplify]: Simplify 1 into 1
16.085 * [backup-simplify]: Simplify (sqrt 0) into 0
16.085 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
16.085 * [taylor]: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k
16.085 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in k
16.085 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k
16.086 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k
16.086 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k
16.086 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
16.086 * [taylor]: Taking taylor expansion of 1/2 in k
16.086 * [backup-simplify]: Simplify 1/2 into 1/2
16.086 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.086 * [taylor]: Taking taylor expansion of 1/2 in k
16.086 * [backup-simplify]: Simplify 1/2 into 1/2
16.086 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.086 * [taylor]: Taking taylor expansion of k in k
16.086 * [backup-simplify]: Simplify 0 into 0
16.086 * [backup-simplify]: Simplify 1 into 1
16.086 * [backup-simplify]: Simplify (/ 1 1) into 1
16.086 * [taylor]: Taking taylor expansion of (log 2) in k
16.086 * [taylor]: Taking taylor expansion of 2 in k
16.086 * [backup-simplify]: Simplify 2 into 2
16.086 * [backup-simplify]: Simplify (log 2) into (log 2)
16.086 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.087 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.087 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.088 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
16.088 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
16.088 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k
16.088 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k
16.088 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k
16.088 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
16.088 * [taylor]: Taking taylor expansion of 1/2 in k
16.088 * [backup-simplify]: Simplify 1/2 into 1/2
16.088 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.088 * [taylor]: Taking taylor expansion of 1/2 in k
16.088 * [backup-simplify]: Simplify 1/2 into 1/2
16.088 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.088 * [taylor]: Taking taylor expansion of k in k
16.088 * [backup-simplify]: Simplify 0 into 0
16.088 * [backup-simplify]: Simplify 1 into 1
16.088 * [backup-simplify]: Simplify (/ 1 1) into 1
16.088 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k
16.088 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.088 * [taylor]: Taking taylor expansion of PI in k
16.088 * [backup-simplify]: Simplify PI into PI
16.088 * [taylor]: Taking taylor expansion of n in k
16.088 * [backup-simplify]: Simplify n into n
16.088 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.088 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n))
16.089 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.089 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.089 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.089 * [backup-simplify]: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
16.089 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))
16.090 * [taylor]: Taking taylor expansion of (sqrt k) in k
16.090 * [taylor]: Taking taylor expansion of k in k
16.090 * [backup-simplify]: Simplify 0 into 0
16.090 * [backup-simplify]: Simplify 1 into 1
16.090 * [backup-simplify]: Simplify (sqrt 0) into 0
16.091 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
16.091 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))
16.091 * [backup-simplify]: Simplify (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0
16.092 * [taylor]: Taking taylor expansion of 0 in n
16.092 * [backup-simplify]: Simplify 0 into 0
16.092 * [backup-simplify]: Simplify 0 into 0
16.092 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0
16.093 * [backup-simplify]: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))
16.093 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n
16.093 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n
16.093 * [taylor]: Taking taylor expansion of +nan.0 in n
16.093 * [backup-simplify]: Simplify +nan.0 into +nan.0
16.093 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
16.093 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
16.093 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
16.093 * [taylor]: Taking taylor expansion of (log 2) in n
16.093 * [taylor]: Taking taylor expansion of 2 in n
16.093 * [backup-simplify]: Simplify 2 into 2
16.093 * [backup-simplify]: Simplify (log 2) into (log 2)
16.093 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.093 * [taylor]: Taking taylor expansion of 1/2 in n
16.093 * [backup-simplify]: Simplify 1/2 into 1/2
16.093 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.093 * [taylor]: Taking taylor expansion of 1/2 in n
16.093 * [backup-simplify]: Simplify 1/2 into 1/2
16.093 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.093 * [taylor]: Taking taylor expansion of k in n
16.093 * [backup-simplify]: Simplify k into k
16.094 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.094 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.094 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.094 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.094 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
16.094 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
16.094 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
16.094 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
16.094 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
16.094 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.094 * [taylor]: Taking taylor expansion of 1/2 in n
16.094 * [backup-simplify]: Simplify 1/2 into 1/2
16.095 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.095 * [taylor]: Taking taylor expansion of 1/2 in n
16.095 * [backup-simplify]: Simplify 1/2 into 1/2
16.095 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.095 * [taylor]: Taking taylor expansion of k in n
16.095 * [backup-simplify]: Simplify k into k
16.095 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.095 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
16.095 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.095 * [taylor]: Taking taylor expansion of PI in n
16.095 * [backup-simplify]: Simplify PI into PI
16.095 * [taylor]: Taking taylor expansion of n in n
16.095 * [backup-simplify]: Simplify 0 into 0
16.095 * [backup-simplify]: Simplify 1 into 1
16.095 * [backup-simplify]: Simplify (/ PI 1) into PI
16.095 * [backup-simplify]: Simplify (log PI) into (log PI)
16.095 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.095 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.096 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.096 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
16.096 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
16.097 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
16.097 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))
16.098 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
16.099 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
16.100 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
16.100 * [backup-simplify]: Simplify 0 into 0
16.102 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
16.103 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0
16.105 * [backup-simplify]: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))
16.105 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n
16.105 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n
16.105 * [taylor]: Taking taylor expansion of +nan.0 in n
16.105 * [backup-simplify]: Simplify +nan.0 into +nan.0
16.105 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
16.105 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
16.105 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
16.105 * [taylor]: Taking taylor expansion of (log 2) in n
16.105 * [taylor]: Taking taylor expansion of 2 in n
16.105 * [backup-simplify]: Simplify 2 into 2
16.105 * [backup-simplify]: Simplify (log 2) into (log 2)
16.105 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.105 * [taylor]: Taking taylor expansion of 1/2 in n
16.106 * [backup-simplify]: Simplify 1/2 into 1/2
16.106 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.106 * [taylor]: Taking taylor expansion of 1/2 in n
16.106 * [backup-simplify]: Simplify 1/2 into 1/2
16.106 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.106 * [taylor]: Taking taylor expansion of k in n
16.106 * [backup-simplify]: Simplify k into k
16.106 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.106 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.106 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.106 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.110 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
16.111 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
16.111 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
16.111 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
16.111 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
16.111 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.112 * [taylor]: Taking taylor expansion of 1/2 in n
16.112 * [backup-simplify]: Simplify 1/2 into 1/2
16.112 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.112 * [taylor]: Taking taylor expansion of 1/2 in n
16.112 * [backup-simplify]: Simplify 1/2 into 1/2
16.112 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.112 * [taylor]: Taking taylor expansion of k in n
16.112 * [backup-simplify]: Simplify k into k
16.112 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.112 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
16.112 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.112 * [taylor]: Taking taylor expansion of PI in n
16.112 * [backup-simplify]: Simplify PI into PI
16.112 * [taylor]: Taking taylor expansion of n in n
16.112 * [backup-simplify]: Simplify 0 into 0
16.112 * [backup-simplify]: Simplify 1 into 1
16.113 * [backup-simplify]: Simplify (/ PI 1) into PI
16.113 * [backup-simplify]: Simplify (log PI) into (log PI)
16.113 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.113 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.113 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.114 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
16.115 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
16.116 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
16.117 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))
16.118 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
16.119 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
16.120 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
16.122 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.123 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
16.124 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.124 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
16.125 * [backup-simplify]: Simplify (- 0) into 0
16.125 * [backup-simplify]: Simplify (+ 0 0) into 0
16.126 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
16.127 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0
16.128 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.128 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.129 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
16.129 * [backup-simplify]: Simplify (- 0) into 0
16.130 * [backup-simplify]: Simplify (+ 0 0) into 0
16.131 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
16.132 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
16.133 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.134 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into 0
16.136 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
16.136 * [backup-simplify]: Simplify (- 0) into 0
16.136 * [backup-simplify]: Simplify 0 into 0
16.136 * [backup-simplify]: Simplify 0 into 0
16.140 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
16.141 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
16.143 * [backup-simplify]: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))
16.143 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n
16.143 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n
16.143 * [taylor]: Taking taylor expansion of +nan.0 in n
16.143 * [backup-simplify]: Simplify +nan.0 into +nan.0
16.143 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
16.143 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
16.143 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
16.143 * [taylor]: Taking taylor expansion of (log 2) in n
16.143 * [taylor]: Taking taylor expansion of 2 in n
16.143 * [backup-simplify]: Simplify 2 into 2
16.144 * [backup-simplify]: Simplify (log 2) into (log 2)
16.144 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.144 * [taylor]: Taking taylor expansion of 1/2 in n
16.144 * [backup-simplify]: Simplify 1/2 into 1/2
16.144 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.144 * [taylor]: Taking taylor expansion of 1/2 in n
16.144 * [backup-simplify]: Simplify 1/2 into 1/2
16.144 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.144 * [taylor]: Taking taylor expansion of k in n
16.144 * [backup-simplify]: Simplify k into k
16.144 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.144 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.144 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.144 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.145 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
16.145 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
16.145 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
16.145 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
16.145 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
16.145 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.145 * [taylor]: Taking taylor expansion of 1/2 in n
16.145 * [backup-simplify]: Simplify 1/2 into 1/2
16.145 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.146 * [taylor]: Taking taylor expansion of 1/2 in n
16.146 * [backup-simplify]: Simplify 1/2 into 1/2
16.146 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.146 * [taylor]: Taking taylor expansion of k in n
16.146 * [backup-simplify]: Simplify k into k
16.146 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.146 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
16.146 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.146 * [taylor]: Taking taylor expansion of PI in n
16.146 * [backup-simplify]: Simplify PI into PI
16.146 * [taylor]: Taking taylor expansion of n in n
16.146 * [backup-simplify]: Simplify 0 into 0
16.146 * [backup-simplify]: Simplify 1 into 1
16.146 * [backup-simplify]: Simplify (/ PI 1) into PI
16.147 * [backup-simplify]: Simplify (log PI) into (log PI)
16.147 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.147 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.147 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.148 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
16.148 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
16.149 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
16.150 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))
16.151 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
16.152 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
16.153 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
16.157 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 3))))))))
16.158 * [backup-simplify]: Simplify (* (/ (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) 1) (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) into (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k)))
16.158 * [approximate]: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (k n) around 0
16.158 * [taylor]: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n
16.158 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
16.158 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.158 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
16.158 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
16.158 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.158 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.158 * [taylor]: Taking taylor expansion of 1/2 in n
16.158 * [backup-simplify]: Simplify 1/2 into 1/2
16.158 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.158 * [taylor]: Taking taylor expansion of k in n
16.159 * [backup-simplify]: Simplify k into k
16.159 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.159 * [taylor]: Taking taylor expansion of 1/2 in n
16.159 * [backup-simplify]: Simplify 1/2 into 1/2
16.159 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
16.159 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
16.159 * [taylor]: Taking taylor expansion of -1 in n
16.159 * [backup-simplify]: Simplify -1 into -1
16.159 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.159 * [taylor]: Taking taylor expansion of PI in n
16.159 * [backup-simplify]: Simplify PI into PI
16.159 * [taylor]: Taking taylor expansion of n in n
16.159 * [backup-simplify]: Simplify 0 into 0
16.159 * [backup-simplify]: Simplify 1 into 1
16.159 * [backup-simplify]: Simplify (/ PI 1) into PI
16.160 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
16.161 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
16.161 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.161 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.162 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
16.164 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
16.165 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
16.165 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.165 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in n
16.165 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in n
16.165 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.165 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.165 * [taylor]: Taking taylor expansion of 1/2 in n
16.165 * [backup-simplify]: Simplify 1/2 into 1/2
16.165 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.165 * [taylor]: Taking taylor expansion of k in n
16.165 * [backup-simplify]: Simplify k into k
16.165 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.165 * [taylor]: Taking taylor expansion of 1/2 in n
16.165 * [backup-simplify]: Simplify 1/2 into 1/2
16.165 * [taylor]: Taking taylor expansion of (log 2) in n
16.165 * [taylor]: Taking taylor expansion of 2 in n
16.165 * [backup-simplify]: Simplify 2 into 2
16.165 * [backup-simplify]: Simplify (log 2) into (log 2)
16.166 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.166 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.166 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
16.167 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
16.167 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
16.167 * [taylor]: Taking taylor expansion of (/ -1 k) in n
16.167 * [taylor]: Taking taylor expansion of -1 in n
16.167 * [backup-simplify]: Simplify -1 into -1
16.167 * [taylor]: Taking taylor expansion of k in n
16.167 * [backup-simplify]: Simplify k into k
16.167 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
16.167 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
16.167 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
16.167 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
16.169 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
16.170 * [backup-simplify]: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (sqrt (/ -1 k)))
16.170 * [taylor]: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k
16.170 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
16.170 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
16.170 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k
16.170 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k
16.171 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
16.171 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.171 * [taylor]: Taking taylor expansion of 1/2 in k
16.171 * [backup-simplify]: Simplify 1/2 into 1/2
16.171 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.171 * [taylor]: Taking taylor expansion of k in k
16.171 * [backup-simplify]: Simplify 0 into 0
16.171 * [backup-simplify]: Simplify 1 into 1
16.171 * [backup-simplify]: Simplify (/ 1 1) into 1
16.171 * [taylor]: Taking taylor expansion of 1/2 in k
16.171 * [backup-simplify]: Simplify 1/2 into 1/2
16.171 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k
16.171 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k
16.171 * [taylor]: Taking taylor expansion of -1 in k
16.171 * [backup-simplify]: Simplify -1 into -1
16.171 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.171 * [taylor]: Taking taylor expansion of PI in k
16.171 * [backup-simplify]: Simplify PI into PI
16.171 * [taylor]: Taking taylor expansion of n in k
16.171 * [backup-simplify]: Simplify n into n
16.171 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.172 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n))
16.172 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n)))
16.172 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.172 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.172 * [backup-simplify]: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
16.173 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
16.173 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
16.173 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k
16.173 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k
16.173 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
16.173 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.173 * [taylor]: Taking taylor expansion of 1/2 in k
16.173 * [backup-simplify]: Simplify 1/2 into 1/2
16.173 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.173 * [taylor]: Taking taylor expansion of k in k
16.173 * [backup-simplify]: Simplify 0 into 0
16.173 * [backup-simplify]: Simplify 1 into 1
16.173 * [backup-simplify]: Simplify (/ 1 1) into 1
16.173 * [taylor]: Taking taylor expansion of 1/2 in k
16.173 * [backup-simplify]: Simplify 1/2 into 1/2
16.173 * [taylor]: Taking taylor expansion of (log 2) in k
16.173 * [taylor]: Taking taylor expansion of 2 in k
16.173 * [backup-simplify]: Simplify 2 into 2
16.173 * [backup-simplify]: Simplify (log 2) into (log 2)
16.174 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.174 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.174 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
16.175 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
16.175 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
16.175 * [taylor]: Taking taylor expansion of (/ -1 k) in k
16.175 * [taylor]: Taking taylor expansion of -1 in k
16.175 * [backup-simplify]: Simplify -1 into -1
16.175 * [taylor]: Taking taylor expansion of k in k
16.175 * [backup-simplify]: Simplify 0 into 0
16.175 * [backup-simplify]: Simplify 1 into 1
16.175 * [backup-simplify]: Simplify (/ -1 1) into -1
16.175 * [backup-simplify]: Simplify (sqrt 0) into 0
16.176 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
16.177 * [backup-simplify]: Simplify (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))
16.177 * [backup-simplify]: Simplify (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))
16.177 * [taylor]: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k
16.177 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
16.177 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
16.177 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k
16.177 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k
16.177 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
16.177 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.177 * [taylor]: Taking taylor expansion of 1/2 in k
16.177 * [backup-simplify]: Simplify 1/2 into 1/2
16.177 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.177 * [taylor]: Taking taylor expansion of k in k
16.177 * [backup-simplify]: Simplify 0 into 0
16.177 * [backup-simplify]: Simplify 1 into 1
16.177 * [backup-simplify]: Simplify (/ 1 1) into 1
16.177 * [taylor]: Taking taylor expansion of 1/2 in k
16.177 * [backup-simplify]: Simplify 1/2 into 1/2
16.177 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k
16.177 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k
16.177 * [taylor]: Taking taylor expansion of -1 in k
16.178 * [backup-simplify]: Simplify -1 into -1
16.178 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.178 * [taylor]: Taking taylor expansion of PI in k
16.178 * [backup-simplify]: Simplify PI into PI
16.178 * [taylor]: Taking taylor expansion of n in k
16.178 * [backup-simplify]: Simplify n into n
16.178 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.178 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n))
16.178 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n)))
16.178 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.178 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.178 * [backup-simplify]: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
16.178 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
16.178 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
16.178 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k
16.179 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k
16.179 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
16.179 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.179 * [taylor]: Taking taylor expansion of 1/2 in k
16.179 * [backup-simplify]: Simplify 1/2 into 1/2
16.179 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.179 * [taylor]: Taking taylor expansion of k in k
16.179 * [backup-simplify]: Simplify 0 into 0
16.179 * [backup-simplify]: Simplify 1 into 1
16.179 * [backup-simplify]: Simplify (/ 1 1) into 1
16.179 * [taylor]: Taking taylor expansion of 1/2 in k
16.179 * [backup-simplify]: Simplify 1/2 into 1/2
16.179 * [taylor]: Taking taylor expansion of (log 2) in k
16.179 * [taylor]: Taking taylor expansion of 2 in k
16.179 * [backup-simplify]: Simplify 2 into 2
16.179 * [backup-simplify]: Simplify (log 2) into (log 2)
16.179 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.180 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.180 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
16.181 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
16.181 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
16.181 * [taylor]: Taking taylor expansion of (/ -1 k) in k
16.181 * [taylor]: Taking taylor expansion of -1 in k
16.181 * [backup-simplify]: Simplify -1 into -1
16.181 * [taylor]: Taking taylor expansion of k in k
16.181 * [backup-simplify]: Simplify 0 into 0
16.181 * [backup-simplify]: Simplify 1 into 1
16.181 * [backup-simplify]: Simplify (/ -1 1) into -1
16.181 * [backup-simplify]: Simplify (sqrt 0) into 0
16.182 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
16.183 * [backup-simplify]: Simplify (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))
16.183 * [backup-simplify]: Simplify (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))
16.183 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
16.183 * [taylor]: Taking taylor expansion of +nan.0 in n
16.183 * [backup-simplify]: Simplify +nan.0 into +nan.0
16.183 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
16.183 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.183 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
16.183 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
16.183 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.183 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.183 * [taylor]: Taking taylor expansion of 1/2 in n
16.183 * [backup-simplify]: Simplify 1/2 into 1/2
16.183 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.183 * [taylor]: Taking taylor expansion of k in n
16.183 * [backup-simplify]: Simplify k into k
16.183 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.183 * [taylor]: Taking taylor expansion of 1/2 in n
16.183 * [backup-simplify]: Simplify 1/2 into 1/2
16.183 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
16.184 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
16.184 * [taylor]: Taking taylor expansion of -1 in n
16.184 * [backup-simplify]: Simplify -1 into -1
16.184 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.184 * [taylor]: Taking taylor expansion of PI in n
16.184 * [backup-simplify]: Simplify PI into PI
16.184 * [taylor]: Taking taylor expansion of n in n
16.184 * [backup-simplify]: Simplify 0 into 0
16.184 * [backup-simplify]: Simplify 1 into 1
16.184 * [backup-simplify]: Simplify (/ PI 1) into PI
16.184 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
16.185 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
16.185 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.185 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.186 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
16.187 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
16.188 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
16.188 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
16.188 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.188 * [taylor]: Taking taylor expansion of (log 2) in n
16.188 * [taylor]: Taking taylor expansion of 2 in n
16.188 * [backup-simplify]: Simplify 2 into 2
16.188 * [backup-simplify]: Simplify (log 2) into (log 2)
16.188 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.188 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.188 * [taylor]: Taking taylor expansion of 1/2 in n
16.188 * [backup-simplify]: Simplify 1/2 into 1/2
16.188 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.188 * [taylor]: Taking taylor expansion of k in n
16.188 * [backup-simplify]: Simplify k into k
16.188 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.188 * [taylor]: Taking taylor expansion of 1/2 in n
16.188 * [backup-simplify]: Simplify 1/2 into 1/2
16.188 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.188 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.189 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
16.189 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
16.190 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
16.191 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
16.192 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
16.193 * [backup-simplify]: Simplify (+ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
16.193 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
16.195 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
16.196 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))))
16.196 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n
16.196 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
16.196 * [taylor]: Taking taylor expansion of +nan.0 in n
16.196 * [backup-simplify]: Simplify +nan.0 into +nan.0
16.196 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
16.196 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.196 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
16.196 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
16.196 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.196 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.196 * [taylor]: Taking taylor expansion of 1/2 in n
16.196 * [backup-simplify]: Simplify 1/2 into 1/2
16.196 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.196 * [taylor]: Taking taylor expansion of k in n
16.196 * [backup-simplify]: Simplify k into k
16.196 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.196 * [taylor]: Taking taylor expansion of 1/2 in n
16.197 * [backup-simplify]: Simplify 1/2 into 1/2
16.197 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
16.197 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
16.197 * [taylor]: Taking taylor expansion of -1 in n
16.197 * [backup-simplify]: Simplify -1 into -1
16.197 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.197 * [taylor]: Taking taylor expansion of PI in n
16.197 * [backup-simplify]: Simplify PI into PI
16.197 * [taylor]: Taking taylor expansion of n in n
16.197 * [backup-simplify]: Simplify 0 into 0
16.197 * [backup-simplify]: Simplify 1 into 1
16.197 * [backup-simplify]: Simplify (/ PI 1) into PI
16.197 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
16.198 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
16.198 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.198 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.199 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
16.200 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
16.200 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
16.200 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
16.200 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.200 * [taylor]: Taking taylor expansion of (log 2) in n
16.200 * [taylor]: Taking taylor expansion of 2 in n
16.200 * [backup-simplify]: Simplify 2 into 2
16.201 * [backup-simplify]: Simplify (log 2) into (log 2)
16.201 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.201 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.201 * [taylor]: Taking taylor expansion of 1/2 in n
16.201 * [backup-simplify]: Simplify 1/2 into 1/2
16.201 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.201 * [taylor]: Taking taylor expansion of k in n
16.201 * [backup-simplify]: Simplify k into k
16.201 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.201 * [taylor]: Taking taylor expansion of 1/2 in n
16.201 * [backup-simplify]: Simplify 1/2 into 1/2
16.201 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.201 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.201 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
16.202 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
16.203 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
16.204 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
16.206 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))))
16.208 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))))
16.208 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.209 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
16.209 * [backup-simplify]: Simplify (+ 0 0) into 0
16.210 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
16.211 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
16.212 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0
16.213 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.214 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0
16.215 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0
16.216 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.216 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
16.216 * [backup-simplify]: Simplify (+ 0 0) into 0
16.218 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
16.219 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0
16.221 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
16.222 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
16.224 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into 0
16.224 * [backup-simplify]: Simplify 0 into 0
16.225 * [backup-simplify]: Simplify (+ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0
16.226 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.230 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
16.232 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))))
16.232 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n
16.233 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
16.233 * [taylor]: Taking taylor expansion of +nan.0 in n
16.233 * [backup-simplify]: Simplify +nan.0 into +nan.0
16.233 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
16.233 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.233 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
16.233 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
16.233 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.233 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.233 * [taylor]: Taking taylor expansion of 1/2 in n
16.233 * [backup-simplify]: Simplify 1/2 into 1/2
16.233 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.233 * [taylor]: Taking taylor expansion of k in n
16.233 * [backup-simplify]: Simplify k into k
16.233 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.233 * [taylor]: Taking taylor expansion of 1/2 in n
16.233 * [backup-simplify]: Simplify 1/2 into 1/2
16.233 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
16.233 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
16.233 * [taylor]: Taking taylor expansion of -1 in n
16.233 * [backup-simplify]: Simplify -1 into -1
16.233 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.233 * [taylor]: Taking taylor expansion of PI in n
16.233 * [backup-simplify]: Simplify PI into PI
16.233 * [taylor]: Taking taylor expansion of n in n
16.233 * [backup-simplify]: Simplify 0 into 0
16.233 * [backup-simplify]: Simplify 1 into 1
16.237 * [backup-simplify]: Simplify (/ PI 1) into PI
16.238 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
16.239 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
16.239 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.239 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.241 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
16.242 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
16.243 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
16.243 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
16.243 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.243 * [taylor]: Taking taylor expansion of (log 2) in n
16.243 * [taylor]: Taking taylor expansion of 2 in n
16.243 * [backup-simplify]: Simplify 2 into 2
16.243 * [backup-simplify]: Simplify (log 2) into (log 2)
16.244 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.244 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.244 * [taylor]: Taking taylor expansion of 1/2 in n
16.244 * [backup-simplify]: Simplify 1/2 into 1/2
16.244 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.244 * [taylor]: Taking taylor expansion of k in n
16.244 * [backup-simplify]: Simplify k into k
16.244 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.244 * [taylor]: Taking taylor expansion of 1/2 in n
16.244 * [backup-simplify]: Simplify 1/2 into 1/2
16.244 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.244 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.244 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
16.245 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
16.246 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
16.248 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
16.250 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))))
16.251 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))))
16.257 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))))))))
16.257 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1)
16.257 * [backup-simplify]: Simplify (* n PI) into (* n PI)
16.257 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0
16.257 * [taylor]: Taking taylor expansion of (* n PI) in n
16.257 * [taylor]: Taking taylor expansion of n in n
16.257 * [backup-simplify]: Simplify 0 into 0
16.257 * [backup-simplify]: Simplify 1 into 1
16.258 * [taylor]: Taking taylor expansion of PI in n
16.258 * [backup-simplify]: Simplify PI into PI
16.258 * [taylor]: Taking taylor expansion of (* n PI) in n
16.258 * [taylor]: Taking taylor expansion of n in n
16.258 * [backup-simplify]: Simplify 0 into 0
16.258 * [backup-simplify]: Simplify 1 into 1
16.258 * [taylor]: Taking taylor expansion of PI in n
16.258 * [backup-simplify]: Simplify PI into PI
16.258 * [backup-simplify]: Simplify (* 0 PI) into 0
16.258 * [backup-simplify]: Simplify 0 into 0
16.260 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.260 * [backup-simplify]: Simplify PI into PI
16.261 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.261 * [backup-simplify]: Simplify 0 into 0
16.262 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
16.262 * [backup-simplify]: Simplify 0 into 0
16.263 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.263 * [backup-simplify]: Simplify 0 into 0
16.265 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.265 * [backup-simplify]: Simplify 0 into 0
16.266 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.266 * [backup-simplify]: Simplify 0 into 0
16.268 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
16.268 * [backup-simplify]: Simplify 0 into 0
16.268 * [backup-simplify]: Simplify (* PI n) into (* n PI)
16.269 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n)
16.269 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0
16.269 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.269 * [taylor]: Taking taylor expansion of PI in n
16.269 * [backup-simplify]: Simplify PI into PI
16.269 * [taylor]: Taking taylor expansion of n in n
16.269 * [backup-simplify]: Simplify 0 into 0
16.269 * [backup-simplify]: Simplify 1 into 1
16.269 * [backup-simplify]: Simplify (/ PI 1) into PI
16.269 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.269 * [taylor]: Taking taylor expansion of PI in n
16.269 * [backup-simplify]: Simplify PI into PI
16.269 * [taylor]: Taking taylor expansion of n in n
16.269 * [backup-simplify]: Simplify 0 into 0
16.269 * [backup-simplify]: Simplify 1 into 1
16.270 * [backup-simplify]: Simplify (/ PI 1) into PI
16.270 * [backup-simplify]: Simplify PI into PI
16.271 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.271 * [backup-simplify]: Simplify 0 into 0
16.272 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.272 * [backup-simplify]: Simplify 0 into 0
16.273 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.273 * [backup-simplify]: Simplify 0 into 0
16.274 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.274 * [backup-simplify]: Simplify 0 into 0
16.275 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.275 * [backup-simplify]: Simplify 0 into 0
16.276 * [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
16.276 * [backup-simplify]: Simplify 0 into 0
16.276 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI)
16.276 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n))
16.276 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0
16.276 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
16.277 * [taylor]: Taking taylor expansion of -1 in n
16.277 * [backup-simplify]: Simplify -1 into -1
16.277 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.277 * [taylor]: Taking taylor expansion of PI in n
16.277 * [backup-simplify]: Simplify PI into PI
16.277 * [taylor]: Taking taylor expansion of n in n
16.277 * [backup-simplify]: Simplify 0 into 0
16.277 * [backup-simplify]: Simplify 1 into 1
16.277 * [backup-simplify]: Simplify (/ PI 1) into PI
16.277 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
16.277 * [taylor]: Taking taylor expansion of -1 in n
16.277 * [backup-simplify]: Simplify -1 into -1
16.277 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.277 * [taylor]: Taking taylor expansion of PI in n
16.277 * [backup-simplify]: Simplify PI into PI
16.277 * [taylor]: Taking taylor expansion of n in n
16.277 * [backup-simplify]: Simplify 0 into 0
16.277 * [backup-simplify]: Simplify 1 into 1
16.278 * [backup-simplify]: Simplify (/ PI 1) into PI
16.278 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
16.279 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
16.280 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.280 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0
16.280 * [backup-simplify]: Simplify 0 into 0
16.281 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.282 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0
16.282 * [backup-simplify]: Simplify 0 into 0
16.283 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.285 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.285 * [backup-simplify]: Simplify 0 into 0
16.286 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.287 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.287 * [backup-simplify]: Simplify 0 into 0
16.288 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.289 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.289 * [backup-simplify]: Simplify 0 into 0
16.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.292 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.292 * [backup-simplify]: Simplify 0 into 0
16.293 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI)
16.293 * * * * [progress]: [ 4 / 4 ] generating series at (2 2)
16.293 * [backup-simplify]: Simplify (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) into (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k)))
16.293 * [approximate]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0
16.293 * [taylor]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k
16.293 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k
16.293 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k
16.293 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k
16.293 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
16.293 * [taylor]: Taking taylor expansion of 1/2 in k
16.293 * [backup-simplify]: Simplify 1/2 into 1/2
16.293 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
16.293 * [taylor]: Taking taylor expansion of 1/2 in k
16.293 * [backup-simplify]: Simplify 1/2 into 1/2
16.294 * [taylor]: Taking taylor expansion of k in k
16.294 * [backup-simplify]: Simplify 0 into 0
16.294 * [backup-simplify]: Simplify 1 into 1
16.294 * [taylor]: Taking taylor expansion of (log (* n PI)) in k
16.294 * [taylor]: Taking taylor expansion of (* n PI) in k
16.294 * [taylor]: Taking taylor expansion of n in k
16.294 * [backup-simplify]: Simplify n into n
16.294 * [taylor]: Taking taylor expansion of PI in k
16.294 * [backup-simplify]: Simplify PI into PI
16.294 * [backup-simplify]: Simplify (* n PI) into (* n PI)
16.294 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI))
16.294 * [backup-simplify]: Simplify (* 1/2 0) into 0
16.295 * [backup-simplify]: Simplify (- 0) into 0
16.295 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.295 * [backup-simplify]: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI)))
16.295 * [backup-simplify]: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2)
16.295 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
16.295 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.295 * [taylor]: Taking taylor expansion of k in k
16.295 * [backup-simplify]: Simplify 0 into 0
16.295 * [backup-simplify]: Simplify 1 into 1
16.296 * [backup-simplify]: Simplify (/ 1 1) into 1
16.296 * [backup-simplify]: Simplify (sqrt 0) into 0
16.298 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
16.298 * [taylor]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n
16.298 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n
16.298 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n
16.298 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n
16.298 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
16.298 * [taylor]: Taking taylor expansion of 1/2 in n
16.298 * [backup-simplify]: Simplify 1/2 into 1/2
16.298 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
16.298 * [taylor]: Taking taylor expansion of 1/2 in n
16.298 * [backup-simplify]: Simplify 1/2 into 1/2
16.298 * [taylor]: Taking taylor expansion of k in n
16.298 * [backup-simplify]: Simplify k into k
16.298 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
16.298 * [taylor]: Taking taylor expansion of (* n PI) in n
16.298 * [taylor]: Taking taylor expansion of n in n
16.298 * [backup-simplify]: Simplify 0 into 0
16.298 * [backup-simplify]: Simplify 1 into 1
16.298 * [taylor]: Taking taylor expansion of PI in n
16.298 * [backup-simplify]: Simplify PI into PI
16.299 * [backup-simplify]: Simplify (* 0 PI) into 0
16.300 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.301 * [backup-simplify]: Simplify (log PI) into (log PI)
16.301 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
16.301 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
16.301 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
16.302 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
16.303 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
16.303 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
16.303 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
16.303 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.303 * [taylor]: Taking taylor expansion of k in n
16.303 * [backup-simplify]: Simplify k into k
16.303 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.303 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
16.303 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.304 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
16.304 * [taylor]: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n
16.304 * [taylor]: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n
16.304 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n
16.304 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n
16.304 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
16.304 * [taylor]: Taking taylor expansion of 1/2 in n
16.304 * [backup-simplify]: Simplify 1/2 into 1/2
16.304 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
16.304 * [taylor]: Taking taylor expansion of 1/2 in n
16.304 * [backup-simplify]: Simplify 1/2 into 1/2
16.304 * [taylor]: Taking taylor expansion of k in n
16.304 * [backup-simplify]: Simplify k into k
16.304 * [taylor]: Taking taylor expansion of (log (* n PI)) in n
16.304 * [taylor]: Taking taylor expansion of (* n PI) in n
16.304 * [taylor]: Taking taylor expansion of n in n
16.304 * [backup-simplify]: Simplify 0 into 0
16.304 * [backup-simplify]: Simplify 1 into 1
16.304 * [taylor]: Taking taylor expansion of PI in n
16.304 * [backup-simplify]: Simplify PI into PI
16.305 * [backup-simplify]: Simplify (* 0 PI) into 0
16.306 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.307 * [backup-simplify]: Simplify (log PI) into (log PI)
16.307 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
16.307 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
16.307 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
16.308 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
16.308 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
16.309 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
16.309 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
16.309 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.309 * [taylor]: Taking taylor expansion of k in n
16.309 * [backup-simplify]: Simplify k into k
16.309 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.309 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
16.309 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.309 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
16.310 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k)))
16.310 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k))) in k
16.310 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) in k
16.310 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) in k
16.310 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
16.310 * [taylor]: Taking taylor expansion of 1/2 in k
16.310 * [backup-simplify]: Simplify 1/2 into 1/2
16.310 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
16.310 * [taylor]: Taking taylor expansion of 1/2 in k
16.310 * [backup-simplify]: Simplify 1/2 into 1/2
16.310 * [taylor]: Taking taylor expansion of k in k
16.310 * [backup-simplify]: Simplify 0 into 0
16.310 * [backup-simplify]: Simplify 1 into 1
16.310 * [taylor]: Taking taylor expansion of (+ (log PI) (log n)) in k
16.310 * [taylor]: Taking taylor expansion of (log PI) in k
16.310 * [taylor]: Taking taylor expansion of PI in k
16.310 * [backup-simplify]: Simplify PI into PI
16.311 * [backup-simplify]: Simplify (log PI) into (log PI)
16.311 * [taylor]: Taking taylor expansion of (log n) in k
16.311 * [taylor]: Taking taylor expansion of n in k
16.311 * [backup-simplify]: Simplify n into n
16.311 * [backup-simplify]: Simplify (log n) into (log n)
16.311 * [backup-simplify]: Simplify (* 1/2 0) into 0
16.311 * [backup-simplify]: Simplify (- 0) into 0
16.312 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.312 * [backup-simplify]: Simplify (+ (log PI) (log n)) into (+ (log PI) (log n))
16.313 * [backup-simplify]: Simplify (* 1/2 (+ (log PI) (log n))) into (* 1/2 (+ (log PI) (log n)))
16.314 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n))))
16.314 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
16.314 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.314 * [taylor]: Taking taylor expansion of k in k
16.314 * [backup-simplify]: Simplify 0 into 0
16.314 * [backup-simplify]: Simplify 1 into 1
16.314 * [backup-simplify]: Simplify (/ 1 1) into 1
16.315 * [backup-simplify]: Simplify (sqrt 0) into 0
16.316 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
16.317 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) 0) into 0
16.317 * [backup-simplify]: Simplify 0 into 0
16.318 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.320 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
16.321 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
16.321 * [backup-simplify]: Simplify (- 0) into 0
16.321 * [backup-simplify]: Simplify (+ 0 0) into 0
16.322 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
16.323 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log PI) (log n)))) into 0
16.324 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
16.325 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 0) (* 0 (sqrt (/ 1 k)))) into 0
16.325 * [taylor]: Taking taylor expansion of 0 in k
16.325 * [backup-simplify]: Simplify 0 into 0
16.326 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
16.327 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
16.327 * [backup-simplify]: Simplify (+ 0 0) into 0
16.328 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
16.328 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.329 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.330 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log PI) (log n)))) into (- (+ (* 1/2 (log PI)) (* 1/2 (log n))))
16.331 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n)))))
16.334 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log PI) (log n)))) +nan.0) (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))))
16.334 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))))
16.334 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.335 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
16.336 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
16.340 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
16.340 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
16.341 * [backup-simplify]: Simplify (- 0) into 0
16.341 * [backup-simplify]: Simplify (+ 0 0) into 0
16.342 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
16.343 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log PI) (log n))))) into 0
16.345 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.346 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
16.346 * [taylor]: Taking taylor expansion of 0 in k
16.346 * [backup-simplify]: Simplify 0 into 0
16.346 * [backup-simplify]: Simplify 0 into 0
16.347 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
16.350 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
16.353 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
16.354 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
16.355 * [backup-simplify]: Simplify (+ 0 0) into 0
16.356 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
16.356 * [backup-simplify]: Simplify (- 0) into 0
16.357 * [backup-simplify]: Simplify (+ 0 0) into 0
16.358 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log PI) (log n))))) into 0
16.361 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n))))))
16.366 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log PI) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) +nan.0) (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))))))))
16.368 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))))))))
16.368 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.369 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
16.370 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.376 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
16.381 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
16.382 * [backup-simplify]: Simplify (- 0) into 0
16.382 * [backup-simplify]: Simplify (+ 0 0) into 0
16.383 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
16.384 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log PI) (log n)))))) into 0
16.386 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
16.388 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
16.388 * [taylor]: Taking taylor expansion of 0 in k
16.388 * [backup-simplify]: Simplify 0 into 0
16.388 * [backup-simplify]: Simplify 0 into 0
16.388 * [backup-simplify]: Simplify 0 into 0
16.389 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.393 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
16.399 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
16.402 * [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
16.403 * [backup-simplify]: Simplify (+ 0 0) into 0
16.404 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
16.404 * [backup-simplify]: Simplify (- 0) into 0
16.405 * [backup-simplify]: Simplify (+ 0 0) into 0
16.406 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log PI) (log n)))))) into 0
16.411 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log PI) 3)) (+ (* 1/16 (* (pow (log PI) 2) (log n))) (* 1/16 (* (log PI) (pow (log n) 2)))))) (exp (* 1/2 (+ (log PI) (log n))))))
16.421 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log PI) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log PI) 3)) (+ (* 1/16 (* (pow (log PI) 2) (log n))) (* 1/16 (* (log PI) (pow (log n) 2)))))) (exp (* 1/2 (+ (log PI) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2))))))))))))))
16.428 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2))))))))))))))
16.438 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (pow k 2)))))))))))))))))))))))
16.438 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k))
16.438 * [approximate]: Taking taylor expansion of (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0
16.438 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k
16.438 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k
16.438 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k
16.438 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k
16.438 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
16.438 * [taylor]: Taking taylor expansion of 1/2 in k
16.438 * [backup-simplify]: Simplify 1/2 into 1/2
16.438 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.438 * [taylor]: Taking taylor expansion of 1/2 in k
16.439 * [backup-simplify]: Simplify 1/2 into 1/2
16.439 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.439 * [taylor]: Taking taylor expansion of k in k
16.439 * [backup-simplify]: Simplify 0 into 0
16.439 * [backup-simplify]: Simplify 1 into 1
16.439 * [backup-simplify]: Simplify (/ 1 1) into 1
16.439 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k
16.439 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.439 * [taylor]: Taking taylor expansion of PI in k
16.439 * [backup-simplify]: Simplify PI into PI
16.439 * [taylor]: Taking taylor expansion of n in k
16.439 * [backup-simplify]: Simplify n into n
16.439 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.439 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n))
16.440 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.440 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.440 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.441 * [backup-simplify]: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
16.441 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))
16.441 * [taylor]: Taking taylor expansion of (sqrt k) in k
16.441 * [taylor]: Taking taylor expansion of k in k
16.441 * [backup-simplify]: Simplify 0 into 0
16.441 * [backup-simplify]: Simplify 1 into 1
16.441 * [backup-simplify]: Simplify (sqrt 0) into 0
16.443 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
16.443 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n
16.443 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
16.443 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
16.443 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
16.443 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.443 * [taylor]: Taking taylor expansion of 1/2 in n
16.443 * [backup-simplify]: Simplify 1/2 into 1/2
16.443 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.443 * [taylor]: Taking taylor expansion of 1/2 in n
16.443 * [backup-simplify]: Simplify 1/2 into 1/2
16.443 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.443 * [taylor]: Taking taylor expansion of k in n
16.443 * [backup-simplify]: Simplify k into k
16.443 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.443 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
16.443 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.443 * [taylor]: Taking taylor expansion of PI in n
16.443 * [backup-simplify]: Simplify PI into PI
16.443 * [taylor]: Taking taylor expansion of n in n
16.443 * [backup-simplify]: Simplify 0 into 0
16.443 * [backup-simplify]: Simplify 1 into 1
16.444 * [backup-simplify]: Simplify (/ PI 1) into PI
16.444 * [backup-simplify]: Simplify (log PI) into (log PI)
16.444 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.444 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.444 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.445 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
16.446 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
16.446 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
16.446 * [taylor]: Taking taylor expansion of (sqrt k) in n
16.446 * [taylor]: Taking taylor expansion of k in n
16.446 * [backup-simplify]: Simplify k into k
16.446 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
16.446 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
16.447 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n
16.447 * [taylor]: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
16.447 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
16.447 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
16.447 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.447 * [taylor]: Taking taylor expansion of 1/2 in n
16.447 * [backup-simplify]: Simplify 1/2 into 1/2
16.447 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.447 * [taylor]: Taking taylor expansion of 1/2 in n
16.447 * [backup-simplify]: Simplify 1/2 into 1/2
16.447 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.447 * [taylor]: Taking taylor expansion of k in n
16.447 * [backup-simplify]: Simplify k into k
16.447 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.447 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n
16.447 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.447 * [taylor]: Taking taylor expansion of PI in n
16.447 * [backup-simplify]: Simplify PI into PI
16.447 * [taylor]: Taking taylor expansion of n in n
16.447 * [backup-simplify]: Simplify 0 into 0
16.447 * [backup-simplify]: Simplify 1 into 1
16.448 * [backup-simplify]: Simplify (/ PI 1) into PI
16.448 * [backup-simplify]: Simplify (log PI) into (log PI)
16.448 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.448 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.448 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.449 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
16.449 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
16.449 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
16.449 * [taylor]: Taking taylor expansion of (sqrt k) in n
16.450 * [taylor]: Taking taylor expansion of k in n
16.450 * [backup-simplify]: Simplify k into k
16.450 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
16.450 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
16.450 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) into (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k))
16.450 * [taylor]: Taking taylor expansion of (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k
16.450 * [taylor]: Taking taylor expansion of (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
16.450 * [taylor]: Taking taylor expansion of (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
16.450 * [taylor]: Taking taylor expansion of (- (log PI) (log n)) in k
16.450 * [taylor]: Taking taylor expansion of (log PI) in k
16.450 * [taylor]: Taking taylor expansion of PI in k
16.450 * [backup-simplify]: Simplify PI into PI
16.450 * [backup-simplify]: Simplify (log PI) into (log PI)
16.450 * [taylor]: Taking taylor expansion of (log n) in k
16.450 * [taylor]: Taking taylor expansion of n in k
16.450 * [backup-simplify]: Simplify n into n
16.451 * [backup-simplify]: Simplify (log n) into (log n)
16.451 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
16.451 * [taylor]: Taking taylor expansion of 1/2 in k
16.451 * [backup-simplify]: Simplify 1/2 into 1/2
16.451 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.451 * [taylor]: Taking taylor expansion of 1/2 in k
16.451 * [backup-simplify]: Simplify 1/2 into 1/2
16.451 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.451 * [taylor]: Taking taylor expansion of k in k
16.451 * [backup-simplify]: Simplify 0 into 0
16.451 * [backup-simplify]: Simplify 1 into 1
16.451 * [backup-simplify]: Simplify (/ 1 1) into 1
16.451 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
16.451 * [backup-simplify]: Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n))
16.452 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.452 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.452 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.452 * [backup-simplify]: Simplify (* (- (log PI) (log n)) -1/2) into (* -1/2 (- (log PI) (log n)))
16.453 * [backup-simplify]: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
16.453 * [taylor]: Taking taylor expansion of (sqrt k) in k
16.453 * [taylor]: Taking taylor expansion of k in k
16.453 * [backup-simplify]: Simplify 0 into 0
16.453 * [backup-simplify]: Simplify 1 into 1
16.453 * [backup-simplify]: Simplify (sqrt 0) into 0
16.454 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
16.454 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0
16.454 * [backup-simplify]: Simplify 0 into 0
16.455 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.456 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
16.456 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.456 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
16.456 * [backup-simplify]: Simplify (- 0) into 0
16.456 * [backup-simplify]: Simplify (+ 0 0) into 0
16.457 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
16.457 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0
16.458 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.459 * [backup-simplify]: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (sqrt k))) into 0
16.459 * [taylor]: Taking taylor expansion of 0 in k
16.459 * [backup-simplify]: Simplify 0 into 0
16.459 * [backup-simplify]: Simplify 0 into 0
16.459 * [backup-simplify]: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
16.460 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
16.460 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
16.461 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.462 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
16.462 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.463 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
16.463 * [backup-simplify]: Simplify (- 0) into 0
16.463 * [backup-simplify]: Simplify (+ 0 0) into 0
16.464 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
16.465 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0
16.466 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.466 * [backup-simplify]: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
16.466 * [taylor]: Taking taylor expansion of 0 in k
16.466 * [backup-simplify]: Simplify 0 into 0
16.466 * [backup-simplify]: Simplify 0 into 0
16.466 * [backup-simplify]: Simplify 0 into 0
16.468 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
16.469 * [backup-simplify]: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
16.469 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
16.470 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
16.470 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.474 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
16.474 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.475 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
16.475 * [backup-simplify]: Simplify (- 0) into 0
16.475 * [backup-simplify]: Simplify (+ 0 0) into 0
16.476 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
16.477 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0
16.478 * [backup-simplify]: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
16.479 * [backup-simplify]: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
16.479 * [taylor]: Taking taylor expansion of 0 in k
16.479 * [backup-simplify]: Simplify 0 into 0
16.479 * [backup-simplify]: Simplify 0 into 0
16.479 * [backup-simplify]: Simplify 0 into 0
16.479 * [backup-simplify]: Simplify 0 into 0
16.482 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
16.483 * [backup-simplify]: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
16.483 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
16.485 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 3))))))))
16.485 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
16.485 * [approximate]: Taking taylor expansion of (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
16.485 * [taylor]: Taking taylor expansion of (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
16.485 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
16.485 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k
16.485 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k
16.485 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
16.485 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.485 * [taylor]: Taking taylor expansion of 1/2 in k
16.485 * [backup-simplify]: Simplify 1/2 into 1/2
16.485 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.485 * [taylor]: Taking taylor expansion of k in k
16.485 * [backup-simplify]: Simplify 0 into 0
16.485 * [backup-simplify]: Simplify 1 into 1
16.486 * [backup-simplify]: Simplify (/ 1 1) into 1
16.486 * [taylor]: Taking taylor expansion of 1/2 in k
16.486 * [backup-simplify]: Simplify 1/2 into 1/2
16.486 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k
16.486 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k
16.486 * [taylor]: Taking taylor expansion of -1 in k
16.486 * [backup-simplify]: Simplify -1 into -1
16.486 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.486 * [taylor]: Taking taylor expansion of PI in k
16.486 * [backup-simplify]: Simplify PI into PI
16.486 * [taylor]: Taking taylor expansion of n in k
16.486 * [backup-simplify]: Simplify n into n
16.486 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.486 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n))
16.487 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n)))
16.487 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.487 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.487 * [backup-simplify]: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
16.488 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
16.488 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
16.488 * [taylor]: Taking taylor expansion of (/ -1 k) in k
16.488 * [taylor]: Taking taylor expansion of -1 in k
16.488 * [backup-simplify]: Simplify -1 into -1
16.488 * [taylor]: Taking taylor expansion of k in k
16.488 * [backup-simplify]: Simplify 0 into 0
16.488 * [backup-simplify]: Simplify 1 into 1
16.488 * [backup-simplify]: Simplify (/ -1 1) into -1
16.489 * [backup-simplify]: Simplify (sqrt 0) into 0
16.490 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
16.490 * [backup-simplify]: Simplify (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)))
16.490 * [taylor]: Taking taylor expansion of (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
16.490 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.490 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
16.490 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
16.490 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.490 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.490 * [taylor]: Taking taylor expansion of 1/2 in n
16.490 * [backup-simplify]: Simplify 1/2 into 1/2
16.490 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.490 * [taylor]: Taking taylor expansion of k in n
16.490 * [backup-simplify]: Simplify k into k
16.490 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.490 * [taylor]: Taking taylor expansion of 1/2 in n
16.490 * [backup-simplify]: Simplify 1/2 into 1/2
16.490 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
16.491 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
16.491 * [taylor]: Taking taylor expansion of -1 in n
16.491 * [backup-simplify]: Simplify -1 into -1
16.491 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.491 * [taylor]: Taking taylor expansion of PI in n
16.491 * [backup-simplify]: Simplify PI into PI
16.491 * [taylor]: Taking taylor expansion of n in n
16.491 * [backup-simplify]: Simplify 0 into 0
16.491 * [backup-simplify]: Simplify 1 into 1
16.491 * [backup-simplify]: Simplify (/ PI 1) into PI
16.492 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
16.493 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
16.493 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.493 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.494 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
16.499 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
16.500 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
16.500 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
16.500 * [taylor]: Taking taylor expansion of (/ -1 k) in n
16.500 * [taylor]: Taking taylor expansion of -1 in n
16.500 * [backup-simplify]: Simplify -1 into -1
16.500 * [taylor]: Taking taylor expansion of k in n
16.500 * [backup-simplify]: Simplify k into k
16.500 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
16.500 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
16.500 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
16.500 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
16.501 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k)))
16.501 * [taylor]: Taking taylor expansion of (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
16.501 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
16.502 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
16.502 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
16.502 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
16.502 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.502 * [taylor]: Taking taylor expansion of 1/2 in n
16.502 * [backup-simplify]: Simplify 1/2 into 1/2
16.502 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.502 * [taylor]: Taking taylor expansion of k in n
16.502 * [backup-simplify]: Simplify k into k
16.502 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.502 * [taylor]: Taking taylor expansion of 1/2 in n
16.502 * [backup-simplify]: Simplify 1/2 into 1/2
16.502 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n
16.502 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
16.502 * [taylor]: Taking taylor expansion of -1 in n
16.502 * [backup-simplify]: Simplify -1 into -1
16.502 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.502 * [taylor]: Taking taylor expansion of PI in n
16.502 * [backup-simplify]: Simplify PI into PI
16.502 * [taylor]: Taking taylor expansion of n in n
16.502 * [backup-simplify]: Simplify 0 into 0
16.502 * [backup-simplify]: Simplify 1 into 1
16.503 * [backup-simplify]: Simplify (/ PI 1) into PI
16.503 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
16.504 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
16.504 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.504 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
16.505 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
16.507 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
16.508 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
16.508 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
16.508 * [taylor]: Taking taylor expansion of (/ -1 k) in n
16.508 * [taylor]: Taking taylor expansion of -1 in n
16.508 * [backup-simplify]: Simplify -1 into -1
16.508 * [taylor]: Taking taylor expansion of k in n
16.508 * [backup-simplify]: Simplify k into k
16.508 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
16.508 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
16.508 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
16.508 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
16.509 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k)))
16.510 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) in k
16.510 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) in k
16.510 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) in k
16.510 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
16.510 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.510 * [taylor]: Taking taylor expansion of 1/2 in k
16.510 * [backup-simplify]: Simplify 1/2 into 1/2
16.510 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.510 * [taylor]: Taking taylor expansion of k in k
16.510 * [backup-simplify]: Simplify 0 into 0
16.510 * [backup-simplify]: Simplify 1 into 1
16.510 * [backup-simplify]: Simplify (/ 1 1) into 1
16.510 * [taylor]: Taking taylor expansion of 1/2 in k
16.510 * [backup-simplify]: Simplify 1/2 into 1/2
16.510 * [taylor]: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k
16.510 * [taylor]: Taking taylor expansion of (log (* -1 PI)) in k
16.510 * [taylor]: Taking taylor expansion of (* -1 PI) in k
16.510 * [taylor]: Taking taylor expansion of -1 in k
16.510 * [backup-simplify]: Simplify -1 into -1
16.510 * [taylor]: Taking taylor expansion of PI in k
16.510 * [backup-simplify]: Simplify PI into PI
16.511 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
16.512 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI))
16.512 * [taylor]: Taking taylor expansion of (log n) in k
16.512 * [taylor]: Taking taylor expansion of n in k
16.512 * [backup-simplify]: Simplify n into n
16.512 * [backup-simplify]: Simplify (log n) into (log n)
16.512 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.513 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.513 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
16.514 * [backup-simplify]: Simplify (+ (log (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n))
16.514 * [backup-simplify]: Simplify (* 1/2 (- (log (* -1 PI)) (log n))) into (* 1/2 (- (log (* -1 PI)) (log n)))
16.515 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
16.515 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
16.515 * [taylor]: Taking taylor expansion of (/ -1 k) in k
16.515 * [taylor]: Taking taylor expansion of -1 in k
16.515 * [backup-simplify]: Simplify -1 into -1
16.515 * [taylor]: Taking taylor expansion of k in k
16.515 * [backup-simplify]: Simplify 0 into 0
16.515 * [backup-simplify]: Simplify 1 into 1
16.515 * [backup-simplify]: Simplify (/ -1 1) into -1
16.516 * [backup-simplify]: Simplify (sqrt 0) into 0
16.516 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
16.517 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
16.518 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
16.518 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.519 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0
16.520 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0
16.520 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.520 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
16.521 * [backup-simplify]: Simplify (+ 0 0) into 0
16.521 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
16.522 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0
16.523 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
16.524 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
16.524 * [taylor]: Taking taylor expansion of 0 in k
16.524 * [backup-simplify]: Simplify 0 into 0
16.524 * [backup-simplify]: Simplify 0 into 0
16.525 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
16.526 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
16.528 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
16.529 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
16.529 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.530 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0
16.532 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0
16.532 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.532 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
16.532 * [backup-simplify]: Simplify (+ 0 0) into 0
16.533 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
16.534 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0
16.536 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.536 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.536 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
16.537 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
16.537 * [taylor]: Taking taylor expansion of 0 in k
16.537 * [backup-simplify]: Simplify 0 into 0
16.537 * [backup-simplify]: Simplify 0 into 0
16.537 * [backup-simplify]: Simplify 0 into 0
16.538 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.540 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
16.542 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
16.543 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
16.547 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))))))))
16.547 * * * [progress]: simplifying candidates
16.547 * * * * [progress]: [ 1 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (exp (* (+ (log n) (log PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
16.547 * * * * [progress]: [ 2 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (exp (* (log (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
16.547 * * * * [progress]: [ 3 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (exp (* (log (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
16.547 * * * * [progress]: [ 4 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))))>
16.547 * * * * [progress]: [ 5 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))))>
16.547 * * * * [progress]: [ 6 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (/ (pow (* n PI) 1/2) (pow (* n PI) (/ k 2))) (sqrt k))))>
16.547 * * * * [progress]: [ 7 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (pow (* n PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))))>
16.548 * * * * [progress]: [ 8 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (pow (* n PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))))>
16.548 * * * * [progress]: [ 9 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (pow (* n PI) 1) (- 1/2 (/ k 2))) (sqrt k))))>
16.548 * * * * [progress]: [ 10 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (pow (* n PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k))))>
16.548 * * * * [progress]: [ 11 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (pow (* n PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k))))>
16.548 * * * * [progress]: [ 12 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (pow (* n PI) 1) (- 1/2 (/ k 2))) (sqrt k))))>
16.548 * * * * [progress]: [ 13 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (pow (* n PI) 1/2) (pow (* n PI) (- (/ k 2)))) (sqrt k))))>
16.548 * * * * [progress]: [ 14 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (pow (* n PI) 1/2) (pow (* n PI) (- (/ k 2)))) (sqrt k))))>
16.548 * * * * [progress]: [ 15 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k))))>
16.548 * * * * [progress]: [ 16 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (pow (* n PI) (- 1/2 (/ k 2))) 1) (sqrt k))))>
16.548 * * * * [progress]: [ 17 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (exp (log (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k))))>
16.548 * * * * [progress]: [ 18 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (log (exp (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k))))>
16.548 * * * * [progress]: [ 19 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k))))>
16.548 * * * * [progress]: [ 20 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (cbrt (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k))))>
16.549 * * * * [progress]: [ 21 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k))))>
16.549 * * * * [progress]: [ 22 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* 1 (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))>
16.549 * * * * [progress]: [ 23 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
16.549 * * * * [progress]: [ 24 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (posit16->real (real->posit16 (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k))))>
16.549 * * * * [progress]: [ 25 / 291 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1))>
16.549 * * * * [progress]: [ 26 / 291 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1))>
16.549 * * * * [progress]: [ 27 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.549 * * * * [progress]: [ 28 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.549 * * * * [progress]: [ 29 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.549 * * * * [progress]: [ 30 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))))>
16.549 * * * * [progress]: [ 31 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.549 * * * * [progress]: [ 32 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.549 * * * * [progress]: [ 33 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.549 * * * * [progress]: [ 34 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.550 * * * * [progress]: [ 35 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))))>
16.550 * * * * [progress]: [ 36 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.550 * * * * [progress]: [ 37 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.550 * * * * [progress]: [ 38 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.550 * * * * [progress]: [ 39 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.550 * * * * [progress]: [ 40 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))))>
16.550 * * * * [progress]: [ 41 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.550 * * * * [progress]: [ 42 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.550 * * * * [progress]: [ 43 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.550 * * * * [progress]: [ 44 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.550 * * * * [progress]: [ 45 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))))>
16.550 * * * * [progress]: [ 46 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.550 * * * * [progress]: [ 47 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (pow 2 (- 1/2 (/ k 2)))) 0) (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.550 * * * * [progress]: [ 48 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (pow 2 (- 1/2 (/ k 2)))) 0) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.551 * * * * [progress]: [ 49 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (pow 2 (- 1/2 (/ k 2)))) 0) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.551 * * * * [progress]: [ 50 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (pow 2 (- 1/2 (/ k 2)))) 0) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))))>
16.551 * * * * [progress]: [ 51 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (pow 2 (- 1/2 (/ k 2)))) 0) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.551 * * * * [progress]: [ 52 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (pow 2 (- 1/2 (/ k 2)))) (log 1)) (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.551 * * * * [progress]: [ 53 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (pow 2 (- 1/2 (/ k 2)))) (log 1)) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.551 * * * * [progress]: [ 54 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (pow 2 (- 1/2 (/ k 2)))) (log 1)) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.551 * * * * [progress]: [ 55 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (pow 2 (- 1/2 (/ k 2)))) (log 1)) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))))>
16.551 * * * * [progress]: [ 56 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (pow 2 (- 1/2 (/ k 2)))) (log 1)) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.551 * * * * [progress]: [ 57 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ (pow 2 (- 1/2 (/ k 2))) 1)) (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.551 * * * * [progress]: [ 58 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ (pow 2 (- 1/2 (/ k 2))) 1)) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.551 * * * * [progress]: [ 59 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ (pow 2 (- 1/2 (/ k 2))) 1)) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.551 * * * * [progress]: [ 60 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ (pow 2 (- 1/2 (/ k 2))) 1)) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))))>
16.551 * * * * [progress]: [ 61 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ (pow 2 (- 1/2 (/ k 2))) 1)) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.552 * * * * [progress]: [ 62 / 291 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.552 * * * * [progress]: [ 63 / 291 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.552 * * * * [progress]: [ 64 / 291 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* 1 1) 1)) (/ (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
16.552 * * * * [progress]: [ 65 / 291 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* 1 1) 1)) (* (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.552 * * * * [progress]: [ 66 / 291 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
16.552 * * * * [progress]: [ 67 / 291 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (pow 2 (- 1/2 (/ k 2))) 1)) (* (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.552 * * * * [progress]: [ 68 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.552 * * * * [progress]: [ 69 / 291 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.552 * * * * [progress]: [ 70 / 291 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.552 * * * * [progress]: [ 71 / 291 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (* 1 (sqrt k))))>
16.552 * * * * [progress]: [ 72 / 291 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.552 * * * * [progress]: [ 73 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (sqrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.552 * * * * [progress]: [ 74 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (sqrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.553 * * * * [progress]: [ 75 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (sqrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.553 * * * * [progress]: [ 76 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (sqrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.553 * * * * [progress]: [ 77 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (sqrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.553 * * * * [progress]: [ 78 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.553 * * * * [progress]: [ 79 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.553 * * * * [progress]: [ 80 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.553 * * * * [progress]: [ 81 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.553 * * * * [progress]: [ 82 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.553 * * * * [progress]: [ 83 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) 1) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) 1) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.553 * * * * [progress]: [ 84 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.553 * * * * [progress]: [ 85 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.553 * * * * [progress]: [ 86 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.554 * * * * [progress]: [ 87 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.554 * * * * [progress]: [ 88 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.554 * * * * [progress]: [ 89 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.554 * * * * [progress]: [ 90 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.554 * * * * [progress]: [ 91 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.554 * * * * [progress]: [ 92 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.554 * * * * [progress]: [ 93 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) 1) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) 1) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.554 * * * * [progress]: [ 94 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.554 * * * * [progress]: [ 95 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.554 * * * * [progress]: [ 96 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.554 * * * * [progress]: [ 97 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.554 * * * * [progress]: [ 98 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.555 * * * * [progress]: [ 99 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.555 * * * * [progress]: [ 100 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.555 * * * * [progress]: [ 101 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.555 * * * * [progress]: [ 102 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.555 * * * * [progress]: [ 103 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) 1) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) 1) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.555 * * * * [progress]: [ 104 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.555 * * * * [progress]: [ 105 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.555 * * * * [progress]: [ 106 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.555 * * * * [progress]: [ 107 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.555 * * * * [progress]: [ 108 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.555 * * * * [progress]: [ 109 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.555 * * * * [progress]: [ 110 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))>
16.556 * * * * [progress]: [ 111 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (cbrt k)))))>
16.556 * * * * [progress]: [ 112 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))>
16.556 * * * * [progress]: [ 113 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (sqrt 1))) (/ (pow (* n PI) (- (/ k 2))) (sqrt k))))>
16.556 * * * * [progress]: [ 114 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))>
16.556 * * * * [progress]: [ 115 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) 1)) (/ (pow (* n PI) (- (/ k 2))) (sqrt k))))>
16.556 * * * * [progress]: [ 116 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))>
16.556 * * * * [progress]: [ 117 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (cbrt k)))))>
16.556 * * * * [progress]: [ 118 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))>
16.556 * * * * [progress]: [ 119 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (sqrt 1))) (/ (pow (* n PI) (- (/ k 2))) (sqrt k))))>
16.556 * * * * [progress]: [ 120 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))>
16.556 * * * * [progress]: [ 121 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) 1)) (/ (pow (* n PI) (- (/ k 2))) (sqrt k))))>
16.556 * * * * [progress]: [ 122 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
16.557 * * * * [progress]: [ 123 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow n (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
16.557 * * * * [progress]: [ 124 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
16.557 * * * * [progress]: [ 125 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow n (- 1/2 (/ k 2))) (sqrt 1))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))>
16.557 * * * * [progress]: [ 126 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
16.557 * * * * [progress]: [ 127 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow n (- 1/2 (/ k 2))) 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))>
16.557 * * * * [progress]: [ 128 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
16.557 * * * * [progress]: [ 129 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
16.557 * * * * [progress]: [ 130 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
16.557 * * * * [progress]: [ 131 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt 1))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))>
16.557 * * * * [progress]: [ 132 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
16.557 * * * * [progress]: [ 133 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1)) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))>
16.557 * * * * [progress]: [ 134 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
16.557 * * * * [progress]: [ 135 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
16.558 * * * * [progress]: [ 136 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
16.558 * * * * [progress]: [ 137 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt 1))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))>
16.558 * * * * [progress]: [ 138 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
16.558 * * * * [progress]: [ 139 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))>
16.558 * * * * [progress]: [ 140 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
16.558 * * * * [progress]: [ 141 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
16.558 * * * * [progress]: [ 142 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
16.558 * * * * [progress]: [ 143 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ 1 (sqrt 1))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
16.558 * * * * [progress]: [ 144 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
16.558 * * * * [progress]: [ 145 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ 1 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
16.558 * * * * [progress]: [ 146 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))>
16.558 * * * * [progress]: [ 147 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))>
16.559 * * * * [progress]: [ 148 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
16.559 * * * * [progress]: [ 149 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
16.559 * * * * [progress]: [ 150 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
16.559 * * * * [progress]: [ 151 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
16.559 * * * * [progress]: [ 152 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
16.559 * * * * [progress]: [ 153 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (pow (* n PI) (- 1/2 (/ k 2)))) (/ 1 (sqrt k))))>
16.559 * * * * [progress]: [ 154 / 291 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (cbrt (/ (pow 2 (- 1/2 (/ k 2))) 1))) (* (cbrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.559 * * * * [progress]: [ 155 / 291 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (* (sqrt (/ (pow 2 (- 1/2 (/ k 2))) 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.559 * * * * [progress]: [ 156 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 1/2) (* (cbrt 1) (cbrt 1))) (* (/ (pow 2 (- (/ k 2))) (cbrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.559 * * * * [progress]: [ 157 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 1/2) (sqrt 1)) (* (/ (pow 2 (- (/ k 2))) (sqrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.559 * * * * [progress]: [ 158 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 1/2) 1) (* (/ (pow 2 (- (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.559 * * * * [progress]: [ 159 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 1/2) (* (cbrt 1) (cbrt 1))) (* (/ (pow 2 (- (/ k 2))) (cbrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.559 * * * * [progress]: [ 160 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 1/2) (sqrt 1)) (* (/ (pow 2 (- (/ k 2))) (sqrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.560 * * * * [progress]: [ 161 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 1/2) 1) (* (/ (pow 2 (- (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.560 * * * * [progress]: [ 162 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (cbrt 2) (cbrt 2)) (- 1/2 (/ k 2))) (* (cbrt 1) (cbrt 1))) (* (/ (pow (cbrt 2) (- 1/2 (/ k 2))) (cbrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.560 * * * * [progress]: [ 163 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (cbrt 2) (cbrt 2)) (- 1/2 (/ k 2))) (sqrt 1)) (* (/ (pow (cbrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.560 * * * * [progress]: [ 164 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (cbrt 2) (cbrt 2)) (- 1/2 (/ k 2))) 1) (* (/ (pow (cbrt 2) (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.560 * * * * [progress]: [ 165 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (* (cbrt 1) (cbrt 1))) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (cbrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.560 * * * * [progress]: [ 166 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.560 * * * * [progress]: [ 167 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) 1) (* (/ (pow (sqrt 2) (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.560 * * * * [progress]: [ 168 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 1 (- 1/2 (/ k 2))) (* (cbrt 1) (cbrt 1))) (* (/ (pow 2 (- 1/2 (/ k 2))) (cbrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.560 * * * * [progress]: [ 169 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 1 (- 1/2 (/ k 2))) (sqrt 1)) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.560 * * * * [progress]: [ 170 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 1 (- 1/2 (/ k 2))) 1) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 171 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) (* (cbrt 1) (cbrt 1))) (* (/ (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 172 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) (sqrt 1)) (* (/ (cbrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 173 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) 1) (* (/ (cbrt (pow 2 (- 1/2 (/ k 2)))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 174 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (cbrt 1) (cbrt 1))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (cbrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 175 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 176 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) 1) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 177 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt 1) (cbrt 1))) (* (/ (pow 2 (- 1/2 (/ k 2))) (cbrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 178 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 179 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 180 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (* (cbrt 1) (cbrt 1))) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (cbrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 181 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 182 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) 1) (* (/ (pow 2 (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.561 * * * * [progress]: [ 183 / 291 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.562 * * * * [progress]: [ 184 / 291 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.562 * * * * [progress]: [ 185 / 291 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>
16.562 * * * * [progress]: [ 186 / 291 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1))>
16.562 * * * * [progress]: [ 187 / 291 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.562 * * * * [progress]: [ 188 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow 2 (- 1/2 (/ k 2))) 1)))>
16.562 * * * * [progress]: [ 189 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (pow (* n PI) 1) (- 1/2 (/ k 2))) (sqrt k))))>
16.562 * * * * [progress]: [ 190 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (pow (* n PI) 1) (- 1/2 (/ k 2))) (sqrt k))))>
16.562 * * * * [progress]: [ 191 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (exp (+ (log n) (log PI))) (- 1/2 (/ k 2))) (sqrt k))))>
16.562 * * * * [progress]: [ 192 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (exp (log (* n PI))) (- 1/2 (/ k 2))) (sqrt k))))>
16.562 * * * * [progress]: [ 193 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (log (exp (* n PI))) (- 1/2 (/ k 2))) (sqrt k))))>
16.562 * * * * [progress]: [ 194 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (cbrt (* (* (* n n) n) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt k))))>
16.562 * * * * [progress]: [ 195 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI))) (- 1/2 (/ k 2))) (sqrt k))))>
16.562 * * * * [progress]: [ 196 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (cbrt (* (* (* n PI) (* n PI)) (* n PI))) (- 1/2 (/ k 2))) (sqrt k))))>
16.562 * * * * [progress]: [ 197 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* (sqrt (* n PI)) (sqrt (* n PI))) (- 1/2 (/ k 2))) (sqrt k))))>
16.562 * * * * [progress]: [ 198 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* 1 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))))>
16.563 * * * * [progress]: [ 199 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k))))>
16.563 * * * * [progress]: [ 200 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* (* n (* (cbrt PI) (cbrt PI))) (cbrt PI)) (- 1/2 (/ k 2))) (sqrt k))))>
16.563 * * * * [progress]: [ 201 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* (* n (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k))))>
16.563 * * * * [progress]: [ 202 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* (* n 1) PI) (- 1/2 (/ k 2))) (sqrt k))))>
16.563 * * * * [progress]: [ 203 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)) (- 1/2 (/ k 2))) (sqrt k))))>
16.563 * * * * [progress]: [ 204 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* (sqrt n) (* (sqrt n) PI)) (- 1/2 (/ k 2))) (sqrt k))))>
16.563 * * * * [progress]: [ 205 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* 1 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))))>
16.563 * * * * [progress]: [ 206 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (posit16->real (real->posit16 (* n PI))) (- 1/2 (/ k 2))) (sqrt k))))>
16.563 * * * * [progress]: [ 207 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt k))))>
16.563 * * * * [progress]: [ 208 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (pow (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1)))>
16.563 * * * * [progress]: [ 209 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (exp (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.563 * * * * [progress]: [ 210 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (exp (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.563 * * * * [progress]: [ 211 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (exp (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
16.563 * * * * [progress]: [ 212 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (exp (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))))>
16.564 * * * * [progress]: [ 213 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (exp (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.564 * * * * [progress]: [ 214 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (log (exp (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.564 * * * * [progress]: [ 215 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (cbrt (/ (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
16.564 * * * * [progress]: [ 216 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (* (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.564 * * * * [progress]: [ 217 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (cbrt (* (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.564 * * * * [progress]: [ 218 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.564 * * * * [progress]: [ 219 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (- (pow (* n PI) (- 1/2 (/ k 2)))) (- (sqrt k)))))>
16.564 * * * * [progress]: [ 220 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))))))>
16.564 * * * * [progress]: [ 221 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (cbrt k))))))>
16.564 * * * * [progress]: [ 222 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) 1/2) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))))>
16.564 * * * * [progress]: [ 223 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) 1/2) (sqrt 1)) (/ (pow (* n PI) (- (/ k 2))) (sqrt k)))))>
16.564 * * * * [progress]: [ 224 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) 1/2) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))))>
16.564 * * * * [progress]: [ 225 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) 1/2) 1) (/ (pow (* n PI) (- (/ k 2))) (sqrt k)))))>
16.565 * * * * [progress]: [ 226 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))))))>
16.565 * * * * [progress]: [ 227 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (cbrt k))))))>
16.565 * * * * [progress]: [ 228 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) 1/2) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))))>
16.565 * * * * [progress]: [ 229 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) 1/2) (sqrt 1)) (/ (pow (* n PI) (- (/ k 2))) (sqrt k)))))>
16.565 * * * * [progress]: [ 230 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) 1/2) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))))>
16.565 * * * * [progress]: [ 231 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) 1/2) 1) (/ (pow (* n PI) (- (/ k 2))) (sqrt k)))))>
16.565 * * * * [progress]: [ 232 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))))>
16.565 * * * * [progress]: [ 233 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k))))))>
16.565 * * * * [progress]: [ 234 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
16.565 * * * * [progress]: [ 235 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))>
16.565 * * * * [progress]: [ 236 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
16.565 * * * * [progress]: [ 237 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow n (- 1/2 (/ k 2))) 1) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))>
16.565 * * * * [progress]: [ 238 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))>
16.566 * * * * [progress]: [ 239 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k))))))>
16.566 * * * * [progress]: [ 240 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.566 * * * * [progress]: [ 241 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt 1)) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
16.566 * * * * [progress]: [ 242 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.566 * * * * [progress]: [ 243 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
16.566 * * * * [progress]: [ 244 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))>
16.566 * * * * [progress]: [ 245 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k))))))>
16.566 * * * * [progress]: [ 246 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.566 * * * * [progress]: [ 247 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
16.566 * * * * [progress]: [ 248 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
16.566 * * * * [progress]: [ 249 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
16.566 * * * * [progress]: [ 250 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))))>
16.566 * * * * [progress]: [ 251 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (cbrt k))))))>
16.567 * * * * [progress]: [ 252 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
16.567 * * * * [progress]: [ 253 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ 1 (sqrt 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.567 * * * * [progress]: [ 254 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
16.567 * * * * [progress]: [ 255 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ 1 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.567 * * * * [progress]: [ 256 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k))))))>
16.567 * * * * [progress]: [ 257 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k))))))>
16.567 * * * * [progress]: [ 258 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.567 * * * * [progress]: [ 259 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
16.567 * * * * [progress]: [ 260 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
16.567 * * * * [progress]: [ 261 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
16.567 * * * * [progress]: [ 262 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* 1 (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
16.567 * * * * [progress]: [ 263 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (pow (* n PI) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))))>
16.567 * * * * [progress]: [ 264 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ 1 (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2)))))))>
16.568 * * * * [progress]: [ 265 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))))>
16.568 * * * * [progress]: [ 266 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k)))))>
16.568 * * * * [progress]: [ 267 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))))>
16.568 * * * * [progress]: [ 268 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k))))>
16.568 * * * * [progress]: [ 269 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))))>
16.568 * * * * [progress]: [ 270 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) 1) (sqrt k))))>
16.568 * * * * [progress]: [ 271 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (/ (sqrt k) (pow (* n PI) (- (/ k 2)))))))>
16.568 * * * * [progress]: [ 272 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (/ (sqrt k) (pow (* n PI) (- (/ k 2)))))))>
16.568 * * * * [progress]: [ 273 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))))>
16.568 * * * * [progress]: [ 274 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))))))>
16.568 * * * * [progress]: [ 275 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n PI) (- 1/2 (/ k 2))))))))>
16.568 * * * * [progress]: [ 276 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ 1 (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2)))))))>
16.569 * * * * [progress]: [ 277 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2))))))>
16.569 * * * * [progress]: [ 278 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) 1/2) (* (sqrt k) (pow (* n PI) (/ k 2))))))>
16.569 * * * * [progress]: [ 279 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (posit16->real (real->posit16 (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
16.569 * * * * [progress]: [ 280 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))))) (sqrt k))))>
16.569 * * * * [progress]: [ 281 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (sqrt k))))>
16.569 * * * * [progress]: [ 282 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (sqrt k))))>
16.569 * * * * [progress]: [ 283 / 291 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))))>
16.569 * * * * [progress]: [ 284 / 291 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 3)))))))))>
16.569 * * * * [progress]: [ 285 / 291 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))))))))))>
16.569 * * * * [progress]: [ 286 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
16.569 * * * * [progress]: [ 287 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
16.569 * * * * [progress]: [ 288 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
16.570 * * * * [progress]: [ 289 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (pow k 2)))))))))))))))))))))))))>
16.570 * * * * [progress]: [ 290 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 3))))))))))>
16.570 * * * * [progress]: [ 291 / 291 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))))))))))>
16.577 * [simplify]: Simplifying:
  (* (+ (log n) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* n PI)) (- 1/2 (/ k 2)))
  (* (log (* n PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n PI) 1/2)
  (pow (* n PI) (/ k 2))
  (pow (* n PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* n PI) 1)
  (pow (* n PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n PI) 1)
  (pow (* n PI) 1/2)
  (pow (* n PI) (- (/ k 2)))
  (pow (* n PI) 1/2)
  (pow (* n PI) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* n PI) (- 1/2 (/ k 2))))
  (exp (pow (* n PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n PI) (- 1/2 (/ k 2))))
  (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* n PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* n PI) (- 1/2 (/ k 2))))
  (pow (* n PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n PI) (- 1/2 (/ k 2))))
  (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) 0) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))
  (+ (- (* (log 2) (- 1/2 (/ k 2))) (log 1)) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (+ (- (log (pow 2 (- 1/2 (/ k 2)))) 0) (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
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  (exp (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
  (* (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* n PI) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n PI) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n PI) 1/2) (sqrt 1))
  (/ (pow (* n PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n PI) 1/2) 1)
  (/ (pow (* n PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n PI) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n PI) 1/2) (sqrt 1))
  (/ (pow (* n PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n PI) 1/2) 1)
  (/ (pow (* n PI) (- (/ k 2))) (sqrt k))
  (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) 1)
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
  (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt 1))
  (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1)
  (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt 1))
  (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1)
  (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))
  (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))
  (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))
  (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) 1)
  (/ (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2))))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n PI) (- 1/2 (/ k 2))) 1)
  (/ (sqrt k) (pow (* n PI) (- (/ k 2))))
  (/ (sqrt k) (pow (* n PI) (- (/ k 2))))
  (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* n PI) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* n PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (sqrt k) (pow (* n PI) (/ k 2)))
  (real->posit16 (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
  (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n)))))
  (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))
  (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))))
  (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))))))))
  (* n PI)
  (* n PI)
  (* n PI)
  (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (pow k 2)))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))))))))
16.584 * * [simplify]: iteration 0: 482 enodes
16.817 * * [simplify]: iteration 1: 1480 enodes
17.524 * * [simplify]: iteration 2: 4417 enodes
18.691 * * [simplify]: iteration complete: 5001 enodes
18.691 * * [simplify]: Extracting #0: cost 152 inf + 0
18.695 * * [simplify]: Extracting #1: cost 805 inf + 2
18.703 * * [simplify]: Extracting #2: cost 1216 inf + 5417
18.720 * * [simplify]: Extracting #3: cost 1294 inf + 35826
18.769 * * [simplify]: Extracting #4: cost 810 inf + 259956
18.857 * * [simplify]: Extracting #5: cost 312 inf + 540630
18.990 * * [simplify]: Extracting #6: cost 70 inf + 660612
19.191 * * [simplify]: Extracting #7: cost 11 inf + 695189
19.343 * * [simplify]: Extracting #8: cost 0 inf + 699001
19.496 * * [simplify]: Extracting #9: cost 0 inf + 697741
19.652 * * [simplify]: Extracting #10: cost 0 inf + 697661
19.793 * [simplify]: Simplified to:
  (* (- 1/2 (/ k 2)) (log (* n PI)))
  (* (- 1/2 (/ k 2)) (log (* n PI)))
  (* (- 1/2 (/ k 2)) (log (* n PI)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* n PI))
  (pow (* n PI) (/ k 2))
  (pow (* n PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n PI) (sqrt (- 1/2 (/ k 2))))
  (* n PI)
  (pow (* n PI) (+ (sqrt (/ k 2)) (sqrt 1/2)))
  (pow (* n PI) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* n PI)
  (sqrt (* n PI))
  (pow (* n PI) (- (/ k 2)))
  (sqrt (* n PI))
  (pow (* n PI) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* n PI)))
  (exp (pow (* n PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n PI) (- 1/2 (/ k 2))))
  (* (pow (* n PI) (- 1/2 (/ k 2))) (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))))
  (sqrt (pow (* n PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* n PI) (- 1/2 (/ k 2))))
  (pow (* n PI) (- 1/4 (/ k 4)))
  (pow (* n PI) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* n PI) (- 1/2 (/ k 2))))
  (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
  (exp (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k)))
  (* (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (cbrt (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k))) (cbrt (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k))))
  (cbrt (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k)))
  (* (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k)))
  (sqrt (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k)))
  (* (pow (* n PI) (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2))))
  (sqrt k)
  (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (pow 2 (- 1/2 (/ k 2)))))
  (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (pow 2 (- 1/2 (/ k 2)))))
  (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (pow 2 (- 1/2 (/ k 2)))))
  (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (sqrt (pow 2 (- 1/2 (/ k 2)))))
  (/ (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/4 (/ (/ k 2) 2)))) (sqrt (sqrt k)))
  (/ (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/4 (/ (/ k 2) 2)))) (sqrt (sqrt k)))
  (/ (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/4 (/ (/ k 2) 2)))) (sqrt (sqrt k)))
  (/ (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/4 (/ (/ k 2) 2)))) (sqrt (sqrt k)))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))
  (/ (* (pow (sqrt 2) (- 1/4 (/ k 4))) (* (pow (sqrt 2) (- 1/4 (/ k 4))) (pow (* n PI) (- 1/4 (/ k 4))))) (sqrt (sqrt k)))
  (/ (* (pow (sqrt 2) (- 1/4 (/ k 4))) (* (pow (sqrt 2) (- 1/4 (/ k 4))) (pow (* n PI) (- 1/4 (/ k 4))))) (sqrt (sqrt k)))
  (/ (* (pow (sqrt 2) (- 1/4 (/ k 4))) (* (pow (sqrt 2) (- 1/4 (/ k 4))) (pow (* n PI) (- 1/4 (/ k 4))))) (sqrt (sqrt k)))
  (/ (* (pow (sqrt 2) (- 1/4 (/ k 4))) (* (pow (sqrt 2) (- 1/4 (/ k 4))) (pow (* n PI) (- 1/4 (/ k 4))))) (sqrt (sqrt k)))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))
  (* (pow (sqrt 2) (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))
  (/ (* (pow (sqrt 2) (- 1/4 (/ k 4))) (* (pow (sqrt 2) (- 1/4 (/ k 4))) (pow (* n PI) (- 1/4 (/ k 4))))) (sqrt (sqrt k)))
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  (* n PI)
  (* n PI)
  (+ (* (- +nan.0) (* (sqrt (* n PI)) (* k k))) (- (* (* (* (sqrt (* n PI)) (* (* k k) (log n))) (log PI)) +nan.0) (+ (+ (* (* +nan.0 (sqrt (* n PI))) (* (* k k) (log n))) (* (- +nan.0) (* (* (log n) (log n)) (* (sqrt (* n PI)) (* k k))))) (- (* (* +nan.0 (* (log PI) (sqrt (* n PI)))) k) (- (* (* (* (sqrt (* n PI)) (* k k)) +nan.0) (* (log PI) (log PI))) (+ (- (* k (* +nan.0 (sqrt (* n PI)))) (* +nan.0 (sqrt (* n PI)))) (* (* +nan.0 (sqrt (* n PI))) (- (* k (log n)) (* (log PI) (* k k))))))))))
  (+ (* (/ (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) (* k k)) (- +nan.0)) (* +nan.0 (- (/ (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) k) (/ (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) (* k (* k k))))))
  (+ (* (/ (pow (/ (- PI) (/ -1 n)) (- 1/2 (/ k 2))) k) (- +nan.0)) (* +nan.0 (- (/ (pow (/ (- PI) (/ -1 n)) (- 1/2 (/ k 2))) (* k k)) (pow (/ (- PI) (/ -1 n)) (- 1/2 (/ k 2))))))
19.846 * * * [progress]: adding candidates to table
21.107 * [progress]: [Phase 3 of 3] Extracting.
21.107 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (cbrt 1) (cbrt 1))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2))))))> #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (/ (* (pow (* (cbrt 2) (cbrt 2)) (- 1/2 (/ k 2))) (* (pow (cbrt 2) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))> #<alt (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))))> #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>)
21.109 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2 PI) n) n k)
21.109 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (* (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (cbrt 1) (cbrt 1))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2))))))> #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (/ (* (pow (* (cbrt 2) (cbrt 2)) (- 1/2 (/ k 2))) (* (pow (cbrt 2) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))> #<alt (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))))> #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>)
21.191 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (cbrt 1) (cbrt 1))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2))))))> #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (/ (* (pow (* (cbrt 2) (cbrt 2)) (- 1/2 (/ k 2))) (* (pow (cbrt 2) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))> #<alt (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))))> #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>)
21.240 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (cbrt 1) (cbrt 1))) (* (/ (sqrt (pow 2 (- 1/2 (/ k 2)))) (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2))))))> #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (/ (* (pow (* (cbrt 2) (cbrt 2)) (- 1/2 (/ k 2))) (* (pow (cbrt 2) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k)))> #<alt (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))))> #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>)
21.291 * * * [regime]: Found split indices: #<option (#s(si 5 255))>
21.291 * [simplify]: Simplifying:
  (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
21.291 * * [simplify]: iteration 0: 13 enodes
21.292 * * [simplify]: iteration 1: 15 enodes
21.292 * * [simplify]: iteration complete: 15 enodes
21.292 * * [simplify]: Extracting #0: cost 1 inf + 0
21.292 * * [simplify]: Extracting #1: cost 3 inf + 0
21.292 * * [simplify]: Extracting #2: cost 6 inf + 0
21.292 * * [simplify]: Extracting #3: cost 8 inf + 1
21.292 * * [simplify]: Extracting #4: cost 10 inf + 43
21.292 * * [simplify]: Extracting #5: cost 6 inf + 88
21.292 * * [simplify]: Extracting #6: cost 2 inf + 841
21.293 * * [simplify]: Extracting #7: cost 0 inf + 2091
21.293 * [simplify]: Simplified to:
  (/ (* (pow (* PI n) (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (sqrt k))
29.886 * [regime-testing]: Baseline error score: 0.40431825225977597
29.888 * [regime-testing]: Oracle error score: 0.0316432413443808
29.893 * [regime-testing]: End program error score: 0.40431825225977597