70.063 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.201 * * * [progress]: [2/2] Setting up program.
0.205 * [progress]: [Phase 2 of 3] Improving.
0.205 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.205 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.205 * * [simplify]: iteration 1: (13 enodes)
0.209 * * [simplify]: iteration 2: (31 enodes)
0.220 * * [simplify]: iteration 3: (62 enodes)
0.238 * * [simplify]: iteration 4: (124 enodes)
0.305 * * [simplify]: iteration 5: (330 enodes)
0.529 * * [simplify]: iteration 6: (827 enodes)
1.411 * * [simplify]: iteration 7: (1992 enodes)
7.750 * * [simplify]: Extracting #0: cost 1 inf + 0
7.751 * * [simplify]: Extracting #1: cost 116 inf + 0
7.754 * * [simplify]: Extracting #2: cost 506 inf + 1
7.758 * * [simplify]: Extracting #3: cost 588 inf + 50
7.764 * * [simplify]: Extracting #4: cost 591 inf + 1270
7.774 * * [simplify]: Extracting #5: cost 475 inf + 39174
7.894 * * [simplify]: Extracting #6: cost 113 inf + 397134
8.106 * * [simplify]: Extracting #7: cost 0 inf + 509518
8.297 * * [simplify]: Extracting #8: cost 0 inf + 492512
8.491 * * [simplify]: Extracting #9: cost 0 inf + 481384
8.644 * * [simplify]: Extracting #10: cost 0 inf + 480399
8.847 * * [simplify]: Extracting #11: cost 0 inf + 480349
9.053 * [simplify]: Simplified to:
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
9.066 * * [progress]: iteration 1 / 4
9.066 * * * [progress]: picking best candidate
9.076 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))>
9.076 * * * [progress]: localizing error
9.118 * * * [progress]: generating rewritten candidates
9.118 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
9.138 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
9.151 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
9.177 * * * [progress]: generating series expansions
9.178 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
9.179 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
9.179 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
9.179 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
9.179 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
9.179 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
9.179 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
9.179 * [taylor]: Taking taylor expansion of 1/2 in k
9.179 * [backup-simplify]: Simplify 1/2 into 1/2
9.179 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
9.179 * [taylor]: Taking taylor expansion of 1/2 in k
9.179 * [backup-simplify]: Simplify 1/2 into 1/2
9.179 * [taylor]: Taking taylor expansion of k in k
9.179 * [backup-simplify]: Simplify 0 into 0
9.179 * [backup-simplify]: Simplify 1 into 1
9.179 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
9.179 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
9.179 * [taylor]: Taking taylor expansion of 2 in k
9.179 * [backup-simplify]: Simplify 2 into 2
9.179 * [taylor]: Taking taylor expansion of (* n PI) in k
9.180 * [taylor]: Taking taylor expansion of n in k
9.180 * [backup-simplify]: Simplify n into n
9.180 * [taylor]: Taking taylor expansion of PI in k
9.180 * [backup-simplify]: Simplify PI into PI
9.180 * [backup-simplify]: Simplify (* n PI) into (* n PI)
9.180 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
9.180 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
9.180 * [backup-simplify]: Simplify (* 1/2 0) into 0
9.181 * [backup-simplify]: Simplify (- 0) into 0
9.181 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.181 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
9.182 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
9.182 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
9.182 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
9.182 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
9.182 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
9.182 * [taylor]: Taking taylor expansion of 1/2 in n
9.182 * [backup-simplify]: Simplify 1/2 into 1/2
9.182 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
9.182 * [taylor]: Taking taylor expansion of 1/2 in n
9.182 * [backup-simplify]: Simplify 1/2 into 1/2
9.182 * [taylor]: Taking taylor expansion of k in n
9.182 * [backup-simplify]: Simplify k into k
9.182 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.182 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.182 * [taylor]: Taking taylor expansion of 2 in n
9.182 * [backup-simplify]: Simplify 2 into 2
9.182 * [taylor]: Taking taylor expansion of (* n PI) in n
9.182 * [taylor]: Taking taylor expansion of n in n
9.182 * [backup-simplify]: Simplify 0 into 0
9.182 * [backup-simplify]: Simplify 1 into 1
9.182 * [taylor]: Taking taylor expansion of PI in n
9.182 * [backup-simplify]: Simplify PI into PI
9.183 * [backup-simplify]: Simplify (* 0 PI) into 0
9.183 * [backup-simplify]: Simplify (* 2 0) into 0
9.185 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.186 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.187 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.187 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
9.187 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
9.187 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
9.188 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.189 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
9.190 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
9.190 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
9.190 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
9.190 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
9.190 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
9.190 * [taylor]: Taking taylor expansion of 1/2 in n
9.190 * [backup-simplify]: Simplify 1/2 into 1/2
9.190 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
9.190 * [taylor]: Taking taylor expansion of 1/2 in n
9.190 * [backup-simplify]: Simplify 1/2 into 1/2
9.190 * [taylor]: Taking taylor expansion of k in n
9.190 * [backup-simplify]: Simplify k into k
9.190 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.190 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.190 * [taylor]: Taking taylor expansion of 2 in n
9.190 * [backup-simplify]: Simplify 2 into 2
9.190 * [taylor]: Taking taylor expansion of (* n PI) in n
9.190 * [taylor]: Taking taylor expansion of n in n
9.190 * [backup-simplify]: Simplify 0 into 0
9.190 * [backup-simplify]: Simplify 1 into 1
9.190 * [taylor]: Taking taylor expansion of PI in n
9.190 * [backup-simplify]: Simplify PI into PI
9.190 * [backup-simplify]: Simplify (* 0 PI) into 0
9.190 * [backup-simplify]: Simplify (* 2 0) into 0
9.191 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.192 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.193 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.193 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
9.193 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
9.193 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
9.194 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.194 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
9.195 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
9.195 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
9.195 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
9.195 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
9.195 * [taylor]: Taking taylor expansion of 1/2 in k
9.195 * [backup-simplify]: Simplify 1/2 into 1/2
9.195 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
9.195 * [taylor]: Taking taylor expansion of 1/2 in k
9.195 * [backup-simplify]: Simplify 1/2 into 1/2
9.195 * [taylor]: Taking taylor expansion of k in k
9.195 * [backup-simplify]: Simplify 0 into 0
9.195 * [backup-simplify]: Simplify 1 into 1
9.195 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
9.196 * [taylor]: Taking taylor expansion of (log n) in k
9.196 * [taylor]: Taking taylor expansion of n in k
9.196 * [backup-simplify]: Simplify n into n
9.196 * [backup-simplify]: Simplify (log n) into (log n)
9.196 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.196 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.196 * [taylor]: Taking taylor expansion of 2 in k
9.196 * [backup-simplify]: Simplify 2 into 2
9.196 * [taylor]: Taking taylor expansion of PI in k
9.196 * [backup-simplify]: Simplify PI into PI
9.196 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.197 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.197 * [backup-simplify]: Simplify (* 1/2 0) into 0
9.197 * [backup-simplify]: Simplify (- 0) into 0
9.198 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.198 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.199 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
9.200 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.200 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.201 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.202 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.202 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.203 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
9.203 * [backup-simplify]: Simplify (- 0) into 0
9.203 * [backup-simplify]: Simplify (+ 0 0) into 0
9.204 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.205 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
9.206 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.206 * [taylor]: Taking taylor expansion of 0 in k
9.206 * [backup-simplify]: Simplify 0 into 0
9.206 * [backup-simplify]: Simplify 0 into 0
9.207 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
9.207 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.208 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.208 * [backup-simplify]: Simplify (+ 0 0) into 0
9.209 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
9.209 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.209 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.210 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
9.212 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.214 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.214 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.215 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.217 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.217 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
9.218 * [backup-simplify]: Simplify (- 0) into 0
9.218 * [backup-simplify]: Simplify (+ 0 0) into 0
9.219 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.220 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.221 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.221 * [taylor]: Taking taylor expansion of 0 in k
9.221 * [backup-simplify]: Simplify 0 into 0
9.221 * [backup-simplify]: Simplify 0 into 0
9.221 * [backup-simplify]: Simplify 0 into 0
9.222 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
9.223 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.224 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.225 * [backup-simplify]: Simplify (+ 0 0) into 0
9.225 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
9.225 * [backup-simplify]: Simplify (- 0) into 0
9.226 * [backup-simplify]: Simplify (+ 0 0) into 0
9.229 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.232 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.236 * [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))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.246 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
9.247 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
9.247 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
9.247 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
9.247 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
9.247 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
9.247 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
9.247 * [taylor]: Taking taylor expansion of 1/2 in k
9.247 * [backup-simplify]: Simplify 1/2 into 1/2
9.247 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.247 * [taylor]: Taking taylor expansion of 1/2 in k
9.247 * [backup-simplify]: Simplify 1/2 into 1/2
9.247 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.247 * [taylor]: Taking taylor expansion of k in k
9.247 * [backup-simplify]: Simplify 0 into 0
9.247 * [backup-simplify]: Simplify 1 into 1
9.248 * [backup-simplify]: Simplify (/ 1 1) into 1
9.248 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
9.248 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
9.248 * [taylor]: Taking taylor expansion of 2 in k
9.248 * [backup-simplify]: Simplify 2 into 2
9.248 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.248 * [taylor]: Taking taylor expansion of PI in k
9.248 * [backup-simplify]: Simplify PI into PI
9.248 * [taylor]: Taking taylor expansion of n in k
9.248 * [backup-simplify]: Simplify n into n
9.248 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.248 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
9.248 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
9.249 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.249 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.250 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.250 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
9.250 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
9.250 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
9.250 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.250 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.250 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
9.250 * [taylor]: Taking taylor expansion of 1/2 in n
9.250 * [backup-simplify]: Simplify 1/2 into 1/2
9.250 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.250 * [taylor]: Taking taylor expansion of 1/2 in n
9.250 * [backup-simplify]: Simplify 1/2 into 1/2
9.250 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.250 * [taylor]: Taking taylor expansion of k in n
9.250 * [backup-simplify]: Simplify k into k
9.250 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.250 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.250 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.250 * [taylor]: Taking taylor expansion of 2 in n
9.251 * [backup-simplify]: Simplify 2 into 2
9.251 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.251 * [taylor]: Taking taylor expansion of PI in n
9.251 * [backup-simplify]: Simplify PI into PI
9.251 * [taylor]: Taking taylor expansion of n in n
9.251 * [backup-simplify]: Simplify 0 into 0
9.251 * [backup-simplify]: Simplify 1 into 1
9.251 * [backup-simplify]: Simplify (/ PI 1) into PI
9.252 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.253 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.253 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.253 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
9.253 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
9.254 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.255 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
9.256 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.256 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
9.257 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.257 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.257 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
9.257 * [taylor]: Taking taylor expansion of 1/2 in n
9.257 * [backup-simplify]: Simplify 1/2 into 1/2
9.257 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.257 * [taylor]: Taking taylor expansion of 1/2 in n
9.257 * [backup-simplify]: Simplify 1/2 into 1/2
9.257 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.257 * [taylor]: Taking taylor expansion of k in n
9.257 * [backup-simplify]: Simplify k into k
9.257 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.257 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.257 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.257 * [taylor]: Taking taylor expansion of 2 in n
9.257 * [backup-simplify]: Simplify 2 into 2
9.257 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.257 * [taylor]: Taking taylor expansion of PI in n
9.257 * [backup-simplify]: Simplify PI into PI
9.257 * [taylor]: Taking taylor expansion of n in n
9.257 * [backup-simplify]: Simplify 0 into 0
9.257 * [backup-simplify]: Simplify 1 into 1
9.258 * [backup-simplify]: Simplify (/ PI 1) into PI
9.258 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.259 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.259 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.259 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
9.259 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
9.261 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.262 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
9.263 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.264 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
9.264 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
9.264 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
9.264 * [taylor]: Taking taylor expansion of 1/2 in k
9.264 * [backup-simplify]: Simplify 1/2 into 1/2
9.264 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.264 * [taylor]: Taking taylor expansion of 1/2 in k
9.264 * [backup-simplify]: Simplify 1/2 into 1/2
9.264 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.264 * [taylor]: Taking taylor expansion of k in k
9.264 * [backup-simplify]: Simplify 0 into 0
9.264 * [backup-simplify]: Simplify 1 into 1
9.264 * [backup-simplify]: Simplify (/ 1 1) into 1
9.264 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
9.264 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.264 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.264 * [taylor]: Taking taylor expansion of 2 in k
9.264 * [backup-simplify]: Simplify 2 into 2
9.264 * [taylor]: Taking taylor expansion of PI in k
9.265 * [backup-simplify]: Simplify PI into PI
9.265 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.266 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.266 * [taylor]: Taking taylor expansion of (log n) in k
9.266 * [taylor]: Taking taylor expansion of n in k
9.266 * [backup-simplify]: Simplify n into n
9.266 * [backup-simplify]: Simplify (log n) into (log n)
9.267 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.267 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.267 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.267 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.268 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
9.269 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
9.270 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.272 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.273 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.273 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.275 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.275 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.276 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
9.276 * [backup-simplify]: Simplify (- 0) into 0
9.277 * [backup-simplify]: Simplify (+ 0 0) into 0
9.278 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.279 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
9.281 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.281 * [taylor]: Taking taylor expansion of 0 in k
9.281 * [backup-simplify]: Simplify 0 into 0
9.281 * [backup-simplify]: Simplify 0 into 0
9.281 * [backup-simplify]: Simplify 0 into 0
9.282 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.283 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.286 * [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
9.287 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.288 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
9.288 * [backup-simplify]: Simplify (- 0) into 0
9.288 * [backup-simplify]: Simplify (+ 0 0) into 0
9.290 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.291 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
9.294 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.294 * [taylor]: Taking taylor expansion of 0 in k
9.294 * [backup-simplify]: Simplify 0 into 0
9.294 * [backup-simplify]: Simplify 0 into 0
9.294 * [backup-simplify]: Simplify 0 into 0
9.294 * [backup-simplify]: Simplify 0 into 0
9.295 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.296 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.302 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.302 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.304 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
9.304 * [backup-simplify]: Simplify (- 0) into 0
9.305 * [backup-simplify]: Simplify (+ 0 0) into 0
9.306 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.308 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
9.312 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.312 * [taylor]: Taking taylor expansion of 0 in k
9.312 * [backup-simplify]: Simplify 0 into 0
9.312 * [backup-simplify]: Simplify 0 into 0
9.313 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
9.314 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
9.314 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
9.314 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
9.314 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
9.314 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
9.314 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
9.314 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.314 * [taylor]: Taking taylor expansion of 1/2 in k
9.314 * [backup-simplify]: Simplify 1/2 into 1/2
9.314 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.314 * [taylor]: Taking taylor expansion of k in k
9.314 * [backup-simplify]: Simplify 0 into 0
9.314 * [backup-simplify]: Simplify 1 into 1
9.315 * [backup-simplify]: Simplify (/ 1 1) into 1
9.315 * [taylor]: Taking taylor expansion of 1/2 in k
9.315 * [backup-simplify]: Simplify 1/2 into 1/2
9.315 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
9.315 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
9.315 * [taylor]: Taking taylor expansion of -2 in k
9.315 * [backup-simplify]: Simplify -2 into -2
9.315 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.315 * [taylor]: Taking taylor expansion of PI in k
9.315 * [backup-simplify]: Simplify PI into PI
9.315 * [taylor]: Taking taylor expansion of n in k
9.315 * [backup-simplify]: Simplify n into n
9.315 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.315 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
9.315 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
9.316 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.316 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.316 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
9.316 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
9.316 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
9.316 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
9.316 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
9.316 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
9.317 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.317 * [taylor]: Taking taylor expansion of 1/2 in n
9.317 * [backup-simplify]: Simplify 1/2 into 1/2
9.317 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.317 * [taylor]: Taking taylor expansion of k in n
9.317 * [backup-simplify]: Simplify k into k
9.317 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.317 * [taylor]: Taking taylor expansion of 1/2 in n
9.317 * [backup-simplify]: Simplify 1/2 into 1/2
9.317 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.317 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.317 * [taylor]: Taking taylor expansion of -2 in n
9.317 * [backup-simplify]: Simplify -2 into -2
9.317 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.317 * [taylor]: Taking taylor expansion of PI in n
9.317 * [backup-simplify]: Simplify PI into PI
9.317 * [taylor]: Taking taylor expansion of n in n
9.317 * [backup-simplify]: Simplify 0 into 0
9.317 * [backup-simplify]: Simplify 1 into 1
9.317 * [backup-simplify]: Simplify (/ PI 1) into PI
9.318 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.319 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.319 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.319 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
9.321 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.322 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
9.323 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.323 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
9.323 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
9.323 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
9.323 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
9.323 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.323 * [taylor]: Taking taylor expansion of 1/2 in n
9.323 * [backup-simplify]: Simplify 1/2 into 1/2
9.323 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.323 * [taylor]: Taking taylor expansion of k in n
9.323 * [backup-simplify]: Simplify k into k
9.323 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.323 * [taylor]: Taking taylor expansion of 1/2 in n
9.323 * [backup-simplify]: Simplify 1/2 into 1/2
9.323 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.323 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.323 * [taylor]: Taking taylor expansion of -2 in n
9.323 * [backup-simplify]: Simplify -2 into -2
9.323 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.323 * [taylor]: Taking taylor expansion of PI in n
9.323 * [backup-simplify]: Simplify PI into PI
9.323 * [taylor]: Taking taylor expansion of n in n
9.323 * [backup-simplify]: Simplify 0 into 0
9.323 * [backup-simplify]: Simplify 1 into 1
9.324 * [backup-simplify]: Simplify (/ PI 1) into PI
9.324 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.325 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.325 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.325 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
9.327 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.328 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
9.329 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.329 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
9.329 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
9.329 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
9.329 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.329 * [taylor]: Taking taylor expansion of 1/2 in k
9.329 * [backup-simplify]: Simplify 1/2 into 1/2
9.329 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.329 * [taylor]: Taking taylor expansion of k in k
9.329 * [backup-simplify]: Simplify 0 into 0
9.329 * [backup-simplify]: Simplify 1 into 1
9.330 * [backup-simplify]: Simplify (/ 1 1) into 1
9.330 * [taylor]: Taking taylor expansion of 1/2 in k
9.330 * [backup-simplify]: Simplify 1/2 into 1/2
9.330 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
9.330 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
9.330 * [taylor]: Taking taylor expansion of (* -2 PI) in k
9.330 * [taylor]: Taking taylor expansion of -2 in k
9.330 * [backup-simplify]: Simplify -2 into -2
9.330 * [taylor]: Taking taylor expansion of PI in k
9.330 * [backup-simplify]: Simplify PI into PI
9.330 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.331 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.332 * [taylor]: Taking taylor expansion of (log n) in k
9.332 * [taylor]: Taking taylor expansion of n in k
9.332 * [backup-simplify]: Simplify n into n
9.332 * [backup-simplify]: Simplify (log n) into (log n)
9.332 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.332 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.333 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.333 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
9.334 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
9.336 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.337 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.338 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.338 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.340 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
9.340 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.341 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
9.341 * [backup-simplify]: Simplify (+ 0 0) into 0
9.343 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.344 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
9.345 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.346 * [taylor]: Taking taylor expansion of 0 in k
9.346 * [backup-simplify]: Simplify 0 into 0
9.346 * [backup-simplify]: Simplify 0 into 0
9.346 * [backup-simplify]: Simplify 0 into 0
9.347 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.348 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.352 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
9.352 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.353 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
9.353 * [backup-simplify]: Simplify (+ 0 0) into 0
9.354 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.356 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
9.358 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.358 * [taylor]: Taking taylor expansion of 0 in k
9.358 * [backup-simplify]: Simplify 0 into 0
9.358 * [backup-simplify]: Simplify 0 into 0
9.358 * [backup-simplify]: Simplify 0 into 0
9.358 * [backup-simplify]: Simplify 0 into 0
9.359 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.361 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.366 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
9.367 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.371 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
9.371 * [backup-simplify]: Simplify (+ 0 0) into 0
9.373 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.375 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
9.377 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.377 * [taylor]: Taking taylor expansion of 0 in k
9.377 * [backup-simplify]: Simplify 0 into 0
9.377 * [backup-simplify]: Simplify 0 into 0
9.378 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
9.379 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
9.379 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
9.379 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
9.379 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.379 * [taylor]: Taking taylor expansion of 2 in n
9.379 * [backup-simplify]: Simplify 2 into 2
9.379 * [taylor]: Taking taylor expansion of (* n PI) in n
9.379 * [taylor]: Taking taylor expansion of n in n
9.379 * [backup-simplify]: Simplify 0 into 0
9.379 * [backup-simplify]: Simplify 1 into 1
9.379 * [taylor]: Taking taylor expansion of PI in n
9.379 * [backup-simplify]: Simplify PI into PI
9.379 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.379 * [taylor]: Taking taylor expansion of 2 in n
9.379 * [backup-simplify]: Simplify 2 into 2
9.379 * [taylor]: Taking taylor expansion of (* n PI) in n
9.379 * [taylor]: Taking taylor expansion of n in n
9.379 * [backup-simplify]: Simplify 0 into 0
9.379 * [backup-simplify]: Simplify 1 into 1
9.379 * [taylor]: Taking taylor expansion of PI in n
9.379 * [backup-simplify]: Simplify PI into PI
9.380 * [backup-simplify]: Simplify (* 0 PI) into 0
9.380 * [backup-simplify]: Simplify (* 2 0) into 0
9.380 * [backup-simplify]: Simplify 0 into 0
9.382 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.383 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.384 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.385 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.386 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.386 * [backup-simplify]: Simplify 0 into 0
9.387 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.388 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.388 * [backup-simplify]: Simplify 0 into 0
9.390 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.391 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
9.391 * [backup-simplify]: Simplify 0 into 0
9.393 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.394 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
9.394 * [backup-simplify]: Simplify 0 into 0
9.396 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.397 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
9.397 * [backup-simplify]: Simplify 0 into 0
9.399 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
9.401 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
9.401 * [backup-simplify]: Simplify 0 into 0
9.402 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
9.403 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
9.403 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
9.403 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.403 * [taylor]: Taking taylor expansion of 2 in n
9.403 * [backup-simplify]: Simplify 2 into 2
9.403 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.403 * [taylor]: Taking taylor expansion of PI in n
9.403 * [backup-simplify]: Simplify PI into PI
9.403 * [taylor]: Taking taylor expansion of n in n
9.403 * [backup-simplify]: Simplify 0 into 0
9.403 * [backup-simplify]: Simplify 1 into 1
9.403 * [backup-simplify]: Simplify (/ PI 1) into PI
9.403 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.403 * [taylor]: Taking taylor expansion of 2 in n
9.404 * [backup-simplify]: Simplify 2 into 2
9.404 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.404 * [taylor]: Taking taylor expansion of PI in n
9.404 * [backup-simplify]: Simplify PI into PI
9.404 * [taylor]: Taking taylor expansion of n in n
9.404 * [backup-simplify]: Simplify 0 into 0
9.404 * [backup-simplify]: Simplify 1 into 1
9.404 * [backup-simplify]: Simplify (/ PI 1) into PI
9.405 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.405 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.407 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.407 * [backup-simplify]: Simplify 0 into 0
9.408 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.409 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.409 * [backup-simplify]: Simplify 0 into 0
9.410 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.411 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.411 * [backup-simplify]: Simplify 0 into 0
9.412 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.413 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.413 * [backup-simplify]: Simplify 0 into 0
9.414 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.416 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.416 * [backup-simplify]: Simplify 0 into 0
9.417 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.418 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.418 * [backup-simplify]: Simplify 0 into 0
9.419 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
9.419 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
9.419 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
9.419 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.419 * [taylor]: Taking taylor expansion of -2 in n
9.419 * [backup-simplify]: Simplify -2 into -2
9.419 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.419 * [taylor]: Taking taylor expansion of PI in n
9.419 * [backup-simplify]: Simplify PI into PI
9.420 * [taylor]: Taking taylor expansion of n in n
9.420 * [backup-simplify]: Simplify 0 into 0
9.420 * [backup-simplify]: Simplify 1 into 1
9.420 * [backup-simplify]: Simplify (/ PI 1) into PI
9.420 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.420 * [taylor]: Taking taylor expansion of -2 in n
9.420 * [backup-simplify]: Simplify -2 into -2
9.420 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.420 * [taylor]: Taking taylor expansion of PI in n
9.420 * [backup-simplify]: Simplify PI into PI
9.420 * [taylor]: Taking taylor expansion of n in n
9.420 * [backup-simplify]: Simplify 0 into 0
9.420 * [backup-simplify]: Simplify 1 into 1
9.421 * [backup-simplify]: Simplify (/ PI 1) into PI
9.421 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.422 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.422 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.423 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.423 * [backup-simplify]: Simplify 0 into 0
9.424 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.425 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.425 * [backup-simplify]: Simplify 0 into 0
9.426 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.427 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.427 * [backup-simplify]: Simplify 0 into 0
9.428 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.429 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.429 * [backup-simplify]: Simplify 0 into 0
9.431 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.432 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.432 * [backup-simplify]: Simplify 0 into 0
9.433 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.435 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.435 * [backup-simplify]: Simplify 0 into 0
9.436 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
9.436 * * * * [progress]: [ 3 / 3 ] generating series at (2)
9.437 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))))
9.437 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
9.437 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
9.437 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.437 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.437 * [taylor]: Taking taylor expansion of k in k
9.437 * [backup-simplify]: Simplify 0 into 0
9.437 * [backup-simplify]: Simplify 1 into 1
9.437 * [backup-simplify]: Simplify (/ 1 1) into 1
9.438 * [backup-simplify]: Simplify (sqrt 0) into 0
9.439 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.439 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
9.439 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
9.439 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
9.439 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
9.439 * [taylor]: Taking taylor expansion of 1/2 in k
9.439 * [backup-simplify]: Simplify 1/2 into 1/2
9.439 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
9.439 * [taylor]: Taking taylor expansion of 1/2 in k
9.439 * [backup-simplify]: Simplify 1/2 into 1/2
9.439 * [taylor]: Taking taylor expansion of k in k
9.440 * [backup-simplify]: Simplify 0 into 0
9.440 * [backup-simplify]: Simplify 1 into 1
9.440 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
9.440 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
9.440 * [taylor]: Taking taylor expansion of 2 in k
9.440 * [backup-simplify]: Simplify 2 into 2
9.440 * [taylor]: Taking taylor expansion of (* n PI) in k
9.440 * [taylor]: Taking taylor expansion of n in k
9.440 * [backup-simplify]: Simplify n into n
9.440 * [taylor]: Taking taylor expansion of PI in k
9.440 * [backup-simplify]: Simplify PI into PI
9.440 * [backup-simplify]: Simplify (* n PI) into (* n PI)
9.440 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
9.440 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
9.440 * [backup-simplify]: Simplify (* 1/2 0) into 0
9.441 * [backup-simplify]: Simplify (- 0) into 0
9.441 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.441 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
9.442 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
9.442 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
9.442 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
9.442 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.442 * [taylor]: Taking taylor expansion of k in n
9.442 * [backup-simplify]: Simplify k into k
9.442 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.442 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
9.442 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.442 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
9.442 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
9.442 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
9.442 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
9.442 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
9.442 * [taylor]: Taking taylor expansion of 1/2 in n
9.442 * [backup-simplify]: Simplify 1/2 into 1/2
9.442 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
9.442 * [taylor]: Taking taylor expansion of 1/2 in n
9.442 * [backup-simplify]: Simplify 1/2 into 1/2
9.442 * [taylor]: Taking taylor expansion of k in n
9.442 * [backup-simplify]: Simplify k into k
9.442 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.442 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.442 * [taylor]: Taking taylor expansion of 2 in n
9.442 * [backup-simplify]: Simplify 2 into 2
9.442 * [taylor]: Taking taylor expansion of (* n PI) in n
9.443 * [taylor]: Taking taylor expansion of n in n
9.443 * [backup-simplify]: Simplify 0 into 0
9.443 * [backup-simplify]: Simplify 1 into 1
9.443 * [taylor]: Taking taylor expansion of PI in n
9.443 * [backup-simplify]: Simplify PI into PI
9.443 * [backup-simplify]: Simplify (* 0 PI) into 0
9.443 * [backup-simplify]: Simplify (* 2 0) into 0
9.444 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.445 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.446 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.446 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
9.446 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
9.446 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
9.447 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.447 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
9.448 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
9.448 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
9.448 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
9.448 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.448 * [taylor]: Taking taylor expansion of k in n
9.448 * [backup-simplify]: Simplify k into k
9.448 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.448 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
9.448 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.448 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
9.448 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
9.448 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
9.448 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
9.448 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
9.448 * [taylor]: Taking taylor expansion of 1/2 in n
9.448 * [backup-simplify]: Simplify 1/2 into 1/2
9.448 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
9.448 * [taylor]: Taking taylor expansion of 1/2 in n
9.448 * [backup-simplify]: Simplify 1/2 into 1/2
9.448 * [taylor]: Taking taylor expansion of k in n
9.449 * [backup-simplify]: Simplify k into k
9.449 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.449 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.449 * [taylor]: Taking taylor expansion of 2 in n
9.449 * [backup-simplify]: Simplify 2 into 2
9.449 * [taylor]: Taking taylor expansion of (* n PI) in n
9.449 * [taylor]: Taking taylor expansion of n in n
9.449 * [backup-simplify]: Simplify 0 into 0
9.449 * [backup-simplify]: Simplify 1 into 1
9.449 * [taylor]: Taking taylor expansion of PI in n
9.449 * [backup-simplify]: Simplify PI into PI
9.449 * [backup-simplify]: Simplify (* 0 PI) into 0
9.449 * [backup-simplify]: Simplify (* 2 0) into 0
9.450 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.451 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.452 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.452 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
9.452 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
9.452 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
9.453 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.453 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
9.454 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
9.455 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k)))
9.455 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
9.455 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
9.455 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
9.455 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
9.455 * [taylor]: Taking taylor expansion of 1/2 in k
9.455 * [backup-simplify]: Simplify 1/2 into 1/2
9.455 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
9.455 * [taylor]: Taking taylor expansion of 1/2 in k
9.455 * [backup-simplify]: Simplify 1/2 into 1/2
9.455 * [taylor]: Taking taylor expansion of k in k
9.455 * [backup-simplify]: Simplify 0 into 0
9.455 * [backup-simplify]: Simplify 1 into 1
9.455 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
9.455 * [taylor]: Taking taylor expansion of (log n) in k
9.455 * [taylor]: Taking taylor expansion of n in k
9.455 * [backup-simplify]: Simplify n into n
9.455 * [backup-simplify]: Simplify (log n) into (log n)
9.455 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.455 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.455 * [taylor]: Taking taylor expansion of 2 in k
9.455 * [backup-simplify]: Simplify 2 into 2
9.455 * [taylor]: Taking taylor expansion of PI in k
9.455 * [backup-simplify]: Simplify PI into PI
9.455 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.456 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.456 * [backup-simplify]: Simplify (* 1/2 0) into 0
9.456 * [backup-simplify]: Simplify (- 0) into 0
9.457 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.457 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.458 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
9.459 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.459 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.459 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.459 * [taylor]: Taking taylor expansion of k in k
9.459 * [backup-simplify]: Simplify 0 into 0
9.459 * [backup-simplify]: Simplify 1 into 1
9.459 * [backup-simplify]: Simplify (/ 1 1) into 1
9.459 * [backup-simplify]: Simplify (sqrt 0) into 0
9.460 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.461 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
9.461 * [backup-simplify]: Simplify 0 into 0
9.461 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.462 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.463 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.463 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
9.463 * [backup-simplify]: Simplify (- 0) into 0
9.463 * [backup-simplify]: Simplify (+ 0 0) into 0
9.464 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.465 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
9.466 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.467 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
9.467 * [taylor]: Taking taylor expansion of 0 in k
9.467 * [backup-simplify]: Simplify 0 into 0
9.467 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
9.468 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.469 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.469 * [backup-simplify]: Simplify (+ 0 0) into 0
9.469 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
9.470 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.470 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.471 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
9.473 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.475 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.476 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.476 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.477 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.479 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.481 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
9.481 * [backup-simplify]: Simplify (- 0) into 0
9.481 * [backup-simplify]: Simplify (+ 0 0) into 0
9.483 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.484 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.490 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.490 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.491 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
9.492 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
9.492 * [taylor]: Taking taylor expansion of 0 in k
9.492 * [backup-simplify]: Simplify 0 into 0
9.493 * [backup-simplify]: Simplify 0 into 0
9.493 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
9.497 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.498 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
9.499 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.503 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.503 * [backup-simplify]: Simplify (+ 0 0) into 0
9.504 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
9.505 * [backup-simplify]: Simplify (- 0) into 0
9.505 * [backup-simplify]: Simplify (+ 0 0) into 0
9.507 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.511 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.516 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
9.519 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
9.519 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.520 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
9.523 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.524 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
9.525 * [backup-simplify]: Simplify (- 0) into 0
9.525 * [backup-simplify]: Simplify (+ 0 0) into 0
9.526 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.527 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
9.529 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.529 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.529 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
9.531 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0
9.531 * [taylor]: Taking taylor expansion of 0 in k
9.531 * [backup-simplify]: Simplify 0 into 0
9.531 * [backup-simplify]: Simplify 0 into 0
9.531 * [backup-simplify]: Simplify 0 into 0
9.531 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.534 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.536 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
9.536 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.539 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.540 * [backup-simplify]: Simplify (+ 0 0) into 0
9.540 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
9.541 * [backup-simplify]: Simplify (- 0) into 0
9.541 * [backup-simplify]: Simplify (+ 0 0) into 0
9.542 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
9.548 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.565 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
9.574 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
9.586 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
9.586 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
9.586 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
9.586 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
9.586 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.586 * [taylor]: Taking taylor expansion of k in k
9.586 * [backup-simplify]: Simplify 0 into 0
9.586 * [backup-simplify]: Simplify 1 into 1
9.587 * [backup-simplify]: Simplify (sqrt 0) into 0
9.588 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.588 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
9.588 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
9.588 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
9.588 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
9.588 * [taylor]: Taking taylor expansion of 1/2 in k
9.588 * [backup-simplify]: Simplify 1/2 into 1/2
9.588 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.588 * [taylor]: Taking taylor expansion of 1/2 in k
9.588 * [backup-simplify]: Simplify 1/2 into 1/2
9.588 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.588 * [taylor]: Taking taylor expansion of k in k
9.588 * [backup-simplify]: Simplify 0 into 0
9.588 * [backup-simplify]: Simplify 1 into 1
9.588 * [backup-simplify]: Simplify (/ 1 1) into 1
9.588 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
9.588 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
9.588 * [taylor]: Taking taylor expansion of 2 in k
9.588 * [backup-simplify]: Simplify 2 into 2
9.588 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.588 * [taylor]: Taking taylor expansion of PI in k
9.588 * [backup-simplify]: Simplify PI into PI
9.588 * [taylor]: Taking taylor expansion of n in k
9.588 * [backup-simplify]: Simplify n into n
9.588 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.588 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
9.588 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
9.590 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.591 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.591 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.591 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
9.591 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
9.591 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
9.591 * [taylor]: Taking taylor expansion of (sqrt k) in n
9.591 * [taylor]: Taking taylor expansion of k in n
9.591 * [backup-simplify]: Simplify k into k
9.591 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
9.591 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
9.591 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
9.591 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.591 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.591 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
9.591 * [taylor]: Taking taylor expansion of 1/2 in n
9.591 * [backup-simplify]: Simplify 1/2 into 1/2
9.591 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.591 * [taylor]: Taking taylor expansion of 1/2 in n
9.591 * [backup-simplify]: Simplify 1/2 into 1/2
9.591 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.591 * [taylor]: Taking taylor expansion of k in n
9.591 * [backup-simplify]: Simplify k into k
9.592 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.592 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.592 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.592 * [taylor]: Taking taylor expansion of 2 in n
9.592 * [backup-simplify]: Simplify 2 into 2
9.592 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.592 * [taylor]: Taking taylor expansion of PI in n
9.592 * [backup-simplify]: Simplify PI into PI
9.592 * [taylor]: Taking taylor expansion of n in n
9.592 * [backup-simplify]: Simplify 0 into 0
9.592 * [backup-simplify]: Simplify 1 into 1
9.592 * [backup-simplify]: Simplify (/ PI 1) into PI
9.592 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.593 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.593 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.593 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
9.593 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
9.594 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.594 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
9.595 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.595 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
9.595 * [taylor]: Taking taylor expansion of (sqrt k) in n
9.595 * [taylor]: Taking taylor expansion of k in n
9.595 * [backup-simplify]: Simplify k into k
9.595 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
9.595 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
9.595 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
9.595 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.595 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.595 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
9.595 * [taylor]: Taking taylor expansion of 1/2 in n
9.595 * [backup-simplify]: Simplify 1/2 into 1/2
9.595 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.595 * [taylor]: Taking taylor expansion of 1/2 in n
9.595 * [backup-simplify]: Simplify 1/2 into 1/2
9.595 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.596 * [taylor]: Taking taylor expansion of k in n
9.596 * [backup-simplify]: Simplify k into k
9.596 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.596 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.596 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.596 * [taylor]: Taking taylor expansion of 2 in n
9.596 * [backup-simplify]: Simplify 2 into 2
9.596 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.596 * [taylor]: Taking taylor expansion of PI in n
9.596 * [backup-simplify]: Simplify PI into PI
9.596 * [taylor]: Taking taylor expansion of n in n
9.596 * [backup-simplify]: Simplify 0 into 0
9.596 * [backup-simplify]: Simplify 1 into 1
9.596 * [backup-simplify]: Simplify (/ PI 1) into PI
9.596 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.597 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.597 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.597 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
9.597 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
9.598 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.598 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
9.599 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.600 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
9.600 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
9.600 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
9.600 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
9.600 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
9.600 * [taylor]: Taking taylor expansion of 1/2 in k
9.600 * [backup-simplify]: Simplify 1/2 into 1/2
9.600 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.600 * [taylor]: Taking taylor expansion of 1/2 in k
9.600 * [backup-simplify]: Simplify 1/2 into 1/2
9.600 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.600 * [taylor]: Taking taylor expansion of k in k
9.600 * [backup-simplify]: Simplify 0 into 0
9.600 * [backup-simplify]: Simplify 1 into 1
9.600 * [backup-simplify]: Simplify (/ 1 1) into 1
9.600 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
9.600 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.600 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.600 * [taylor]: Taking taylor expansion of 2 in k
9.600 * [backup-simplify]: Simplify 2 into 2
9.601 * [taylor]: Taking taylor expansion of PI in k
9.601 * [backup-simplify]: Simplify PI into PI
9.601 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.601 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.601 * [taylor]: Taking taylor expansion of (log n) in k
9.601 * [taylor]: Taking taylor expansion of n in k
9.601 * [backup-simplify]: Simplify n into n
9.601 * [backup-simplify]: Simplify (log n) into (log n)
9.602 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.602 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.602 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.602 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.603 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
9.604 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
9.604 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.604 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.604 * [taylor]: Taking taylor expansion of k in k
9.604 * [backup-simplify]: Simplify 0 into 0
9.604 * [backup-simplify]: Simplify 1 into 1
9.605 * [backup-simplify]: Simplify (sqrt 0) into 0
9.606 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.606 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
9.606 * [backup-simplify]: Simplify 0 into 0
9.607 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.608 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.609 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.610 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.610 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
9.611 * [backup-simplify]: Simplify (- 0) into 0
9.611 * [backup-simplify]: Simplify (+ 0 0) into 0
9.612 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.613 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
9.615 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.616 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
9.616 * [taylor]: Taking taylor expansion of 0 in k
9.616 * [backup-simplify]: Simplify 0 into 0
9.616 * [backup-simplify]: Simplify 0 into 0
9.618 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
9.619 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
9.620 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.620 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.622 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.622 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.622 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
9.623 * [backup-simplify]: Simplify (- 0) into 0
9.623 * [backup-simplify]: Simplify (+ 0 0) into 0
9.624 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.625 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
9.626 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.626 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
9.627 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
9.627 * [taylor]: Taking taylor expansion of 0 in k
9.627 * [backup-simplify]: Simplify 0 into 0
9.627 * [backup-simplify]: Simplify 0 into 0
9.628 * [backup-simplify]: Simplify 0 into 0
9.629 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.630 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
9.631 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
9.632 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.633 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.636 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.636 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.637 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
9.637 * [backup-simplify]: Simplify (- 0) into 0
9.637 * [backup-simplify]: Simplify (+ 0 0) into 0
9.638 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.639 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
9.640 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.641 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
9.642 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0
9.642 * [taylor]: Taking taylor expansion of 0 in k
9.642 * [backup-simplify]: Simplify 0 into 0
9.642 * [backup-simplify]: Simplify 0 into 0
9.642 * [backup-simplify]: Simplify 0 into 0
9.642 * [backup-simplify]: Simplify 0 into 0
9.645 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.646 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
9.647 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
9.650 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
9.650 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
9.650 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
9.650 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
9.650 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
9.650 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
9.650 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
9.650 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
9.650 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.650 * [taylor]: Taking taylor expansion of 1/2 in k
9.650 * [backup-simplify]: Simplify 1/2 into 1/2
9.650 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.650 * [taylor]: Taking taylor expansion of k in k
9.650 * [backup-simplify]: Simplify 0 into 0
9.650 * [backup-simplify]: Simplify 1 into 1
9.651 * [backup-simplify]: Simplify (/ 1 1) into 1
9.651 * [taylor]: Taking taylor expansion of 1/2 in k
9.651 * [backup-simplify]: Simplify 1/2 into 1/2
9.651 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
9.651 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
9.651 * [taylor]: Taking taylor expansion of -2 in k
9.651 * [backup-simplify]: Simplify -2 into -2
9.651 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.651 * [taylor]: Taking taylor expansion of PI in k
9.651 * [backup-simplify]: Simplify PI into PI
9.651 * [taylor]: Taking taylor expansion of n in k
9.651 * [backup-simplify]: Simplify n into n
9.651 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.651 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
9.651 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
9.651 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.652 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.652 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
9.652 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
9.652 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.652 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.652 * [taylor]: Taking taylor expansion of -1 in k
9.652 * [backup-simplify]: Simplify -1 into -1
9.652 * [taylor]: Taking taylor expansion of k in k
9.652 * [backup-simplify]: Simplify 0 into 0
9.652 * [backup-simplify]: Simplify 1 into 1
9.653 * [backup-simplify]: Simplify (/ -1 1) into -1
9.653 * [backup-simplify]: Simplify (sqrt 0) into 0
9.655 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.655 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
9.655 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
9.655 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
9.655 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
9.655 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
9.655 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
9.655 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.655 * [taylor]: Taking taylor expansion of 1/2 in n
9.655 * [backup-simplify]: Simplify 1/2 into 1/2
9.655 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.655 * [taylor]: Taking taylor expansion of k in n
9.655 * [backup-simplify]: Simplify k into k
9.655 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.655 * [taylor]: Taking taylor expansion of 1/2 in n
9.655 * [backup-simplify]: Simplify 1/2 into 1/2
9.655 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.655 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.655 * [taylor]: Taking taylor expansion of -2 in n
9.655 * [backup-simplify]: Simplify -2 into -2
9.655 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.656 * [taylor]: Taking taylor expansion of PI in n
9.656 * [backup-simplify]: Simplify PI into PI
9.656 * [taylor]: Taking taylor expansion of n in n
9.656 * [backup-simplify]: Simplify 0 into 0
9.656 * [backup-simplify]: Simplify 1 into 1
9.656 * [backup-simplify]: Simplify (/ PI 1) into PI
9.656 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.657 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.657 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.657 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
9.658 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.658 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
9.659 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.659 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
9.659 * [taylor]: Taking taylor expansion of (/ -1 k) in n
9.659 * [taylor]: Taking taylor expansion of -1 in n
9.659 * [backup-simplify]: Simplify -1 into -1
9.659 * [taylor]: Taking taylor expansion of k in n
9.659 * [backup-simplify]: Simplify k into k
9.659 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
9.659 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
9.659 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
9.659 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
9.660 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
9.660 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
9.660 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
9.660 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
9.660 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
9.660 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
9.660 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.660 * [taylor]: Taking taylor expansion of 1/2 in n
9.660 * [backup-simplify]: Simplify 1/2 into 1/2
9.660 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.660 * [taylor]: Taking taylor expansion of k in n
9.660 * [backup-simplify]: Simplify k into k
9.660 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.660 * [taylor]: Taking taylor expansion of 1/2 in n
9.660 * [backup-simplify]: Simplify 1/2 into 1/2
9.660 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.660 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.660 * [taylor]: Taking taylor expansion of -2 in n
9.660 * [backup-simplify]: Simplify -2 into -2
9.660 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.660 * [taylor]: Taking taylor expansion of PI in n
9.660 * [backup-simplify]: Simplify PI into PI
9.660 * [taylor]: Taking taylor expansion of n in n
9.660 * [backup-simplify]: Simplify 0 into 0
9.660 * [backup-simplify]: Simplify 1 into 1
9.661 * [backup-simplify]: Simplify (/ PI 1) into PI
9.661 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.662 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.662 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.662 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
9.663 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.663 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
9.664 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.664 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
9.664 * [taylor]: Taking taylor expansion of (/ -1 k) in n
9.664 * [taylor]: Taking taylor expansion of -1 in n
9.664 * [backup-simplify]: Simplify -1 into -1
9.664 * [taylor]: Taking taylor expansion of k in n
9.664 * [backup-simplify]: Simplify k into k
9.664 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
9.664 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
9.664 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
9.664 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
9.665 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
9.665 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
9.665 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
9.665 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
9.665 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
9.665 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.665 * [taylor]: Taking taylor expansion of 1/2 in k
9.665 * [backup-simplify]: Simplify 1/2 into 1/2
9.665 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.665 * [taylor]: Taking taylor expansion of k in k
9.665 * [backup-simplify]: Simplify 0 into 0
9.665 * [backup-simplify]: Simplify 1 into 1
9.665 * [backup-simplify]: Simplify (/ 1 1) into 1
9.665 * [taylor]: Taking taylor expansion of 1/2 in k
9.666 * [backup-simplify]: Simplify 1/2 into 1/2
9.666 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
9.666 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
9.666 * [taylor]: Taking taylor expansion of (* -2 PI) in k
9.666 * [taylor]: Taking taylor expansion of -2 in k
9.666 * [backup-simplify]: Simplify -2 into -2
9.666 * [taylor]: Taking taylor expansion of PI in k
9.666 * [backup-simplify]: Simplify PI into PI
9.666 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.666 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.666 * [taylor]: Taking taylor expansion of (log n) in k
9.667 * [taylor]: Taking taylor expansion of n in k
9.667 * [backup-simplify]: Simplify n into n
9.667 * [backup-simplify]: Simplify (log n) into (log n)
9.667 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.667 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.667 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.668 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
9.668 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
9.669 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.669 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.669 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.669 * [taylor]: Taking taylor expansion of -1 in k
9.669 * [backup-simplify]: Simplify -1 into -1
9.669 * [taylor]: Taking taylor expansion of k in k
9.669 * [backup-simplify]: Simplify 0 into 0
9.669 * [backup-simplify]: Simplify 1 into 1
9.669 * [backup-simplify]: Simplify (/ -1 1) into -1
9.670 * [backup-simplify]: Simplify (sqrt 0) into 0
9.670 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.671 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
9.672 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
9.672 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.673 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.674 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
9.674 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.674 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
9.674 * [backup-simplify]: Simplify (+ 0 0) into 0
9.675 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.676 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
9.677 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.678 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
9.678 * [taylor]: Taking taylor expansion of 0 in k
9.678 * [backup-simplify]: Simplify 0 into 0
9.678 * [backup-simplify]: Simplify 0 into 0
9.678 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
9.680 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.683 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
9.684 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
9.685 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.685 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.687 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
9.687 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.688 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
9.688 * [backup-simplify]: Simplify (+ 0 0) into 0
9.689 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.690 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
9.691 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.692 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.692 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
9.693 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
9.693 * [taylor]: Taking taylor expansion of 0 in k
9.693 * [backup-simplify]: Simplify 0 into 0
9.693 * [backup-simplify]: Simplify 0 into 0
9.693 * [backup-simplify]: Simplify 0 into 0
9.694 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.696 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.698 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
9.699 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
9.701 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
9.701 * * * [progress]: simplifying candidates
9.701 * * * * [progress]: [ 1 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
9.701 * * * * [progress]: [ 2 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
9.701 * * * * [progress]: [ 3 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
9.702 * * * * [progress]: [ 4 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
9.702 * * * * [progress]: [ 5 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
9.702 * * * * [progress]: [ 6 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
9.702 * * * * [progress]: [ 7 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
9.702 * * * * [progress]: [ 8 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))>
9.702 * * * * [progress]: [ 9 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
9.702 * * * * [progress]: [ 10 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
9.702 * * * * [progress]: [ 11 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
9.702 * * * * [progress]: [ 12 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))>
9.702 * * * * [progress]: [ 13 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))>
9.702 * * * * [progress]: [ 14 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
9.702 * * * * [progress]: [ 15 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt k)))>
9.702 * * * * [progress]: [ 16 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt k)))>
9.702 * * * * [progress]: [ 17 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt k)))>
9.702 * * * * [progress]: [ 18 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
9.702 * * * * [progress]: [ 19 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
9.703 * * * * [progress]: [ 20 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
9.703 * * * * [progress]: [ 21 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
9.703 * * * * [progress]: [ 22 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
9.703 * * * * [progress]: [ 23 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
9.703 * * * * [progress]: [ 24 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
9.703 * * * * [progress]: [ 25 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
9.703 * * * * [progress]: [ 26 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
9.703 * * * * [progress]: [ 27 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
9.703 * * * * [progress]: [ 28 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
9.703 * * * * [progress]: [ 29 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
9.703 * * * * [progress]: [ 30 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.703 * * * * [progress]: [ 31 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 32 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 33 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 34 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 35 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 36 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 37 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 38 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 39 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 40 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 41 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 42 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 43 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 44 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 45 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))>
9.704 * * * * [progress]: [ 46 / 127 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) 1))>
9.705 * * * * [progress]: [ 47 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
9.705 * * * * [progress]: [ 48 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
9.705 * * * * [progress]: [ 49 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
9.705 * * * * [progress]: [ 50 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
9.705 * * * * [progress]: [ 51 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
9.705 * * * * [progress]: [ 52 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
9.705 * * * * [progress]: [ 53 / 127 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
9.705 * * * * [progress]: [ 54 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
9.705 * * * * [progress]: [ 55 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
9.705 * * * * [progress]: [ 56 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
9.705 * * * * [progress]: [ 57 / 127 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
9.705 * * * * [progress]: [ 58 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (- (sqrt k))))>
9.705 * * * * [progress]: [ 59 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
9.705 * * * * [progress]: [ 60 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))))>
9.705 * * * * [progress]: [ 61 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
9.706 * * * * [progress]: [ 62 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1)) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
9.706 * * * * [progress]: [ 63 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
9.706 * * * * [progress]: [ 64 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
9.706 * * * * [progress]: [ 65 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
9.706 * * * * [progress]: [ 66 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))))>
9.706 * * * * [progress]: [ 67 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
9.706 * * * * [progress]: [ 68 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1)) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
9.706 * * * * [progress]: [ 69 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
9.706 * * * * [progress]: [ 70 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
9.706 * * * * [progress]: [ 71 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
9.706 * * * * [progress]: [ 72 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
9.706 * * * * [progress]: [ 73 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
9.706 * * * * [progress]: [ 74 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))>
9.706 * * * * [progress]: [ 75 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
9.706 * * * * [progress]: [ 76 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) 1) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))>
9.706 * * * * [progress]: [ 77 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
9.707 * * * * [progress]: [ 78 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
9.707 * * * * [progress]: [ 79 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
9.707 * * * * [progress]: [ 80 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt 1)) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
9.707 * * * * [progress]: [ 81 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
9.707 * * * * [progress]: [ 82 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
9.707 * * * * [progress]: [ 83 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
9.707 * * * * [progress]: [ 84 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
9.707 * * * * [progress]: [ 85 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
9.707 * * * * [progress]: [ 86 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
9.707 * * * * [progress]: [ 87 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
9.707 * * * * [progress]: [ 88 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
9.707 * * * * [progress]: [ 89 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
9.707 * * * * [progress]: [ 90 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
9.707 * * * * [progress]: [ 91 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
9.707 * * * * [progress]: [ 92 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
9.708 * * * * [progress]: [ 93 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
9.708 * * * * [progress]: [ 94 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
9.708 * * * * [progress]: [ 95 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))>
9.708 * * * * [progress]: [ 96 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))>
9.708 * * * * [progress]: [ 97 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
9.708 * * * * [progress]: [ 98 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
9.708 * * * * [progress]: [ 99 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
9.708 * * * * [progress]: [ 100 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
9.708 * * * * [progress]: [ 101 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
9.708 * * * * [progress]: [ 102 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
9.708 * * * * [progress]: [ 103 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
9.708 * * * * [progress]: [ 104 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
9.708 * * * * [progress]: [ 105 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
9.708 * * * * [progress]: [ 106 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
9.708 * * * * [progress]: [ 107 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k)))>
9.709 * * * * [progress]: [ 108 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
9.709 * * * * [progress]: [ 109 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
9.709 * * * * [progress]: [ 110 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
9.709 * * * * [progress]: [ 111 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
9.709 * * * * [progress]: [ 112 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
9.709 * * * * [progress]: [ 113 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.709 * * * * [progress]: [ 114 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.709 * * * * [progress]: [ 115 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
9.709 * * * * [progress]: [ 116 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
9.709 * * * * [progress]: [ 117 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))>
9.709 * * * * [progress]: [ 118 / 127 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
9.709 * * * * [progress]: [ 119 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
9.709 * * * * [progress]: [ 120 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
9.709 * * * * [progress]: [ 121 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
9.710 * * * * [progress]: [ 122 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
9.710 * * * * [progress]: [ 123 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
9.710 * * * * [progress]: [ 124 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
9.710 * * * * [progress]: [ 125 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
9.710 * * * * [progress]: [ 126 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
9.710 * * * * [progress]: [ 127 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
9.713 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (log (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (exp (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (* (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) 1)
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) 1)
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))
  (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) 1)
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt 1))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) 1)
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1)
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1)
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1)
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))
  (real->posit16 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
9.718 * * [simplify]: iteration 1: (267 enodes)
9.840 * * [simplify]: iteration 2: (645 enodes)
10.390 * * [simplify]: Extracting #0: cost 97 inf + 0
10.392 * * [simplify]: Extracting #1: cost 377 inf + 1
10.398 * * [simplify]: Extracting #2: cost 524 inf + 14272
10.416 * * [simplify]: Extracting #3: cost 450 inf + 67790
10.440 * * [simplify]: Extracting #4: cost 250 inf + 153269
10.489 * * [simplify]: Extracting #5: cost 139 inf + 201974
10.555 * * [simplify]: Extracting #6: cost 93 inf + 229429
10.595 * * [simplify]: Extracting #7: cost 31 inf + 262243
10.659 * * [simplify]: Extracting #8: cost 6 inf + 282585
10.737 * * [simplify]: Extracting #9: cost 0 inf + 289225
10.826 * * [simplify]: Extracting #10: cost 0 inf + 289105
10.917 * [simplify]: Simplified to:
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2))))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* PI 2) n) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* PI 2) n)
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (- (/ k 2)))
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* (* n n) (* n 8)) PI) (* PI PI))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* 2 (* PI (cbrt n)))
  (* (sqrt n) (* PI 2))
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (exp (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (/ (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (sqrt k)) k)
  (* (cbrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (* (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)) (* (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* (* PI 2) n)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* PI 2) n))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* PI 2) n))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* (* PI 2) n)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* PI 2) n))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* PI 2) n))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))
  (/ (/ (pow n (- 1/2 (/ k 2))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow n (- 1/2 (/ k 2)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow n (- 1/2 (/ k 2)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt k))
  (* (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (* (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (fabs (cbrt k))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (* (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k))
  (* (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (fabs (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/2 (/ k 2)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/2 (/ k 2)))
  (/ (sqrt k) (pow (* (* PI 2) n) (- (/ k 2))))
  (/ (sqrt k) (pow (* (* PI 2) n) (- (/ k 2))))
  (/ (sqrt k) (pow (* PI 2) (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (* (sqrt k) (pow (* (* PI 2) n) (/ k 2)))
  (real->posit16 (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (+ (+ (* (* 1/4 (log (* PI 2))) (* (* (sqrt (* (* PI 2) n)) (log n)) (* k k))) (* (* 1/8 (* (* (log n) (log n)) (sqrt (* (* PI 2) n)))) (* k k))) (- (+ (* (* (* k k) (* (log (* PI 2)) (* (sqrt (* (* PI 2) n)) (log (* PI 2))))) 1/8) (sqrt (* (* PI 2) n))) (* 1/2 (* k (+ (* (sqrt (* (* PI 2) n)) (log n)) (* (sqrt (* (* PI 2) n)) (log (* PI 2))))))))
  (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
  (+ (* (- (* (log (* PI 2)) +nan.0)) (* (* (sqrt (* (* PI 2) n)) (log n)) (* k k))) (- (* +nan.0 (* (* (sqrt (* (* PI 2) n)) (log (* PI 2))) (* k k))) (- (* (* (sqrt (* (* PI 2) n)) +nan.0) (* (* k (log n)) (* k (log n)))) (+ (- (* (* k (sqrt (* (* PI 2) n))) +nan.0) (* (sqrt (* (* PI 2) n)) +nan.0)) (+ (- (* (* (* k k) (* (log (* PI 2)) (* (sqrt (* (* PI 2) n)) (log (* PI 2))))) +nan.0) (* +nan.0 (* (* (sqrt (* (* PI 2) n)) (log n)) (* k k)))) (+ (- (* (* k k) (* (sqrt (* (* PI 2) n)) +nan.0)) (* +nan.0 (* k (* (sqrt (* (* PI 2) n)) (log (* PI 2)))))) (* (* (log n) k) (* (sqrt (* (* PI 2) n)) +nan.0))))))))
  (- (+ (- (* (/ (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) (* k (* k k))) +nan.0) (/ (* (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) +nan.0) k)) (/ (* (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) +nan.0) (* k k))))
  (- (- (* +nan.0 (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) k)) (* +nan.0 (- (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* k k)) (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))))))
10.933 * * * [progress]: adding candidates to table
12.370 * * [progress]: iteration 2 / 4
12.370 * * * [progress]: picking best candidate
12.419 * * * * [pick]: Picked  #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
12.420 * * * [progress]: localizing error
12.474 * * * [progress]: generating rewritten candidates
12.474 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2)
12.491 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1)
12.504 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2)
12.514 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
12.547 * * * [progress]: generating series expansions
12.548 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2)
12.548 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
12.548 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
12.548 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
12.548 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
12.548 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
12.548 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.549 * [taylor]: Taking taylor expansion of 1/2 in k
12.549 * [backup-simplify]: Simplify 1/2 into 1/2
12.549 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.549 * [taylor]: Taking taylor expansion of 1/2 in k
12.549 * [backup-simplify]: Simplify 1/2 into 1/2
12.549 * [taylor]: Taking taylor expansion of k in k
12.549 * [backup-simplify]: Simplify 0 into 0
12.549 * [backup-simplify]: Simplify 1 into 1
12.549 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.549 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.549 * [taylor]: Taking taylor expansion of 2 in k
12.549 * [backup-simplify]: Simplify 2 into 2
12.549 * [taylor]: Taking taylor expansion of (* n PI) in k
12.549 * [taylor]: Taking taylor expansion of n in k
12.549 * [backup-simplify]: Simplify n into n
12.549 * [taylor]: Taking taylor expansion of PI in k
12.549 * [backup-simplify]: Simplify PI into PI
12.549 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.549 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.549 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.549 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.549 * [backup-simplify]: Simplify (- 0) into 0
12.550 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.550 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
12.550 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
12.550 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
12.550 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
12.550 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
12.550 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.550 * [taylor]: Taking taylor expansion of 1/2 in n
12.550 * [backup-simplify]: Simplify 1/2 into 1/2
12.550 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.550 * [taylor]: Taking taylor expansion of 1/2 in n
12.550 * [backup-simplify]: Simplify 1/2 into 1/2
12.550 * [taylor]: Taking taylor expansion of k in n
12.550 * [backup-simplify]: Simplify k into k
12.550 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.550 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.550 * [taylor]: Taking taylor expansion of 2 in n
12.550 * [backup-simplify]: Simplify 2 into 2
12.550 * [taylor]: Taking taylor expansion of (* n PI) in n
12.550 * [taylor]: Taking taylor expansion of n in n
12.550 * [backup-simplify]: Simplify 0 into 0
12.550 * [backup-simplify]: Simplify 1 into 1
12.550 * [taylor]: Taking taylor expansion of PI in n
12.550 * [backup-simplify]: Simplify PI into PI
12.551 * [backup-simplify]: Simplify (* 0 PI) into 0
12.551 * [backup-simplify]: Simplify (* 2 0) into 0
12.552 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.553 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.553 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.553 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.553 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.553 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.554 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.555 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
12.556 * [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)))))
12.556 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
12.556 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
12.556 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
12.556 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.556 * [taylor]: Taking taylor expansion of 1/2 in n
12.556 * [backup-simplify]: Simplify 1/2 into 1/2
12.556 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.556 * [taylor]: Taking taylor expansion of 1/2 in n
12.556 * [backup-simplify]: Simplify 1/2 into 1/2
12.556 * [taylor]: Taking taylor expansion of k in n
12.556 * [backup-simplify]: Simplify k into k
12.556 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.556 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.556 * [taylor]: Taking taylor expansion of 2 in n
12.556 * [backup-simplify]: Simplify 2 into 2
12.556 * [taylor]: Taking taylor expansion of (* n PI) in n
12.556 * [taylor]: Taking taylor expansion of n in n
12.556 * [backup-simplify]: Simplify 0 into 0
12.556 * [backup-simplify]: Simplify 1 into 1
12.556 * [taylor]: Taking taylor expansion of PI in n
12.556 * [backup-simplify]: Simplify PI into PI
12.556 * [backup-simplify]: Simplify (* 0 PI) into 0
12.557 * [backup-simplify]: Simplify (* 2 0) into 0
12.557 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.558 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.559 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.559 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.559 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.560 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.561 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.563 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
12.564 * [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)))))
12.564 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
12.564 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
12.564 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.564 * [taylor]: Taking taylor expansion of 1/2 in k
12.564 * [backup-simplify]: Simplify 1/2 into 1/2
12.564 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.564 * [taylor]: Taking taylor expansion of 1/2 in k
12.564 * [backup-simplify]: Simplify 1/2 into 1/2
12.564 * [taylor]: Taking taylor expansion of k in k
12.564 * [backup-simplify]: Simplify 0 into 0
12.564 * [backup-simplify]: Simplify 1 into 1
12.564 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
12.564 * [taylor]: Taking taylor expansion of (log n) in k
12.564 * [taylor]: Taking taylor expansion of n in k
12.564 * [backup-simplify]: Simplify n into n
12.564 * [backup-simplify]: Simplify (log n) into (log n)
12.564 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.564 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.564 * [taylor]: Taking taylor expansion of 2 in k
12.564 * [backup-simplify]: Simplify 2 into 2
12.564 * [taylor]: Taking taylor expansion of PI in k
12.564 * [backup-simplify]: Simplify PI into PI
12.565 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.566 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.566 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.567 * [backup-simplify]: Simplify (- 0) into 0
12.567 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.568 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.569 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
12.570 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
12.571 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
12.572 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.574 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.575 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.576 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
12.576 * [backup-simplify]: Simplify (- 0) into 0
12.577 * [backup-simplify]: Simplify (+ 0 0) into 0
12.578 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.579 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
12.581 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.581 * [taylor]: Taking taylor expansion of 0 in k
12.581 * [backup-simplify]: Simplify 0 into 0
12.581 * [backup-simplify]: Simplify 0 into 0
12.582 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.582 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.584 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.585 * [backup-simplify]: Simplify (+ 0 0) into 0
12.585 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
12.586 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.586 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.587 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
12.589 * [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)))))))
12.591 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
12.592 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.592 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.594 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
12.595 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
12.595 * [backup-simplify]: Simplify (- 0) into 0
12.595 * [backup-simplify]: Simplify (+ 0 0) into 0
12.596 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.597 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.598 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.598 * [taylor]: Taking taylor expansion of 0 in k
12.598 * [backup-simplify]: Simplify 0 into 0
12.598 * [backup-simplify]: Simplify 0 into 0
12.599 * [backup-simplify]: Simplify 0 into 0
12.600 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.600 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.602 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
12.602 * [backup-simplify]: Simplify (+ 0 0) into 0
12.603 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
12.603 * [backup-simplify]: Simplify (- 0) into 0
12.603 * [backup-simplify]: Simplify (+ 0 0) into 0
12.604 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.607 * [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)))))
12.610 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
12.615 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
12.616 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
12.616 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
12.616 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
12.616 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.616 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.616 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.616 * [taylor]: Taking taylor expansion of 1/2 in k
12.616 * [backup-simplify]: Simplify 1/2 into 1/2
12.616 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.616 * [taylor]: Taking taylor expansion of 1/2 in k
12.616 * [backup-simplify]: Simplify 1/2 into 1/2
12.616 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.616 * [taylor]: Taking taylor expansion of k in k
12.616 * [backup-simplify]: Simplify 0 into 0
12.616 * [backup-simplify]: Simplify 1 into 1
12.616 * [backup-simplify]: Simplify (/ 1 1) into 1
12.616 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.616 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.616 * [taylor]: Taking taylor expansion of 2 in k
12.616 * [backup-simplify]: Simplify 2 into 2
12.616 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.616 * [taylor]: Taking taylor expansion of PI in k
12.616 * [backup-simplify]: Simplify PI into PI
12.616 * [taylor]: Taking taylor expansion of n in k
12.616 * [backup-simplify]: Simplify n into n
12.616 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.617 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.617 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.617 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.617 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.617 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.617 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.618 * [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))))
12.618 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.618 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.618 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.618 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.618 * [taylor]: Taking taylor expansion of 1/2 in n
12.618 * [backup-simplify]: Simplify 1/2 into 1/2
12.618 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.618 * [taylor]: Taking taylor expansion of 1/2 in n
12.618 * [backup-simplify]: Simplify 1/2 into 1/2
12.618 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.618 * [taylor]: Taking taylor expansion of k in n
12.618 * [backup-simplify]: Simplify k into k
12.618 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.618 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.618 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.618 * [taylor]: Taking taylor expansion of 2 in n
12.618 * [backup-simplify]: Simplify 2 into 2
12.618 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.618 * [taylor]: Taking taylor expansion of PI in n
12.618 * [backup-simplify]: Simplify PI into PI
12.618 * [taylor]: Taking taylor expansion of n in n
12.618 * [backup-simplify]: Simplify 0 into 0
12.618 * [backup-simplify]: Simplify 1 into 1
12.618 * [backup-simplify]: Simplify (/ PI 1) into PI
12.619 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.619 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.619 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.619 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.619 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.620 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.621 * [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)))
12.622 * [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))))
12.622 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.622 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.622 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.622 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.622 * [taylor]: Taking taylor expansion of 1/2 in n
12.622 * [backup-simplify]: Simplify 1/2 into 1/2
12.622 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.622 * [taylor]: Taking taylor expansion of 1/2 in n
12.622 * [backup-simplify]: Simplify 1/2 into 1/2
12.622 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.622 * [taylor]: Taking taylor expansion of k in n
12.622 * [backup-simplify]: Simplify k into k
12.622 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.622 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.622 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.622 * [taylor]: Taking taylor expansion of 2 in n
12.622 * [backup-simplify]: Simplify 2 into 2
12.622 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.622 * [taylor]: Taking taylor expansion of PI in n
12.622 * [backup-simplify]: Simplify PI into PI
12.622 * [taylor]: Taking taylor expansion of n in n
12.622 * [backup-simplify]: Simplify 0 into 0
12.622 * [backup-simplify]: Simplify 1 into 1
12.622 * [backup-simplify]: Simplify (/ PI 1) into PI
12.623 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.623 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.623 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.623 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.624 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.624 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.625 * [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)))
12.626 * [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))))
12.626 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
12.626 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
12.626 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.626 * [taylor]: Taking taylor expansion of 1/2 in k
12.626 * [backup-simplify]: Simplify 1/2 into 1/2
12.626 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.626 * [taylor]: Taking taylor expansion of 1/2 in k
12.626 * [backup-simplify]: Simplify 1/2 into 1/2
12.626 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.626 * [taylor]: Taking taylor expansion of k in k
12.626 * [backup-simplify]: Simplify 0 into 0
12.626 * [backup-simplify]: Simplify 1 into 1
12.626 * [backup-simplify]: Simplify (/ 1 1) into 1
12.626 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
12.626 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.626 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.626 * [taylor]: Taking taylor expansion of 2 in k
12.626 * [backup-simplify]: Simplify 2 into 2
12.626 * [taylor]: Taking taylor expansion of PI in k
12.626 * [backup-simplify]: Simplify PI into PI
12.627 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.627 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.627 * [taylor]: Taking taylor expansion of (log n) in k
12.627 * [taylor]: Taking taylor expansion of n in k
12.627 * [backup-simplify]: Simplify n into n
12.627 * [backup-simplify]: Simplify (log n) into (log n)
12.628 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.628 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.628 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.628 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.629 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
12.629 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
12.634 * [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))))
12.635 * [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))))
12.636 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.636 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.637 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.637 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.638 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.638 * [backup-simplify]: Simplify (- 0) into 0
12.638 * [backup-simplify]: Simplify (+ 0 0) into 0
12.639 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.640 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
12.641 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.641 * [taylor]: Taking taylor expansion of 0 in k
12.641 * [backup-simplify]: Simplify 0 into 0
12.641 * [backup-simplify]: Simplify 0 into 0
12.641 * [backup-simplify]: Simplify 0 into 0
12.642 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.642 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.644 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
12.644 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.645 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.645 * [backup-simplify]: Simplify (- 0) into 0
12.645 * [backup-simplify]: Simplify (+ 0 0) into 0
12.646 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.647 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
12.648 * [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
12.648 * [taylor]: Taking taylor expansion of 0 in k
12.648 * [backup-simplify]: Simplify 0 into 0
12.649 * [backup-simplify]: Simplify 0 into 0
12.649 * [backup-simplify]: Simplify 0 into 0
12.649 * [backup-simplify]: Simplify 0 into 0
12.649 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.650 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.654 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
12.654 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.655 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.655 * [backup-simplify]: Simplify (- 0) into 0
12.655 * [backup-simplify]: Simplify (+ 0 0) into 0
12.656 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.657 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
12.659 * [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
12.659 * [taylor]: Taking taylor expansion of 0 in k
12.659 * [backup-simplify]: Simplify 0 into 0
12.659 * [backup-simplify]: Simplify 0 into 0
12.659 * [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)))))
12.660 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
12.660 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
12.660 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
12.660 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
12.660 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
12.660 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.660 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.660 * [taylor]: Taking taylor expansion of 1/2 in k
12.660 * [backup-simplify]: Simplify 1/2 into 1/2
12.660 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.660 * [taylor]: Taking taylor expansion of k in k
12.660 * [backup-simplify]: Simplify 0 into 0
12.660 * [backup-simplify]: Simplify 1 into 1
12.660 * [backup-simplify]: Simplify (/ 1 1) into 1
12.660 * [taylor]: Taking taylor expansion of 1/2 in k
12.660 * [backup-simplify]: Simplify 1/2 into 1/2
12.660 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.660 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.660 * [taylor]: Taking taylor expansion of -2 in k
12.661 * [backup-simplify]: Simplify -2 into -2
12.661 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.661 * [taylor]: Taking taylor expansion of PI in k
12.661 * [backup-simplify]: Simplify PI into PI
12.661 * [taylor]: Taking taylor expansion of n in k
12.661 * [backup-simplify]: Simplify n into n
12.661 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.661 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.661 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.661 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.661 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.661 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
12.661 * [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)))
12.661 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.662 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
12.662 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
12.662 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.662 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.662 * [taylor]: Taking taylor expansion of 1/2 in n
12.662 * [backup-simplify]: Simplify 1/2 into 1/2
12.662 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.662 * [taylor]: Taking taylor expansion of k in n
12.662 * [backup-simplify]: Simplify k into k
12.662 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.662 * [taylor]: Taking taylor expansion of 1/2 in n
12.662 * [backup-simplify]: Simplify 1/2 into 1/2
12.662 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.662 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.662 * [taylor]: Taking taylor expansion of -2 in n
12.662 * [backup-simplify]: Simplify -2 into -2
12.662 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.662 * [taylor]: Taking taylor expansion of PI in n
12.662 * [backup-simplify]: Simplify PI into PI
12.662 * [taylor]: Taking taylor expansion of n in n
12.662 * [backup-simplify]: Simplify 0 into 0
12.662 * [backup-simplify]: Simplify 1 into 1
12.662 * [backup-simplify]: Simplify (/ PI 1) into PI
12.662 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.663 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.663 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.663 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.664 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.665 * [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)))
12.665 * [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))))
12.665 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.665 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
12.665 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
12.665 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.665 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.665 * [taylor]: Taking taylor expansion of 1/2 in n
12.665 * [backup-simplify]: Simplify 1/2 into 1/2
12.665 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.665 * [taylor]: Taking taylor expansion of k in n
12.665 * [backup-simplify]: Simplify k into k
12.666 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.666 * [taylor]: Taking taylor expansion of 1/2 in n
12.666 * [backup-simplify]: Simplify 1/2 into 1/2
12.666 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.666 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.666 * [taylor]: Taking taylor expansion of -2 in n
12.666 * [backup-simplify]: Simplify -2 into -2
12.666 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.666 * [taylor]: Taking taylor expansion of PI in n
12.666 * [backup-simplify]: Simplify PI into PI
12.666 * [taylor]: Taking taylor expansion of n in n
12.666 * [backup-simplify]: Simplify 0 into 0
12.666 * [backup-simplify]: Simplify 1 into 1
12.666 * [backup-simplify]: Simplify (/ PI 1) into PI
12.666 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.667 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.667 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.667 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.668 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.668 * [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)))
12.669 * [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))))
12.669 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
12.669 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
12.669 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.669 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.669 * [taylor]: Taking taylor expansion of 1/2 in k
12.669 * [backup-simplify]: Simplify 1/2 into 1/2
12.669 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.669 * [taylor]: Taking taylor expansion of k in k
12.669 * [backup-simplify]: Simplify 0 into 0
12.669 * [backup-simplify]: Simplify 1 into 1
12.670 * [backup-simplify]: Simplify (/ 1 1) into 1
12.670 * [taylor]: Taking taylor expansion of 1/2 in k
12.670 * [backup-simplify]: Simplify 1/2 into 1/2
12.670 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
12.670 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
12.670 * [taylor]: Taking taylor expansion of (* -2 PI) in k
12.670 * [taylor]: Taking taylor expansion of -2 in k
12.670 * [backup-simplify]: Simplify -2 into -2
12.670 * [taylor]: Taking taylor expansion of PI in k
12.670 * [backup-simplify]: Simplify PI into PI
12.670 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.671 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.671 * [taylor]: Taking taylor expansion of (log n) in k
12.671 * [taylor]: Taking taylor expansion of n in k
12.671 * [backup-simplify]: Simplify n into n
12.671 * [backup-simplify]: Simplify (log n) into (log n)
12.671 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.671 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.671 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.672 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
12.673 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
12.673 * [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))))
12.674 * [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))))
12.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.675 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.676 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
12.676 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.676 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.677 * [backup-simplify]: Simplify (+ 0 0) into 0
12.678 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.678 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
12.679 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.680 * [taylor]: Taking taylor expansion of 0 in k
12.680 * [backup-simplify]: Simplify 0 into 0
12.680 * [backup-simplify]: Simplify 0 into 0
12.680 * [backup-simplify]: Simplify 0 into 0
12.680 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.681 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.683 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
12.683 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.684 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.684 * [backup-simplify]: Simplify (+ 0 0) into 0
12.685 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.686 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
12.687 * [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
12.687 * [taylor]: Taking taylor expansion of 0 in k
12.687 * [backup-simplify]: Simplify 0 into 0
12.687 * [backup-simplify]: Simplify 0 into 0
12.687 * [backup-simplify]: Simplify 0 into 0
12.687 * [backup-simplify]: Simplify 0 into 0
12.688 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.689 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.692 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
12.692 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.693 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.693 * [backup-simplify]: Simplify (+ 0 0) into 0
12.694 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.695 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
12.697 * [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
12.697 * [taylor]: Taking taylor expansion of 0 in k
12.697 * [backup-simplify]: Simplify 0 into 0
12.697 * [backup-simplify]: Simplify 0 into 0
12.698 * [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)))))
12.698 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1)
12.698 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
12.698 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
12.698 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.698 * [taylor]: Taking taylor expansion of 2 in n
12.698 * [backup-simplify]: Simplify 2 into 2
12.698 * [taylor]: Taking taylor expansion of (* n PI) in n
12.698 * [taylor]: Taking taylor expansion of n in n
12.698 * [backup-simplify]: Simplify 0 into 0
12.698 * [backup-simplify]: Simplify 1 into 1
12.698 * [taylor]: Taking taylor expansion of PI in n
12.698 * [backup-simplify]: Simplify PI into PI
12.698 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.698 * [taylor]: Taking taylor expansion of 2 in n
12.698 * [backup-simplify]: Simplify 2 into 2
12.698 * [taylor]: Taking taylor expansion of (* n PI) in n
12.698 * [taylor]: Taking taylor expansion of n in n
12.698 * [backup-simplify]: Simplify 0 into 0
12.698 * [backup-simplify]: Simplify 1 into 1
12.698 * [taylor]: Taking taylor expansion of PI in n
12.698 * [backup-simplify]: Simplify PI into PI
12.699 * [backup-simplify]: Simplify (* 0 PI) into 0
12.699 * [backup-simplify]: Simplify (* 2 0) into 0
12.699 * [backup-simplify]: Simplify 0 into 0
12.700 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.701 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.701 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.702 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.702 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.703 * [backup-simplify]: Simplify 0 into 0
12.703 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.704 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.704 * [backup-simplify]: Simplify 0 into 0
12.705 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.706 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.706 * [backup-simplify]: Simplify 0 into 0
12.707 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.707 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
12.707 * [backup-simplify]: Simplify 0 into 0
12.708 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.709 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
12.709 * [backup-simplify]: Simplify 0 into 0
12.710 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
12.711 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
12.711 * [backup-simplify]: Simplify 0 into 0
12.712 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
12.712 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
12.712 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
12.712 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.712 * [taylor]: Taking taylor expansion of 2 in n
12.712 * [backup-simplify]: Simplify 2 into 2
12.712 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.712 * [taylor]: Taking taylor expansion of PI in n
12.712 * [backup-simplify]: Simplify PI into PI
12.712 * [taylor]: Taking taylor expansion of n in n
12.712 * [backup-simplify]: Simplify 0 into 0
12.712 * [backup-simplify]: Simplify 1 into 1
12.712 * [backup-simplify]: Simplify (/ PI 1) into PI
12.713 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.713 * [taylor]: Taking taylor expansion of 2 in n
12.713 * [backup-simplify]: Simplify 2 into 2
12.713 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.713 * [taylor]: Taking taylor expansion of PI in n
12.713 * [backup-simplify]: Simplify PI into PI
12.713 * [taylor]: Taking taylor expansion of n in n
12.713 * [backup-simplify]: Simplify 0 into 0
12.713 * [backup-simplify]: Simplify 1 into 1
12.713 * [backup-simplify]: Simplify (/ PI 1) into PI
12.713 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.714 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.714 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.715 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.715 * [backup-simplify]: Simplify 0 into 0
12.715 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.716 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.716 * [backup-simplify]: Simplify 0 into 0
12.716 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.717 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.717 * [backup-simplify]: Simplify 0 into 0
12.718 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.718 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.718 * [backup-simplify]: Simplify 0 into 0
12.719 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.720 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.720 * [backup-simplify]: Simplify 0 into 0
12.722 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.723 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.723 * [backup-simplify]: Simplify 0 into 0
12.724 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
12.725 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
12.725 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
12.725 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.725 * [taylor]: Taking taylor expansion of -2 in n
12.725 * [backup-simplify]: Simplify -2 into -2
12.725 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.725 * [taylor]: Taking taylor expansion of PI in n
12.725 * [backup-simplify]: Simplify PI into PI
12.725 * [taylor]: Taking taylor expansion of n in n
12.725 * [backup-simplify]: Simplify 0 into 0
12.725 * [backup-simplify]: Simplify 1 into 1
12.725 * [backup-simplify]: Simplify (/ PI 1) into PI
12.725 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.725 * [taylor]: Taking taylor expansion of -2 in n
12.725 * [backup-simplify]: Simplify -2 into -2
12.725 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.725 * [taylor]: Taking taylor expansion of PI in n
12.725 * [backup-simplify]: Simplify PI into PI
12.725 * [taylor]: Taking taylor expansion of n in n
12.726 * [backup-simplify]: Simplify 0 into 0
12.726 * [backup-simplify]: Simplify 1 into 1
12.726 * [backup-simplify]: Simplify (/ PI 1) into PI
12.727 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.727 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.728 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.729 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.729 * [backup-simplify]: Simplify 0 into 0
12.730 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.731 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.731 * [backup-simplify]: Simplify 0 into 0
12.732 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.733 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.733 * [backup-simplify]: Simplify 0 into 0
12.734 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.736 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.736 * [backup-simplify]: Simplify 0 into 0
12.737 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.738 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.738 * [backup-simplify]: Simplify 0 into 0
12.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.741 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.741 * [backup-simplify]: Simplify 0 into 0
12.742 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
12.742 * * * * [progress]: [ 3 / 4 ] generating series at (2 2)
12.743 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k))
12.743 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0
12.743 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n
12.743 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
12.743 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
12.743 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
12.743 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
12.743 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.743 * [taylor]: Taking taylor expansion of 1/2 in n
12.743 * [backup-simplify]: Simplify 1/2 into 1/2
12.743 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.743 * [taylor]: Taking taylor expansion of 1/2 in n
12.743 * [backup-simplify]: Simplify 1/2 into 1/2
12.743 * [taylor]: Taking taylor expansion of k in n
12.743 * [backup-simplify]: Simplify k into k
12.743 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.743 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.743 * [taylor]: Taking taylor expansion of 2 in n
12.743 * [backup-simplify]: Simplify 2 into 2
12.743 * [taylor]: Taking taylor expansion of (* n PI) in n
12.743 * [taylor]: Taking taylor expansion of n in n
12.743 * [backup-simplify]: Simplify 0 into 0
12.743 * [backup-simplify]: Simplify 1 into 1
12.744 * [taylor]: Taking taylor expansion of PI in n
12.744 * [backup-simplify]: Simplify PI into PI
12.744 * [backup-simplify]: Simplify (* 0 PI) into 0
12.745 * [backup-simplify]: Simplify (* 2 0) into 0
12.746 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.748 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.749 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.749 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.749 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.749 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.751 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.752 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
12.753 * [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)))))
12.754 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
12.754 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.754 * [taylor]: Taking taylor expansion of k in n
12.754 * [backup-simplify]: Simplify k into k
12.754 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.754 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.754 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k
12.755 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
12.755 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
12.755 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
12.755 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
12.755 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.755 * [taylor]: Taking taylor expansion of 1/2 in k
12.755 * [backup-simplify]: Simplify 1/2 into 1/2
12.755 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.755 * [taylor]: Taking taylor expansion of 1/2 in k
12.755 * [backup-simplify]: Simplify 1/2 into 1/2
12.755 * [taylor]: Taking taylor expansion of k in k
12.755 * [backup-simplify]: Simplify 0 into 0
12.755 * [backup-simplify]: Simplify 1 into 1
12.755 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.755 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.755 * [taylor]: Taking taylor expansion of 2 in k
12.755 * [backup-simplify]: Simplify 2 into 2
12.755 * [taylor]: Taking taylor expansion of (* n PI) in k
12.755 * [taylor]: Taking taylor expansion of n in k
12.755 * [backup-simplify]: Simplify n into n
12.755 * [taylor]: Taking taylor expansion of PI in k
12.755 * [backup-simplify]: Simplify PI into PI
12.755 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.755 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.755 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.756 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.756 * [backup-simplify]: Simplify (- 0) into 0
12.757 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.757 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
12.757 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
12.757 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2))))
12.757 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.757 * [taylor]: Taking taylor expansion of k in k
12.757 * [backup-simplify]: Simplify 0 into 0
12.757 * [backup-simplify]: Simplify 1 into 1
12.758 * [backup-simplify]: Simplify (sqrt 0) into 0
12.759 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.759 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k
12.759 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
12.759 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
12.759 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
12.760 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
12.760 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.760 * [taylor]: Taking taylor expansion of 1/2 in k
12.760 * [backup-simplify]: Simplify 1/2 into 1/2
12.760 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.760 * [taylor]: Taking taylor expansion of 1/2 in k
12.760 * [backup-simplify]: Simplify 1/2 into 1/2
12.760 * [taylor]: Taking taylor expansion of k in k
12.760 * [backup-simplify]: Simplify 0 into 0
12.760 * [backup-simplify]: Simplify 1 into 1
12.760 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.760 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.760 * [taylor]: Taking taylor expansion of 2 in k
12.760 * [backup-simplify]: Simplify 2 into 2
12.760 * [taylor]: Taking taylor expansion of (* n PI) in k
12.760 * [taylor]: Taking taylor expansion of n in k
12.760 * [backup-simplify]: Simplify n into n
12.760 * [taylor]: Taking taylor expansion of PI in k
12.760 * [backup-simplify]: Simplify PI into PI
12.760 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.760 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.760 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.761 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.761 * [backup-simplify]: Simplify (- 0) into 0
12.762 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.762 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
12.762 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
12.762 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2))))
12.762 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.762 * [taylor]: Taking taylor expansion of k in k
12.762 * [backup-simplify]: Simplify 0 into 0
12.762 * [backup-simplify]: Simplify 1 into 1
12.762 * [backup-simplify]: Simplify (sqrt 0) into 0
12.764 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.764 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0
12.764 * [taylor]: Taking taylor expansion of 0 in n
12.764 * [backup-simplify]: Simplify 0 into 0
12.764 * [backup-simplify]: Simplify 0 into 0
12.765 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
12.765 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
12.766 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
12.767 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
12.767 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.768 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.768 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
12.768 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))
12.769 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))
12.771 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))
12.772 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n
12.772 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n
12.772 * [taylor]: Taking taylor expansion of +nan.0 in n
12.772 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.772 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n
12.772 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
12.772 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n
12.772 * [taylor]: Taking taylor expansion of (* n PI) in n
12.772 * [taylor]: Taking taylor expansion of n in n
12.772 * [backup-simplify]: Simplify 0 into 0
12.772 * [backup-simplify]: Simplify 1 into 1
12.772 * [taylor]: Taking taylor expansion of PI in n
12.772 * [backup-simplify]: Simplify PI into PI
12.772 * [backup-simplify]: Simplify (* 0 PI) into 0
12.774 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.774 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI)
12.775 * [backup-simplify]: Simplify (sqrt 0) into 0
12.777 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
12.777 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n
12.777 * [taylor]: Taking taylor expansion of 1/2 in n
12.777 * [backup-simplify]: Simplify 1/2 into 1/2
12.777 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2)
12.778 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
12.781 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
12.782 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0
12.787 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
12.790 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
12.793 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
12.793 * [backup-simplify]: Simplify 0 into 0
12.796 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.797 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
12.798 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
12.800 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
12.801 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
12.801 * [backup-simplify]: Simplify (- 0) into 0
12.801 * [backup-simplify]: Simplify (+ 0 0) into 0
12.802 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
12.803 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))
12.806 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))))
12.813 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))))
12.813 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n
12.813 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n
12.813 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n
12.813 * [taylor]: Taking taylor expansion of +nan.0 in n
12.813 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.813 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n
12.813 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n
12.813 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.813 * [taylor]: Taking taylor expansion of 2 in n
12.813 * [backup-simplify]: Simplify 2 into 2
12.813 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.814 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.814 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n
12.814 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.814 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.814 * [taylor]: Taking taylor expansion of 2 in n
12.814 * [backup-simplify]: Simplify 2 into 2
12.814 * [taylor]: Taking taylor expansion of (* n PI) in n
12.814 * [taylor]: Taking taylor expansion of n in n
12.814 * [backup-simplify]: Simplify 0 into 0
12.814 * [backup-simplify]: Simplify 1 into 1
12.814 * [taylor]: Taking taylor expansion of PI in n
12.814 * [backup-simplify]: Simplify PI into PI
12.815 * [backup-simplify]: Simplify (* 0 PI) into 0
12.815 * [backup-simplify]: Simplify (* 2 0) into 0
12.817 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.818 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.819 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.819 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n
12.819 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n
12.819 * [taylor]: Taking taylor expansion of 1/2 in n
12.819 * [backup-simplify]: Simplify 1/2 into 1/2
12.820 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2)
12.820 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
12.820 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
12.820 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n
12.820 * [taylor]: Taking taylor expansion of (* n PI) in n
12.820 * [taylor]: Taking taylor expansion of n in n
12.821 * [backup-simplify]: Simplify 0 into 0
12.821 * [backup-simplify]: Simplify 1 into 1
12.821 * [taylor]: Taking taylor expansion of PI in n
12.821 * [backup-simplify]: Simplify PI into PI
12.821 * [backup-simplify]: Simplify (* 0 PI) into 0
12.822 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.823 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI)
12.823 * [backup-simplify]: Simplify (sqrt 0) into 0
12.825 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
12.825 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n
12.825 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n
12.825 * [taylor]: Taking taylor expansion of +nan.0 in n
12.825 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.826 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n
12.826 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
12.826 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n
12.826 * [taylor]: Taking taylor expansion of (* n PI) in n
12.826 * [taylor]: Taking taylor expansion of n in n
12.826 * [backup-simplify]: Simplify 0 into 0
12.826 * [backup-simplify]: Simplify 1 into 1
12.826 * [taylor]: Taking taylor expansion of PI in n
12.826 * [backup-simplify]: Simplify PI into PI
12.826 * [backup-simplify]: Simplify (* 0 PI) into 0
12.827 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.828 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI)
12.828 * [backup-simplify]: Simplify (sqrt 0) into 0
12.830 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
12.830 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n
12.830 * [taylor]: Taking taylor expansion of 1/2 in n
12.830 * [backup-simplify]: Simplify 1/2 into 1/2
12.831 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2)
12.831 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
12.833 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.834 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2)
12.835 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))
12.837 * [backup-simplify]: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))
12.839 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.840 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0
12.841 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.841 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.843 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.845 * [backup-simplify]: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0
12.847 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0
12.851 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))
12.853 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0
12.869 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))
12.872 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
12.873 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0
12.878 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
12.882 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
12.896 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
12.914 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
12.932 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
12.933 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0
12.934 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.935 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0
12.939 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2))
12.943 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
12.949 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
12.951 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
12.953 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
12.968 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI)))))))))))
12.969 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k)))
12.970 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0
12.970 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n
12.970 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
12.970 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.970 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.970 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.970 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.970 * [taylor]: Taking taylor expansion of 1/2 in n
12.970 * [backup-simplify]: Simplify 1/2 into 1/2
12.970 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.970 * [taylor]: Taking taylor expansion of 1/2 in n
12.970 * [backup-simplify]: Simplify 1/2 into 1/2
12.970 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.970 * [taylor]: Taking taylor expansion of k in n
12.970 * [backup-simplify]: Simplify k into k
12.970 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.970 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.970 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.970 * [taylor]: Taking taylor expansion of 2 in n
12.970 * [backup-simplify]: Simplify 2 into 2
12.970 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.970 * [taylor]: Taking taylor expansion of PI in n
12.970 * [backup-simplify]: Simplify PI into PI
12.970 * [taylor]: Taking taylor expansion of n in n
12.970 * [backup-simplify]: Simplify 0 into 0
12.970 * [backup-simplify]: Simplify 1 into 1
12.971 * [backup-simplify]: Simplify (/ PI 1) into PI
12.972 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.972 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.973 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.973 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.973 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.974 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.975 * [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)))
12.976 * [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))))
12.977 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
12.977 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.977 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.977 * [taylor]: Taking taylor expansion of k in n
12.977 * [backup-simplify]: Simplify k into k
12.978 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.978 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.978 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.978 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.978 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k
12.978 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
12.978 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
12.978 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.978 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.978 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.978 * [taylor]: Taking taylor expansion of 1/2 in k
12.978 * [backup-simplify]: Simplify 1/2 into 1/2
12.978 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.978 * [taylor]: Taking taylor expansion of 1/2 in k
12.978 * [backup-simplify]: Simplify 1/2 into 1/2
12.978 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.978 * [taylor]: Taking taylor expansion of k in k
12.978 * [backup-simplify]: Simplify 0 into 0
12.978 * [backup-simplify]: Simplify 1 into 1
12.981 * [backup-simplify]: Simplify (/ 1 1) into 1
12.981 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.981 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.981 * [taylor]: Taking taylor expansion of 2 in k
12.981 * [backup-simplify]: Simplify 2 into 2
12.981 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.981 * [taylor]: Taking taylor expansion of PI in k
12.981 * [backup-simplify]: Simplify PI into PI
12.981 * [taylor]: Taking taylor expansion of n in k
12.981 * [backup-simplify]: Simplify n into n
12.981 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.981 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.981 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.982 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.983 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.983 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.983 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.983 * [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))))
12.983 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
12.983 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.983 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.983 * [taylor]: Taking taylor expansion of k in k
12.983 * [backup-simplify]: Simplify 0 into 0
12.983 * [backup-simplify]: Simplify 1 into 1
12.984 * [backup-simplify]: Simplify (/ 1 1) into 1
12.984 * [backup-simplify]: Simplify (sqrt 0) into 0
12.985 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.985 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k
12.985 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
12.985 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
12.985 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.985 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.985 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.985 * [taylor]: Taking taylor expansion of 1/2 in k
12.985 * [backup-simplify]: Simplify 1/2 into 1/2
12.985 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.985 * [taylor]: Taking taylor expansion of 1/2 in k
12.985 * [backup-simplify]: Simplify 1/2 into 1/2
12.985 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.985 * [taylor]: Taking taylor expansion of k in k
12.985 * [backup-simplify]: Simplify 0 into 0
12.985 * [backup-simplify]: Simplify 1 into 1
12.985 * [backup-simplify]: Simplify (/ 1 1) into 1
12.985 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.985 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.985 * [taylor]: Taking taylor expansion of 2 in k
12.985 * [backup-simplify]: Simplify 2 into 2
12.985 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.985 * [taylor]: Taking taylor expansion of PI in k
12.985 * [backup-simplify]: Simplify PI into PI
12.985 * [taylor]: Taking taylor expansion of n in k
12.985 * [backup-simplify]: Simplify n into n
12.985 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.986 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.986 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.986 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.986 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.986 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.986 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.987 * [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))))
12.987 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
12.987 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.987 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.987 * [taylor]: Taking taylor expansion of k in k
12.987 * [backup-simplify]: Simplify 0 into 0
12.987 * [backup-simplify]: Simplify 1 into 1
12.987 * [backup-simplify]: Simplify (/ 1 1) into 1
12.987 * [backup-simplify]: Simplify (sqrt 0) into 0
12.988 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.988 * [backup-simplify]: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0
12.988 * [taylor]: Taking taylor expansion of 0 in n
12.988 * [backup-simplify]: Simplify 0 into 0
12.988 * [backup-simplify]: Simplify 0 into 0
12.989 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
12.989 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))
12.989 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n
12.989 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n
12.989 * [taylor]: Taking taylor expansion of +nan.0 in n
12.989 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.989 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
12.989 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.989 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.989 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.989 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.989 * [taylor]: Taking taylor expansion of 1/2 in n
12.989 * [backup-simplify]: Simplify 1/2 into 1/2
12.989 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.989 * [taylor]: Taking taylor expansion of 1/2 in n
12.989 * [backup-simplify]: Simplify 1/2 into 1/2
12.989 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.989 * [taylor]: Taking taylor expansion of k in n
12.989 * [backup-simplify]: Simplify k into k
12.989 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.989 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.989 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.989 * [taylor]: Taking taylor expansion of 2 in n
12.989 * [backup-simplify]: Simplify 2 into 2
12.989 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.989 * [taylor]: Taking taylor expansion of PI in n
12.989 * [backup-simplify]: Simplify PI into PI
12.989 * [taylor]: Taking taylor expansion of n in n
12.989 * [backup-simplify]: Simplify 0 into 0
12.989 * [backup-simplify]: Simplify 1 into 1
12.990 * [backup-simplify]: Simplify (/ PI 1) into PI
12.990 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.990 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.991 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.991 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.991 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.992 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.992 * [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)))
12.993 * [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))))
12.994 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
12.994 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
12.995 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
12.996 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
12.996 * [backup-simplify]: Simplify 0 into 0
12.996 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.998 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.998 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
12.999 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))
12.999 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n
12.999 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n
12.999 * [taylor]: Taking taylor expansion of +nan.0 in n
12.999 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.999 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
12.999 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.999 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.999 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.999 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.999 * [taylor]: Taking taylor expansion of 1/2 in n
12.999 * [backup-simplify]: Simplify 1/2 into 1/2
12.999 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.999 * [taylor]: Taking taylor expansion of 1/2 in n
12.999 * [backup-simplify]: Simplify 1/2 into 1/2
12.999 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.999 * [taylor]: Taking taylor expansion of k in n
12.999 * [backup-simplify]: Simplify k into k
12.999 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.999 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.999 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.999 * [taylor]: Taking taylor expansion of 2 in n
12.999 * [backup-simplify]: Simplify 2 into 2
12.999 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.999 * [taylor]: Taking taylor expansion of PI in n
12.999 * [backup-simplify]: Simplify PI into PI
12.999 * [taylor]: Taking taylor expansion of n in n
12.999 * [backup-simplify]: Simplify 0 into 0
12.999 * [backup-simplify]: Simplify 1 into 1
12.999 * [backup-simplify]: Simplify (/ PI 1) into PI
13.000 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.000 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.000 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.000 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
13.000 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
13.001 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.002 * [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)))
13.003 * [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))))
13.003 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
13.004 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
13.005 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
13.005 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
13.006 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.006 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.007 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.007 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.008 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
13.008 * [backup-simplify]: Simplify (- 0) into 0
13.008 * [backup-simplify]: Simplify (+ 0 0) into 0
13.009 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.010 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
13.011 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
13.013 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0
13.014 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
13.015 * [backup-simplify]: Simplify (- 0) into 0
13.015 * [backup-simplify]: Simplify 0 into 0
13.015 * [backup-simplify]: Simplify 0 into 0
13.016 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.019 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.020 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
13.021 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))
13.021 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n
13.021 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n
13.021 * [taylor]: Taking taylor expansion of +nan.0 in n
13.021 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.022 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
13.022 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
13.022 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.022 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.022 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
13.022 * [taylor]: Taking taylor expansion of 1/2 in n
13.022 * [backup-simplify]: Simplify 1/2 into 1/2
13.022 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.022 * [taylor]: Taking taylor expansion of 1/2 in n
13.022 * [backup-simplify]: Simplify 1/2 into 1/2
13.022 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.022 * [taylor]: Taking taylor expansion of k in n
13.022 * [backup-simplify]: Simplify k into k
13.022 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.022 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.022 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.022 * [taylor]: Taking taylor expansion of 2 in n
13.022 * [backup-simplify]: Simplify 2 into 2
13.022 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.022 * [taylor]: Taking taylor expansion of PI in n
13.022 * [backup-simplify]: Simplify PI into PI
13.022 * [taylor]: Taking taylor expansion of n in n
13.022 * [backup-simplify]: Simplify 0 into 0
13.022 * [backup-simplify]: Simplify 1 into 1
13.023 * [backup-simplify]: Simplify (/ PI 1) into PI
13.023 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.024 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.024 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.024 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
13.024 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
13.025 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.025 * [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)))
13.026 * [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))))
13.027 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
13.027 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
13.028 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
13.029 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
13.031 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))))))))
13.032 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)))
13.032 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0
13.032 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n
13.032 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
13.032 * [taylor]: Taking taylor expansion of (/ -1 k) in n
13.032 * [taylor]: Taking taylor expansion of -1 in n
13.032 * [backup-simplify]: Simplify -1 into -1
13.032 * [taylor]: Taking taylor expansion of k in n
13.032 * [backup-simplify]: Simplify k into k
13.032 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
13.032 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
13.032 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
13.032 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
13.032 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.032 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
13.032 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
13.032 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.032 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.032 * [taylor]: Taking taylor expansion of 1/2 in n
13.032 * [backup-simplify]: Simplify 1/2 into 1/2
13.032 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.032 * [taylor]: Taking taylor expansion of k in n
13.032 * [backup-simplify]: Simplify k into k
13.032 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.032 * [taylor]: Taking taylor expansion of 1/2 in n
13.032 * [backup-simplify]: Simplify 1/2 into 1/2
13.032 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.032 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.032 * [taylor]: Taking taylor expansion of -2 in n
13.032 * [backup-simplify]: Simplify -2 into -2
13.032 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.032 * [taylor]: Taking taylor expansion of PI in n
13.032 * [backup-simplify]: Simplify PI into PI
13.032 * [taylor]: Taking taylor expansion of n in n
13.032 * [backup-simplify]: Simplify 0 into 0
13.032 * [backup-simplify]: Simplify 1 into 1
13.033 * [backup-simplify]: Simplify (/ PI 1) into PI
13.033 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.033 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.033 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.034 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.034 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.035 * [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)))
13.036 * [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))))
13.036 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
13.037 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k
13.037 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.037 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.037 * [taylor]: Taking taylor expansion of -1 in k
13.037 * [backup-simplify]: Simplify -1 into -1
13.037 * [taylor]: Taking taylor expansion of k in k
13.037 * [backup-simplify]: Simplify 0 into 0
13.037 * [backup-simplify]: Simplify 1 into 1
13.037 * [backup-simplify]: Simplify (/ -1 1) into -1
13.037 * [backup-simplify]: Simplify (sqrt 0) into 0
13.038 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.038 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
13.038 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
13.038 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
13.038 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
13.038 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.038 * [taylor]: Taking taylor expansion of 1/2 in k
13.038 * [backup-simplify]: Simplify 1/2 into 1/2
13.038 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.038 * [taylor]: Taking taylor expansion of k in k
13.038 * [backup-simplify]: Simplify 0 into 0
13.038 * [backup-simplify]: Simplify 1 into 1
13.039 * [backup-simplify]: Simplify (/ 1 1) into 1
13.039 * [taylor]: Taking taylor expansion of 1/2 in k
13.039 * [backup-simplify]: Simplify 1/2 into 1/2
13.039 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.039 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.039 * [taylor]: Taking taylor expansion of -2 in k
13.039 * [backup-simplify]: Simplify -2 into -2
13.039 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.039 * [taylor]: Taking taylor expansion of PI in k
13.039 * [backup-simplify]: Simplify PI into PI
13.039 * [taylor]: Taking taylor expansion of n in k
13.039 * [backup-simplify]: Simplify n into n
13.039 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.039 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.039 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.040 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.040 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.040 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
13.040 * [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)))
13.040 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
13.040 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k
13.040 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.040 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.040 * [taylor]: Taking taylor expansion of -1 in k
13.040 * [backup-simplify]: Simplify -1 into -1
13.040 * [taylor]: Taking taylor expansion of k in k
13.040 * [backup-simplify]: Simplify 0 into 0
13.040 * [backup-simplify]: Simplify 1 into 1
13.041 * [backup-simplify]: Simplify (/ -1 1) into -1
13.041 * [backup-simplify]: Simplify (sqrt 0) into 0
13.042 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.042 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
13.042 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
13.042 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
13.042 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
13.042 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.042 * [taylor]: Taking taylor expansion of 1/2 in k
13.042 * [backup-simplify]: Simplify 1/2 into 1/2
13.042 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.042 * [taylor]: Taking taylor expansion of k in k
13.042 * [backup-simplify]: Simplify 0 into 0
13.042 * [backup-simplify]: Simplify 1 into 1
13.042 * [backup-simplify]: Simplify (/ 1 1) into 1
13.042 * [taylor]: Taking taylor expansion of 1/2 in k
13.042 * [backup-simplify]: Simplify 1/2 into 1/2
13.042 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.042 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.042 * [taylor]: Taking taylor expansion of -2 in k
13.042 * [backup-simplify]: Simplify -2 into -2
13.042 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.042 * [taylor]: Taking taylor expansion of PI in k
13.042 * [backup-simplify]: Simplify PI into PI
13.042 * [taylor]: Taking taylor expansion of n in k
13.042 * [backup-simplify]: Simplify n into n
13.042 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.042 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.042 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.043 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.043 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.043 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
13.043 * [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)))
13.043 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
13.043 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
13.043 * [taylor]: Taking taylor expansion of +nan.0 in n
13.043 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.043 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n
13.044 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.044 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.044 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.044 * [taylor]: Taking taylor expansion of -2 in n
13.044 * [backup-simplify]: Simplify -2 into -2
13.044 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.044 * [taylor]: Taking taylor expansion of PI in n
13.044 * [backup-simplify]: Simplify PI into PI
13.044 * [taylor]: Taking taylor expansion of n in n
13.044 * [backup-simplify]: Simplify 0 into 0
13.044 * [backup-simplify]: Simplify 1 into 1
13.044 * [backup-simplify]: Simplify (/ PI 1) into PI
13.044 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.045 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.045 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.045 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.045 * [taylor]: Taking taylor expansion of 1/2 in n
13.045 * [backup-simplify]: Simplify 1/2 into 1/2
13.045 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.045 * [taylor]: Taking taylor expansion of k in n
13.045 * [backup-simplify]: Simplify k into k
13.045 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.045 * [taylor]: Taking taylor expansion of 1/2 in n
13.045 * [backup-simplify]: Simplify 1/2 into 1/2
13.046 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.046 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.046 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.047 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
13.047 * [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))))
13.048 * [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)))))
13.049 * [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)))))
13.049 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
13.051 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.052 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))
13.052 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n
13.052 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
13.052 * [taylor]: Taking taylor expansion of +nan.0 in n
13.052 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.052 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
13.052 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n
13.052 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.052 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.052 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.052 * [taylor]: Taking taylor expansion of -2 in n
13.052 * [backup-simplify]: Simplify -2 into -2
13.052 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.052 * [taylor]: Taking taylor expansion of PI in n
13.052 * [backup-simplify]: Simplify PI into PI
13.052 * [taylor]: Taking taylor expansion of n in n
13.052 * [backup-simplify]: Simplify 0 into 0
13.052 * [backup-simplify]: Simplify 1 into 1
13.052 * [backup-simplify]: Simplify (/ PI 1) into PI
13.052 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.053 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.053 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.053 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.053 * [taylor]: Taking taylor expansion of 1/2 in n
13.053 * [backup-simplify]: Simplify 1/2 into 1/2
13.053 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.053 * [taylor]: Taking taylor expansion of k in n
13.053 * [backup-simplify]: Simplify k into k
13.053 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.053 * [taylor]: Taking taylor expansion of 1/2 in n
13.053 * [backup-simplify]: Simplify 1/2 into 1/2
13.054 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.054 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.054 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.055 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
13.056 * [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))))
13.056 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
13.057 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
13.058 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
13.058 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
13.059 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.059 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.060 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
13.060 * [backup-simplify]: Simplify (+ 0 0) into 0
13.060 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.061 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.062 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
13.062 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
13.064 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
13.067 * [backup-simplify]: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0
13.067 * [backup-simplify]: Simplify 0 into 0
13.069 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.073 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.074 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))
13.074 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n
13.074 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
13.074 * [taylor]: Taking taylor expansion of +nan.0 in n
13.074 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.074 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
13.074 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n
13.074 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.074 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.074 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.074 * [taylor]: Taking taylor expansion of -2 in n
13.074 * [backup-simplify]: Simplify -2 into -2
13.074 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.074 * [taylor]: Taking taylor expansion of PI in n
13.074 * [backup-simplify]: Simplify PI into PI
13.074 * [taylor]: Taking taylor expansion of n in n
13.074 * [backup-simplify]: Simplify 0 into 0
13.074 * [backup-simplify]: Simplify 1 into 1
13.075 * [backup-simplify]: Simplify (/ PI 1) into PI
13.078 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.079 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.079 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.079 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.079 * [taylor]: Taking taylor expansion of 1/2 in n
13.079 * [backup-simplify]: Simplify 1/2 into 1/2
13.079 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.079 * [taylor]: Taking taylor expansion of k in n
13.079 * [backup-simplify]: Simplify k into k
13.079 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.079 * [taylor]: Taking taylor expansion of 1/2 in n
13.079 * [backup-simplify]: Simplify 1/2 into 1/2
13.081 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.081 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.081 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.082 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
13.083 * [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))))
13.084 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
13.085 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
13.086 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
13.088 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
13.091 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
13.092 * * * * [progress]: [ 4 / 4 ] generating series at (2)
13.092 * [backup-simplify]: Simplify (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))))
13.092 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0
13.092 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
13.093 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.093 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.093 * [taylor]: Taking taylor expansion of k in n
13.093 * [backup-simplify]: Simplify k into k
13.093 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.093 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.093 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.093 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.093 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
13.093 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
13.093 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
13.093 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
13.093 * [taylor]: Taking taylor expansion of 1/2 in n
13.093 * [backup-simplify]: Simplify 1/2 into 1/2
13.093 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
13.093 * [taylor]: Taking taylor expansion of 1/2 in n
13.093 * [backup-simplify]: Simplify 1/2 into 1/2
13.093 * [taylor]: Taking taylor expansion of k in n
13.093 * [backup-simplify]: Simplify k into k
13.093 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.093 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.093 * [taylor]: Taking taylor expansion of 2 in n
13.093 * [backup-simplify]: Simplify 2 into 2
13.093 * [taylor]: Taking taylor expansion of (* n PI) in n
13.093 * [taylor]: Taking taylor expansion of n in n
13.093 * [backup-simplify]: Simplify 0 into 0
13.093 * [backup-simplify]: Simplify 1 into 1
13.093 * [taylor]: Taking taylor expansion of PI in n
13.093 * [backup-simplify]: Simplify PI into PI
13.094 * [backup-simplify]: Simplify (* 0 PI) into 0
13.094 * [backup-simplify]: Simplify (* 2 0) into 0
13.095 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.096 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.097 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.097 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
13.097 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
13.097 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
13.098 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.099 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
13.099 * [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)))))
13.099 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
13.099 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.099 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.099 * [taylor]: Taking taylor expansion of k in k
13.099 * [backup-simplify]: Simplify 0 into 0
13.099 * [backup-simplify]: Simplify 1 into 1
13.100 * [backup-simplify]: Simplify (/ 1 1) into 1
13.100 * [backup-simplify]: Simplify (sqrt 0) into 0
13.101 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.101 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
13.101 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
13.101 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
13.101 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
13.101 * [taylor]: Taking taylor expansion of 1/2 in k
13.101 * [backup-simplify]: Simplify 1/2 into 1/2
13.101 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
13.101 * [taylor]: Taking taylor expansion of 1/2 in k
13.101 * [backup-simplify]: Simplify 1/2 into 1/2
13.101 * [taylor]: Taking taylor expansion of k in k
13.101 * [backup-simplify]: Simplify 0 into 0
13.101 * [backup-simplify]: Simplify 1 into 1
13.101 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
13.101 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
13.101 * [taylor]: Taking taylor expansion of 2 in k
13.101 * [backup-simplify]: Simplify 2 into 2
13.101 * [taylor]: Taking taylor expansion of (* n PI) in k
13.101 * [taylor]: Taking taylor expansion of n in k
13.101 * [backup-simplify]: Simplify n into n
13.101 * [taylor]: Taking taylor expansion of PI in k
13.101 * [backup-simplify]: Simplify PI into PI
13.101 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.101 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
13.101 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
13.101 * [backup-simplify]: Simplify (* 1/2 0) into 0
13.102 * [backup-simplify]: Simplify (- 0) into 0
13.102 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.102 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
13.102 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
13.102 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
13.102 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.102 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.102 * [taylor]: Taking taylor expansion of k in k
13.102 * [backup-simplify]: Simplify 0 into 0
13.102 * [backup-simplify]: Simplify 1 into 1
13.102 * [backup-simplify]: Simplify (/ 1 1) into 1
13.103 * [backup-simplify]: Simplify (sqrt 0) into 0
13.103 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.103 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
13.103 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
13.104 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
13.104 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
13.104 * [taylor]: Taking taylor expansion of 1/2 in k
13.104 * [backup-simplify]: Simplify 1/2 into 1/2
13.104 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
13.104 * [taylor]: Taking taylor expansion of 1/2 in k
13.104 * [backup-simplify]: Simplify 1/2 into 1/2
13.104 * [taylor]: Taking taylor expansion of k in k
13.104 * [backup-simplify]: Simplify 0 into 0
13.104 * [backup-simplify]: Simplify 1 into 1
13.104 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
13.104 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
13.104 * [taylor]: Taking taylor expansion of 2 in k
13.104 * [backup-simplify]: Simplify 2 into 2
13.104 * [taylor]: Taking taylor expansion of (* n PI) in k
13.104 * [taylor]: Taking taylor expansion of n in k
13.104 * [backup-simplify]: Simplify n into n
13.104 * [taylor]: Taking taylor expansion of PI in k
13.104 * [backup-simplify]: Simplify PI into PI
13.104 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.104 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
13.104 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
13.104 * [backup-simplify]: Simplify (* 1/2 0) into 0
13.104 * [backup-simplify]: Simplify (- 0) into 0
13.105 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.105 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
13.105 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
13.105 * [backup-simplify]: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0
13.105 * [taylor]: Taking taylor expansion of 0 in n
13.105 * [backup-simplify]: Simplify 0 into 0
13.105 * [backup-simplify]: Simplify 0 into 0
13.105 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
13.106 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
13.106 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
13.107 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
13.107 * [backup-simplify]: Simplify (- 1/2) into -1/2
13.107 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
13.107 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
13.108 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))
13.108 * [backup-simplify]: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
13.108 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
13.108 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
13.108 * [taylor]: Taking taylor expansion of +nan.0 in n
13.108 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.108 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
13.108 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.108 * [taylor]: Taking taylor expansion of 2 in n
13.108 * [backup-simplify]: Simplify 2 into 2
13.108 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.109 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.109 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
13.109 * [taylor]: Taking taylor expansion of (* n PI) in n
13.109 * [taylor]: Taking taylor expansion of n in n
13.109 * [backup-simplify]: Simplify 0 into 0
13.109 * [backup-simplify]: Simplify 1 into 1
13.109 * [taylor]: Taking taylor expansion of PI in n
13.109 * [backup-simplify]: Simplify PI into PI
13.109 * [backup-simplify]: Simplify (* 0 PI) into 0
13.110 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.110 * [backup-simplify]: Simplify (sqrt 0) into 0
13.111 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
13.111 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
13.111 * [backup-simplify]: Simplify (* +nan.0 0) into 0
13.112 * [backup-simplify]: Simplify (- 0) into 0
13.112 * [backup-simplify]: Simplify 0 into 0
13.112 * [backup-simplify]: Simplify 0 into 0
13.112 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
13.113 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
13.114 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
13.114 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
13.115 * [backup-simplify]: Simplify (- 0) into 0
13.115 * [backup-simplify]: Simplify (+ 0 0) into 0
13.115 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
13.116 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))
13.116 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
13.118 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.119 * [backup-simplify]: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))
13.119 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n
13.119 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n
13.119 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
13.119 * [taylor]: Taking taylor expansion of +nan.0 in n
13.119 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.119 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
13.119 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
13.119 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.119 * [taylor]: Taking taylor expansion of 2 in n
13.119 * [backup-simplify]: Simplify 2 into 2
13.119 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.120 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.120 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.120 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.120 * [taylor]: Taking taylor expansion of 2 in n
13.120 * [backup-simplify]: Simplify 2 into 2
13.120 * [taylor]: Taking taylor expansion of (* n PI) in n
13.120 * [taylor]: Taking taylor expansion of n in n
13.120 * [backup-simplify]: Simplify 0 into 0
13.120 * [backup-simplify]: Simplify 1 into 1
13.120 * [taylor]: Taking taylor expansion of PI in n
13.120 * [backup-simplify]: Simplify PI into PI
13.120 * [backup-simplify]: Simplify (* 0 PI) into 0
13.121 * [backup-simplify]: Simplify (* 2 0) into 0
13.122 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.123 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.123 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.123 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
13.123 * [taylor]: Taking taylor expansion of (* n PI) in n
13.123 * [taylor]: Taking taylor expansion of n in n
13.123 * [backup-simplify]: Simplify 0 into 0
13.123 * [backup-simplify]: Simplify 1 into 1
13.123 * [taylor]: Taking taylor expansion of PI in n
13.123 * [backup-simplify]: Simplify PI into PI
13.124 * [backup-simplify]: Simplify (* 0 PI) into 0
13.125 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.125 * [backup-simplify]: Simplify (sqrt 0) into 0
13.126 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
13.126 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
13.126 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
13.126 * [taylor]: Taking taylor expansion of +nan.0 in n
13.126 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.126 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
13.126 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.126 * [taylor]: Taking taylor expansion of 2 in n
13.126 * [backup-simplify]: Simplify 2 into 2
13.126 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.126 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.126 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
13.126 * [taylor]: Taking taylor expansion of (* n PI) in n
13.126 * [taylor]: Taking taylor expansion of n in n
13.127 * [backup-simplify]: Simplify 0 into 0
13.127 * [backup-simplify]: Simplify 1 into 1
13.127 * [taylor]: Taking taylor expansion of PI in n
13.127 * [backup-simplify]: Simplify PI into PI
13.127 * [backup-simplify]: Simplify (* 0 PI) into 0
13.128 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.128 * [backup-simplify]: Simplify (sqrt 0) into 0
13.129 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
13.130 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.130 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
13.131 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
13.132 * [backup-simplify]: Simplify (* +nan.0 0) into 0
13.132 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
13.132 * [backup-simplify]: Simplify (* +nan.0 0) into 0
13.132 * [backup-simplify]: Simplify (- 0) into 0
13.133 * [backup-simplify]: Simplify (+ 0 0) into 0
13.133 * [backup-simplify]: Simplify (- 0) into 0
13.133 * [backup-simplify]: Simplify 0 into 0
13.135 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
13.138 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
13.140 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
13.141 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
13.141 * [backup-simplify]: Simplify 0 into 0
13.142 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.143 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
13.144 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0
13.145 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
13.145 * [backup-simplify]: Simplify (- 0) into 0
13.146 * [backup-simplify]: Simplify (+ 0 0) into 0
13.146 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
13.147 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))
13.148 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.150 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.151 * [backup-simplify]: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))))
13.151 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n
13.151 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n
13.151 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
13.151 * [taylor]: Taking taylor expansion of +nan.0 in n
13.151 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.151 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
13.151 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
13.151 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.151 * [taylor]: Taking taylor expansion of 2 in n
13.151 * [backup-simplify]: Simplify 2 into 2
13.152 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.152 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.152 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.152 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.152 * [taylor]: Taking taylor expansion of 2 in n
13.152 * [backup-simplify]: Simplify 2 into 2
13.152 * [taylor]: Taking taylor expansion of (* n PI) in n
13.152 * [taylor]: Taking taylor expansion of n in n
13.152 * [backup-simplify]: Simplify 0 into 0
13.152 * [backup-simplify]: Simplify 1 into 1
13.152 * [taylor]: Taking taylor expansion of PI in n
13.152 * [backup-simplify]: Simplify PI into PI
13.153 * [backup-simplify]: Simplify (* 0 PI) into 0
13.153 * [backup-simplify]: Simplify (* 2 0) into 0
13.154 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.155 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.156 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.156 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
13.156 * [taylor]: Taking taylor expansion of (* n PI) in n
13.156 * [taylor]: Taking taylor expansion of n in n
13.156 * [backup-simplify]: Simplify 0 into 0
13.156 * [backup-simplify]: Simplify 1 into 1
13.156 * [taylor]: Taking taylor expansion of PI in n
13.156 * [backup-simplify]: Simplify PI into PI
13.156 * [backup-simplify]: Simplify (* 0 PI) into 0
13.158 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.158 * [backup-simplify]: Simplify (sqrt 0) into 0
13.160 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
13.160 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n
13.160 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n
13.160 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
13.160 * [taylor]: Taking taylor expansion of +nan.0 in n
13.160 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.160 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
13.160 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
13.160 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.160 * [taylor]: Taking taylor expansion of 2 in n
13.160 * [backup-simplify]: Simplify 2 into 2
13.160 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.161 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.161 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
13.161 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.161 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.161 * [taylor]: Taking taylor expansion of 2 in n
13.161 * [backup-simplify]: Simplify 2 into 2
13.161 * [taylor]: Taking taylor expansion of (* n PI) in n
13.161 * [taylor]: Taking taylor expansion of n in n
13.161 * [backup-simplify]: Simplify 0 into 0
13.161 * [backup-simplify]: Simplify 1 into 1
13.161 * [taylor]: Taking taylor expansion of PI in n
13.161 * [backup-simplify]: Simplify PI into PI
13.162 * [backup-simplify]: Simplify (* 0 PI) into 0
13.162 * [backup-simplify]: Simplify (* 2 0) into 0
13.164 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.165 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.166 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.168 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.168 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
13.168 * [taylor]: Taking taylor expansion of (* n PI) in n
13.168 * [taylor]: Taking taylor expansion of n in n
13.168 * [backup-simplify]: Simplify 0 into 0
13.168 * [backup-simplify]: Simplify 1 into 1
13.168 * [taylor]: Taking taylor expansion of PI in n
13.168 * [backup-simplify]: Simplify PI into PI
13.168 * [backup-simplify]: Simplify (* 0 PI) into 0
13.170 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.170 * [backup-simplify]: Simplify (sqrt 0) into 0
13.171 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
13.171 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
13.172 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
13.172 * [taylor]: Taking taylor expansion of +nan.0 in n
13.172 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.172 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
13.172 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.172 * [taylor]: Taking taylor expansion of 2 in n
13.172 * [backup-simplify]: Simplify 2 into 2
13.172 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.173 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.173 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
13.173 * [taylor]: Taking taylor expansion of (* n PI) in n
13.173 * [taylor]: Taking taylor expansion of n in n
13.173 * [backup-simplify]: Simplify 0 into 0
13.173 * [backup-simplify]: Simplify 1 into 1
13.173 * [taylor]: Taking taylor expansion of PI in n
13.173 * [backup-simplify]: Simplify PI into PI
13.174 * [backup-simplify]: Simplify (* 0 PI) into 0
13.175 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.176 * [backup-simplify]: Simplify (sqrt 0) into 0
13.177 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
13.182 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.183 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
13.185 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
13.185 * [backup-simplify]: Simplify (* +nan.0 0) into 0
13.187 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.188 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.189 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
13.190 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
13.191 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
13.191 * [backup-simplify]: Simplify (* +nan.0 0) into 0
13.191 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
13.192 * [backup-simplify]: Simplify (* +nan.0 0) into 0
13.192 * [backup-simplify]: Simplify (- 0) into 0
13.192 * [backup-simplify]: Simplify (+ 0 0) into 0
13.193 * [backup-simplify]: Simplify (- 0) into 0
13.193 * [backup-simplify]: Simplify (+ 0 0) into 0
13.193 * [backup-simplify]: Simplify (- 0) into 0
13.193 * [backup-simplify]: Simplify 0 into 0
13.194 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.194 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.195 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.196 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.197 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
13.199 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
13.202 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
13.204 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
13.207 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
13.209 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
13.214 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))
13.218 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))))
13.223 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))))
13.224 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.229 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
13.230 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
13.234 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
13.241 * [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))))
13.244 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
13.245 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
13.253 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
13.254 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
13.254 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0
13.254 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
13.254 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.254 * [taylor]: Taking taylor expansion of k in n
13.254 * [backup-simplify]: Simplify k into k
13.254 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.254 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.254 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
13.254 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.254 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.254 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
13.254 * [taylor]: Taking taylor expansion of 1/2 in n
13.254 * [backup-simplify]: Simplify 1/2 into 1/2
13.254 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.254 * [taylor]: Taking taylor expansion of 1/2 in n
13.254 * [backup-simplify]: Simplify 1/2 into 1/2
13.254 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.254 * [taylor]: Taking taylor expansion of k in n
13.254 * [backup-simplify]: Simplify k into k
13.254 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.254 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.254 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.254 * [taylor]: Taking taylor expansion of 2 in n
13.254 * [backup-simplify]: Simplify 2 into 2
13.254 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.254 * [taylor]: Taking taylor expansion of PI in n
13.254 * [backup-simplify]: Simplify PI into PI
13.254 * [taylor]: Taking taylor expansion of n in n
13.254 * [backup-simplify]: Simplify 0 into 0
13.254 * [backup-simplify]: Simplify 1 into 1
13.255 * [backup-simplify]: Simplify (/ PI 1) into PI
13.255 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.256 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.256 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.256 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
13.256 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
13.257 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.257 * [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)))
13.258 * [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))))
13.258 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
13.258 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.258 * [taylor]: Taking taylor expansion of k in k
13.258 * [backup-simplify]: Simplify 0 into 0
13.258 * [backup-simplify]: Simplify 1 into 1
13.258 * [backup-simplify]: Simplify (sqrt 0) into 0
13.259 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.259 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
13.259 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
13.259 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
13.259 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
13.259 * [taylor]: Taking taylor expansion of 1/2 in k
13.259 * [backup-simplify]: Simplify 1/2 into 1/2
13.259 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.259 * [taylor]: Taking taylor expansion of 1/2 in k
13.259 * [backup-simplify]: Simplify 1/2 into 1/2
13.259 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.259 * [taylor]: Taking taylor expansion of k in k
13.259 * [backup-simplify]: Simplify 0 into 0
13.259 * [backup-simplify]: Simplify 1 into 1
13.260 * [backup-simplify]: Simplify (/ 1 1) into 1
13.260 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
13.260 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
13.260 * [taylor]: Taking taylor expansion of 2 in k
13.260 * [backup-simplify]: Simplify 2 into 2
13.260 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.260 * [taylor]: Taking taylor expansion of PI in k
13.260 * [backup-simplify]: Simplify PI into PI
13.260 * [taylor]: Taking taylor expansion of n in k
13.260 * [backup-simplify]: Simplify n into n
13.260 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.260 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
13.260 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
13.260 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.261 * [backup-simplify]: Simplify (- 1/2) into -1/2
13.261 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
13.261 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
13.261 * [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))))
13.261 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
13.261 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.261 * [taylor]: Taking taylor expansion of k in k
13.261 * [backup-simplify]: Simplify 0 into 0
13.261 * [backup-simplify]: Simplify 1 into 1
13.261 * [backup-simplify]: Simplify (sqrt 0) into 0
13.262 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.262 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
13.262 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
13.262 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
13.262 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
13.262 * [taylor]: Taking taylor expansion of 1/2 in k
13.262 * [backup-simplify]: Simplify 1/2 into 1/2
13.262 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.262 * [taylor]: Taking taylor expansion of 1/2 in k
13.262 * [backup-simplify]: Simplify 1/2 into 1/2
13.262 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.262 * [taylor]: Taking taylor expansion of k in k
13.262 * [backup-simplify]: Simplify 0 into 0
13.262 * [backup-simplify]: Simplify 1 into 1
13.263 * [backup-simplify]: Simplify (/ 1 1) into 1
13.263 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
13.263 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
13.263 * [taylor]: Taking taylor expansion of 2 in k
13.263 * [backup-simplify]: Simplify 2 into 2
13.263 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.263 * [taylor]: Taking taylor expansion of PI in k
13.263 * [backup-simplify]: Simplify PI into PI
13.263 * [taylor]: Taking taylor expansion of n in k
13.263 * [backup-simplify]: Simplify n into n
13.263 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.263 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
13.263 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
13.263 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.263 * [backup-simplify]: Simplify (- 1/2) into -1/2
13.264 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
13.264 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
13.264 * [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))))
13.264 * [backup-simplify]: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0
13.264 * [taylor]: Taking taylor expansion of 0 in n
13.264 * [backup-simplify]: Simplify 0 into 0
13.264 * [backup-simplify]: Simplify 0 into 0
13.264 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))
13.264 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n
13.265 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
13.265 * [taylor]: Taking taylor expansion of +nan.0 in n
13.265 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.265 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
13.265 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.265 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.265 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
13.265 * [taylor]: Taking taylor expansion of 1/2 in n
13.265 * [backup-simplify]: Simplify 1/2 into 1/2
13.265 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.265 * [taylor]: Taking taylor expansion of 1/2 in n
13.265 * [backup-simplify]: Simplify 1/2 into 1/2
13.265 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.265 * [taylor]: Taking taylor expansion of k in n
13.265 * [backup-simplify]: Simplify k into k
13.265 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.265 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.265 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.265 * [taylor]: Taking taylor expansion of 2 in n
13.265 * [backup-simplify]: Simplify 2 into 2
13.265 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.265 * [taylor]: Taking taylor expansion of PI in n
13.265 * [backup-simplify]: Simplify PI into PI
13.265 * [taylor]: Taking taylor expansion of n in n
13.265 * [backup-simplify]: Simplify 0 into 0
13.265 * [backup-simplify]: Simplify 1 into 1
13.265 * [backup-simplify]: Simplify (/ PI 1) into PI
13.266 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.266 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.266 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.266 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
13.266 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
13.268 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.269 * [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)))
13.270 * [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))))
13.271 * [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)))))
13.275 * [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))))))
13.277 * [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))))))
13.277 * [backup-simplify]: Simplify 0 into 0
13.280 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.281 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))
13.281 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n
13.281 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
13.281 * [taylor]: Taking taylor expansion of +nan.0 in n
13.281 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.282 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
13.282 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.282 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.282 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
13.282 * [taylor]: Taking taylor expansion of 1/2 in n
13.282 * [backup-simplify]: Simplify 1/2 into 1/2
13.282 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.282 * [taylor]: Taking taylor expansion of 1/2 in n
13.282 * [backup-simplify]: Simplify 1/2 into 1/2
13.282 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.282 * [taylor]: Taking taylor expansion of k in n
13.282 * [backup-simplify]: Simplify k into k
13.282 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.282 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.282 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.282 * [taylor]: Taking taylor expansion of 2 in n
13.282 * [backup-simplify]: Simplify 2 into 2
13.282 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.282 * [taylor]: Taking taylor expansion of PI in n
13.282 * [backup-simplify]: Simplify PI into PI
13.282 * [taylor]: Taking taylor expansion of n in n
13.282 * [backup-simplify]: Simplify 0 into 0
13.282 * [backup-simplify]: Simplify 1 into 1
13.283 * [backup-simplify]: Simplify (/ PI 1) into PI
13.283 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.284 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.284 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.284 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
13.284 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
13.286 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.287 * [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)))
13.288 * [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))))
13.289 * [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)))))
13.290 * [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))))))
13.291 * [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))))))
13.292 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.293 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.295 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.295 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.295 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
13.296 * [backup-simplify]: Simplify (- 0) into 0
13.296 * [backup-simplify]: Simplify (+ 0 0) into 0
13.297 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.298 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
13.300 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
13.302 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
13.302 * [backup-simplify]: Simplify (- 0) into 0
13.302 * [backup-simplify]: Simplify 0 into 0
13.302 * [backup-simplify]: Simplify 0 into 0
13.306 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.308 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))
13.308 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n
13.308 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
13.308 * [taylor]: Taking taylor expansion of +nan.0 in n
13.308 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.308 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
13.308 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.308 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.308 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
13.308 * [taylor]: Taking taylor expansion of 1/2 in n
13.308 * [backup-simplify]: Simplify 1/2 into 1/2
13.308 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.308 * [taylor]: Taking taylor expansion of 1/2 in n
13.308 * [backup-simplify]: Simplify 1/2 into 1/2
13.308 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.308 * [taylor]: Taking taylor expansion of k in n
13.308 * [backup-simplify]: Simplify k into k
13.309 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.309 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.309 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.309 * [taylor]: Taking taylor expansion of 2 in n
13.309 * [backup-simplify]: Simplify 2 into 2
13.309 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.309 * [taylor]: Taking taylor expansion of PI in n
13.309 * [backup-simplify]: Simplify PI into PI
13.309 * [taylor]: Taking taylor expansion of n in n
13.309 * [backup-simplify]: Simplify 0 into 0
13.309 * [backup-simplify]: Simplify 1 into 1
13.309 * [backup-simplify]: Simplify (/ PI 1) into PI
13.310 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.311 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.311 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.311 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
13.311 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
13.312 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.313 * [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)))
13.314 * [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))))
13.316 * [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)))))
13.317 * [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))))))
13.318 * [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))))))
13.322 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
13.322 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
13.323 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0
13.323 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
13.323 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.323 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
13.323 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
13.323 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.323 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.323 * [taylor]: Taking taylor expansion of 1/2 in n
13.323 * [backup-simplify]: Simplify 1/2 into 1/2
13.323 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.323 * [taylor]: Taking taylor expansion of k in n
13.323 * [backup-simplify]: Simplify k into k
13.323 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.323 * [taylor]: Taking taylor expansion of 1/2 in n
13.323 * [backup-simplify]: Simplify 1/2 into 1/2
13.323 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.323 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.323 * [taylor]: Taking taylor expansion of -2 in n
13.323 * [backup-simplify]: Simplify -2 into -2
13.323 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.323 * [taylor]: Taking taylor expansion of PI in n
13.323 * [backup-simplify]: Simplify PI into PI
13.323 * [taylor]: Taking taylor expansion of n in n
13.323 * [backup-simplify]: Simplify 0 into 0
13.323 * [backup-simplify]: Simplify 1 into 1
13.324 * [backup-simplify]: Simplify (/ PI 1) into PI
13.324 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.325 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.325 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.325 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.327 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.328 * [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)))
13.329 * [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))))
13.329 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
13.329 * [taylor]: Taking taylor expansion of (/ -1 k) in n
13.329 * [taylor]: Taking taylor expansion of -1 in n
13.329 * [backup-simplify]: Simplify -1 into -1
13.329 * [taylor]: Taking taylor expansion of k in n
13.329 * [backup-simplify]: Simplify k into k
13.329 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
13.329 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
13.329 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
13.329 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
13.330 * [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)))
13.330 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
13.331 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
13.331 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
13.331 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
13.331 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
13.331 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.331 * [taylor]: Taking taylor expansion of 1/2 in k
13.331 * [backup-simplify]: Simplify 1/2 into 1/2
13.331 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.331 * [taylor]: Taking taylor expansion of k in k
13.331 * [backup-simplify]: Simplify 0 into 0
13.331 * [backup-simplify]: Simplify 1 into 1
13.331 * [backup-simplify]: Simplify (/ 1 1) into 1
13.331 * [taylor]: Taking taylor expansion of 1/2 in k
13.331 * [backup-simplify]: Simplify 1/2 into 1/2
13.331 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.331 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.331 * [taylor]: Taking taylor expansion of -2 in k
13.331 * [backup-simplify]: Simplify -2 into -2
13.331 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.331 * [taylor]: Taking taylor expansion of PI in k
13.331 * [backup-simplify]: Simplify PI into PI
13.331 * [taylor]: Taking taylor expansion of n in k
13.331 * [backup-simplify]: Simplify n into n
13.332 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.332 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.332 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.332 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.333 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.333 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
13.333 * [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)))
13.333 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.333 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.333 * [taylor]: Taking taylor expansion of -1 in k
13.333 * [backup-simplify]: Simplify -1 into -1
13.333 * [taylor]: Taking taylor expansion of k in k
13.333 * [backup-simplify]: Simplify 0 into 0
13.333 * [backup-simplify]: Simplify 1 into 1
13.334 * [backup-simplify]: Simplify (/ -1 1) into -1
13.334 * [backup-simplify]: Simplify (sqrt 0) into 0
13.336 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.336 * [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))))
13.336 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
13.336 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
13.336 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
13.336 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
13.336 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
13.336 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.336 * [taylor]: Taking taylor expansion of 1/2 in k
13.336 * [backup-simplify]: Simplify 1/2 into 1/2
13.336 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.336 * [taylor]: Taking taylor expansion of k in k
13.336 * [backup-simplify]: Simplify 0 into 0
13.336 * [backup-simplify]: Simplify 1 into 1
13.336 * [backup-simplify]: Simplify (/ 1 1) into 1
13.336 * [taylor]: Taking taylor expansion of 1/2 in k
13.337 * [backup-simplify]: Simplify 1/2 into 1/2
13.337 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.337 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.337 * [taylor]: Taking taylor expansion of -2 in k
13.337 * [backup-simplify]: Simplify -2 into -2
13.337 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.337 * [taylor]: Taking taylor expansion of PI in k
13.337 * [backup-simplify]: Simplify PI into PI
13.337 * [taylor]: Taking taylor expansion of n in k
13.337 * [backup-simplify]: Simplify n into n
13.337 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.337 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.337 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.337 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.338 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.338 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
13.338 * [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)))
13.338 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.338 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.338 * [taylor]: Taking taylor expansion of -1 in k
13.338 * [backup-simplify]: Simplify -1 into -1
13.338 * [taylor]: Taking taylor expansion of k in k
13.338 * [backup-simplify]: Simplify 0 into 0
13.338 * [backup-simplify]: Simplify 1 into 1
13.339 * [backup-simplify]: Simplify (/ -1 1) into -1
13.339 * [backup-simplify]: Simplify (sqrt 0) into 0
13.340 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.341 * [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))))
13.341 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
13.341 * [taylor]: Taking taylor expansion of +nan.0 in n
13.341 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.341 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n
13.341 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.341 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.341 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.341 * [taylor]: Taking taylor expansion of -2 in n
13.341 * [backup-simplify]: Simplify -2 into -2
13.341 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.341 * [taylor]: Taking taylor expansion of PI in n
13.341 * [backup-simplify]: Simplify PI into PI
13.341 * [taylor]: Taking taylor expansion of n in n
13.341 * [backup-simplify]: Simplify 0 into 0
13.341 * [backup-simplify]: Simplify 1 into 1
13.342 * [backup-simplify]: Simplify (/ PI 1) into PI
13.342 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.343 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.343 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.343 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.343 * [taylor]: Taking taylor expansion of 1/2 in n
13.343 * [backup-simplify]: Simplify 1/2 into 1/2
13.343 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.343 * [taylor]: Taking taylor expansion of k in n
13.343 * [backup-simplify]: Simplify k into k
13.343 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.343 * [taylor]: Taking taylor expansion of 1/2 in n
13.343 * [backup-simplify]: Simplify 1/2 into 1/2
13.345 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.345 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.345 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.346 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
13.347 * [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))))
13.348 * [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)))))
13.349 * [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)))))
13.350 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
13.353 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.354 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))
13.354 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
13.354 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
13.354 * [taylor]: Taking taylor expansion of +nan.0 in n
13.354 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.354 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n
13.355 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.355 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.355 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.355 * [taylor]: Taking taylor expansion of -2 in n
13.355 * [backup-simplify]: Simplify -2 into -2
13.355 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.355 * [taylor]: Taking taylor expansion of PI in n
13.355 * [backup-simplify]: Simplify PI into PI
13.355 * [taylor]: Taking taylor expansion of n in n
13.355 * [backup-simplify]: Simplify 0 into 0
13.355 * [backup-simplify]: Simplify 1 into 1
13.355 * [backup-simplify]: Simplify (/ PI 1) into PI
13.356 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.357 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.357 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.357 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.357 * [taylor]: Taking taylor expansion of 1/2 in n
13.357 * [backup-simplify]: Simplify 1/2 into 1/2
13.357 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.357 * [taylor]: Taking taylor expansion of k in n
13.357 * [backup-simplify]: Simplify k into k
13.357 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.357 * [taylor]: Taking taylor expansion of 1/2 in n
13.357 * [backup-simplify]: Simplify 1/2 into 1/2
13.358 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.358 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.358 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.360 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
13.361 * [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))))
13.362 * [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)))))
13.364 * [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))))))
13.365 * [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))))))
13.366 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.367 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.367 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
13.367 * [backup-simplify]: Simplify (+ 0 0) into 0
13.368 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.368 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.369 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
13.370 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
13.371 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
13.372 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0
13.372 * [backup-simplify]: Simplify 0 into 0
13.373 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.375 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.376 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))
13.376 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
13.376 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
13.376 * [taylor]: Taking taylor expansion of +nan.0 in n
13.376 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.376 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n
13.376 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.376 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.376 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.376 * [taylor]: Taking taylor expansion of -2 in n
13.376 * [backup-simplify]: Simplify -2 into -2
13.376 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.376 * [taylor]: Taking taylor expansion of PI in n
13.376 * [backup-simplify]: Simplify PI into PI
13.376 * [taylor]: Taking taylor expansion of n in n
13.376 * [backup-simplify]: Simplify 0 into 0
13.376 * [backup-simplify]: Simplify 1 into 1
13.376 * [backup-simplify]: Simplify (/ PI 1) into PI
13.377 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.377 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.377 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.377 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.377 * [taylor]: Taking taylor expansion of 1/2 in n
13.377 * [backup-simplify]: Simplify 1/2 into 1/2
13.377 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.377 * [taylor]: Taking taylor expansion of k in n
13.377 * [backup-simplify]: Simplify k into k
13.378 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.378 * [taylor]: Taking taylor expansion of 1/2 in n
13.378 * [backup-simplify]: Simplify 1/2 into 1/2
13.378 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.378 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.378 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.379 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
13.380 * [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))))
13.381 * [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)))))
13.381 * [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))))))
13.382 * [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))))))
13.385 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
13.385 * * * [progress]: simplifying candidates
13.385 * * * * [progress]: [ 1 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))))))>
13.385 * * * * [progress]: [ 2 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))))))>
13.385 * * * * [progress]: [ 3 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))))))>
13.385 * * * * [progress]: [ 4 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))))))>
13.385 * * * * [progress]: [ 5 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))))))>
13.385 * * * * [progress]: [ 6 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))))))>
13.385 * * * * [progress]: [ 7 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))))))>
13.385 * * * * [progress]: [ 8 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2))))))>
13.385 * * * * [progress]: [ 9 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))))>
13.385 * * * * [progress]: [ 10 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))))))>
13.385 * * * * [progress]: [ 11 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))))))>
13.385 * * * * [progress]: [ 12 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))))))>
13.385 * * * * [progress]: [ 13 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))))))>
13.385 * * * * [progress]: [ 14 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))))))>
13.385 * * * * [progress]: [ 15 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.385 * * * * [progress]: [ 16 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.386 * * * * [progress]: [ 17 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.386 * * * * [progress]: [ 18 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1))))>
13.386 * * * * [progress]: [ 19 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.386 * * * * [progress]: [ 20 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.386 * * * * [progress]: [ 21 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.386 * * * * [progress]: [ 22 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.386 * * * * [progress]: [ 23 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.386 * * * * [progress]: [ 24 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.386 * * * * [progress]: [ 25 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.386 * * * * [progress]: [ 26 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.386 * * * * [progress]: [ 27 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))))))>
13.386 * * * * [progress]: [ 28 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))))))>
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13.387 * * * * [progress]: [ 47 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))))))>
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13.387 * * * * [progress]: [ 54 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.387 * * * * [progress]: [ 55 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.387 * * * * [progress]: [ 56 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.387 * * * * [progress]: [ 57 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.387 * * * * [progress]: [ 58 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (- (sqrt k)) (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
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13.387 * * * * [progress]: [ 61 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2)))) (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.388 * * * * [progress]: [ 62 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.388 * * * * [progress]: [ 63 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.388 * * * * [progress]: [ 64 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.388 * * * * [progress]: [ 65 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.388 * * * * [progress]: [ 66 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2)) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
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13.388 * * * * [progress]: [ 78 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
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13.388 * * * * [progress]: [ 80 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2)) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
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13.389 * * * * [progress]: [ 83 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.389 * * * * [progress]: [ 84 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
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13.389 * * * * [progress]: [ 103 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
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13.390 * * * * [progress]: [ 114 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
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13.390 * * * * [progress]: [ 118 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (posit16->real (real->posit16 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
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13.391 * * * * [progress]: [ 137 / 355 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))))))>
13.391 * * * * [progress]: [ 138 / 355 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.391 * * * * [progress]: [ 139 / 355 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (log (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.391 * * * * [progress]: [ 140 / 355 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.391 * * * * [progress]: [ 141 / 355 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.391 * * * * [progress]: [ 142 / 355 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* 1 1) 1) (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.391 * * * * [progress]: [ 143 / 355 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* 1 1) 1) (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.391 * * * * [progress]: [ 144 / 355 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (cbrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (cbrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.391 * * * * [progress]: [ 145 / 355 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.391 * * * * [progress]: [ 146 / 355 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (sqrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.391 * * * * [progress]: [ 147 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (- 1) (- (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.391 * * * * [progress]: [ 148 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.391 * * * * [progress]: [ 149 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.391 * * * * [progress]: [ 150 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.391 * * * * [progress]: [ 151 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.392 * * * * [progress]: [ 152 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.392 * * * * [progress]: [ 153 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.392 * * * * [progress]: [ 154 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.392 * * * * [progress]: [ 155 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.392 * * * * [progress]: [ 156 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.392 * * * * [progress]: [ 157 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.392 * * * * [progress]: [ 158 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.392 * * * * [progress]: [ 159 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2))))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.392 * * * * [progress]: [ 160 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.392 * * * * [progress]: [ 161 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.392 * * * * [progress]: [ 162 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.392 * * * * [progress]: [ 163 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.392 * * * * [progress]: [ 164 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.392 * * * * [progress]: [ 165 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.392 * * * * [progress]: [ 166 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.392 * * * * [progress]: [ 167 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.392 * * * * [progress]: [ 168 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.392 * * * * [progress]: [ 169 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) 1)) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.392 * * * * [progress]: [ 170 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.392 * * * * [progress]: [ 171 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.392 * * * * [progress]: [ 172 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.393 * * * * [progress]: [ 173 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (pow n (- 1/2 (/ k 2))))) (/ (cbrt 1) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.393 * * * * [progress]: [ 174 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.393 * * * * [progress]: [ 175 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.393 * * * * [progress]: [ 176 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) 1)) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.393 * * * * [progress]: [ 177 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.393 * * * * [progress]: [ 178 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.393 * * * * [progress]: [ 179 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.393 * * * * [progress]: [ 180 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.393 * * * * [progress]: [ 181 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.393 * * * * [progress]: [ 182 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.393 * * * * [progress]: [ 183 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) 1)) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.393 * * * * [progress]: [ 184 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.393 * * * * [progress]: [ 185 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.393 * * * * [progress]: [ 186 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.393 * * * * [progress]: [ 187 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (pow n (- 1/2 (/ k 2))))) (/ (cbrt 1) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.393 * * * * [progress]: [ 188 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.393 * * * * [progress]: [ 189 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.393 * * * * [progress]: [ 190 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 1)) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.393 * * * * [progress]: [ 191 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.393 * * * * [progress]: [ 192 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.393 * * * * [progress]: [ 193 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt k)) (/ (cbrt 1) (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.393 * * * * [progress]: [ 194 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt 1) (pow (* n (* 2 PI)) (/ k 2)))))>
13.394 * * * * [progress]: [ 195 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.394 * * * * [progress]: [ 196 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.394 * * * * [progress]: [ 197 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.394 * * * * [progress]: [ 198 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.394 * * * * [progress]: [ 199 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.394 * * * * [progress]: [ 200 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.394 * * * * [progress]: [ 201 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.394 * * * * [progress]: [ 202 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.394 * * * * [progress]: [ 203 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.394 * * * * [progress]: [ 204 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.394 * * * * [progress]: [ 205 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.394 * * * * [progress]: [ 206 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2))))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.394 * * * * [progress]: [ 207 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.394 * * * * [progress]: [ 208 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.394 * * * * [progress]: [ 209 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.394 * * * * [progress]: [ 210 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.394 * * * * [progress]: [ 211 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.394 * * * * [progress]: [ 212 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.394 * * * * [progress]: [ 213 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.394 * * * * [progress]: [ 214 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.394 * * * * [progress]: [ 215 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.394 * * * * [progress]: [ 216 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) 1)) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.395 * * * * [progress]: [ 217 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.395 * * * * [progress]: [ 218 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.395 * * * * [progress]: [ 219 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.395 * * * * [progress]: [ 220 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (pow n (- 1/2 (/ k 2))))) (/ (sqrt 1) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.395 * * * * [progress]: [ 221 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.395 * * * * [progress]: [ 222 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.395 * * * * [progress]: [ 223 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) 1)) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.395 * * * * [progress]: [ 224 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.395 * * * * [progress]: [ 225 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.395 * * * * [progress]: [ 226 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.395 * * * * [progress]: [ 227 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.396 * * * * [progress]: [ 228 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.396 * * * * [progress]: [ 229 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.396 * * * * [progress]: [ 230 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) 1)) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.396 * * * * [progress]: [ 231 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.396 * * * * [progress]: [ 232 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.397 * * * * [progress]: [ 233 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.397 * * * * [progress]: [ 234 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (pow n (- 1/2 (/ k 2))))) (/ (sqrt 1) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.397 * * * * [progress]: [ 235 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.397 * * * * [progress]: [ 236 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.397 * * * * [progress]: [ 237 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 1)) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.397 * * * * [progress]: [ 238 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.397 * * * * [progress]: [ 239 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.397 * * * * [progress]: [ 240 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt k)) (/ (sqrt 1) (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.397 * * * * [progress]: [ 241 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt 1) (pow (* n (* 2 PI)) (/ k 2)))))>
13.397 * * * * [progress]: [ 242 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.397 * * * * [progress]: [ 243 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.397 * * * * [progress]: [ 244 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.398 * * * * [progress]: [ 245 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.398 * * * * [progress]: [ 246 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.398 * * * * [progress]: [ 247 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.398 * * * * [progress]: [ 248 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.398 * * * * [progress]: [ 249 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.398 * * * * [progress]: [ 250 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.398 * * * * [progress]: [ 251 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.398 * * * * [progress]: [ 252 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.398 * * * * [progress]: [ 253 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.398 * * * * [progress]: [ 254 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.398 * * * * [progress]: [ 255 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.398 * * * * [progress]: [ 256 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.398 * * * * [progress]: [ 257 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.399 * * * * [progress]: [ 258 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.399 * * * * [progress]: [ 259 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.399 * * * * [progress]: [ 260 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.399 * * * * [progress]: [ 261 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.399 * * * * [progress]: [ 262 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.399 * * * * [progress]: [ 263 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) 1)) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.399 * * * * [progress]: [ 264 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.399 * * * * [progress]: [ 265 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.399 * * * * [progress]: [ 266 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.399 * * * * [progress]: [ 267 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.399 * * * * [progress]: [ 268 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.399 * * * * [progress]: [ 269 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.399 * * * * [progress]: [ 270 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) 1)) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.400 * * * * [progress]: [ 271 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.400 * * * * [progress]: [ 272 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.400 * * * * [progress]: [ 273 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.400 * * * * [progress]: [ 274 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.400 * * * * [progress]: [ 275 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.400 * * * * [progress]: [ 276 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.400 * * * * [progress]: [ 277 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) 1)) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.400 * * * * [progress]: [ 278 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.400 * * * * [progress]: [ 279 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.400 * * * * [progress]: [ 280 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))))>
13.400 * * * * [progress]: [ 281 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))))>
13.400 * * * * [progress]: [ 282 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.400 * * * * [progress]: [ 283 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.400 * * * * [progress]: [ 284 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 1)) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.401 * * * * [progress]: [ 285 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))))>
13.401 * * * * [progress]: [ 286 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.401 * * * * [progress]: [ 287 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ 1 (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.401 * * * * [progress]: [ 288 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))) (/ 1 (pow (* n (* 2 PI)) (/ k 2)))))>
13.401 * * * * [progress]: [ 289 / 355 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.401 * * * * [progress]: [ 290 / 355 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.401 * * * * [progress]: [ 291 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1)))>
13.401 * * * * [progress]: [ 292 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.401 * * * * [progress]: [ 293 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.401 * * * * [progress]: [ 294 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
13.401 * * * * [progress]: [ 295 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
13.401 * * * * [progress]: [ 296 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
13.401 * * * * [progress]: [ 297 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.401 * * * * [progress]: [ 298 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.402 * * * * [progress]: [ 299 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
13.402 * * * * [progress]: [ 300 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.402 * * * * [progress]: [ 301 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
13.402 * * * * [progress]: [ 302 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
13.402 * * * * [progress]: [ 303 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2))))) (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
13.402 * * * * [progress]: [ 304 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.402 * * * * [progress]: [ 305 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.402 * * * * [progress]: [ 306 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
13.402 * * * * [progress]: [ 307 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.402 * * * * [progress]: [ 308 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
13.402 * * * * [progress]: [ 309 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
13.402 * * * * [progress]: [ 310 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
13.402 * * * * [progress]: [ 311 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.402 * * * * [progress]: [ 312 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.402 * * * * [progress]: [ 313 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
13.403 * * * * [progress]: [ 314 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.403 * * * * [progress]: [ 315 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
13.403 * * * * [progress]: [ 316 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
13.403 * * * * [progress]: [ 317 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (pow n (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
13.403 * * * * [progress]: [ 318 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.403 * * * * [progress]: [ 319 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.403 * * * * [progress]: [ 320 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
13.403 * * * * [progress]: [ 321 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.403 * * * * [progress]: [ 322 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
13.403 * * * * [progress]: [ 323 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))))>
13.403 * * * * [progress]: [ 324 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
13.403 * * * * [progress]: [ 325 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.403 * * * * [progress]: [ 326 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.404 * * * * [progress]: [ 327 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
13.404 * * * * [progress]: [ 328 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.404 * * * * [progress]: [ 329 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
13.404 * * * * [progress]: [ 330 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2))) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
13.404 * * * * [progress]: [ 331 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow n (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
13.404 * * * * [progress]: [ 332 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.404 * * * * [progress]: [ 333 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
13.404 * * * * [progress]: [ 334 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
13.404 * * * * [progress]: [ 335 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
13.404 * * * * [progress]: [ 336 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 1) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
13.404 * * * * [progress]: [ 337 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (sqrt k)) (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
13.404 * * * * [progress]: [ 338 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))) (pow (* n (* 2 PI)) (/ k 2))))>
13.404 * * * * [progress]: [ 339 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt 1) (cbrt 1)) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt 1))))>
13.404 * * * * [progress]: [ 340 / 355 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt 1) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1))))>
13.404 * * * * [progress]: [ 341 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1)))>
13.405 * * * * [progress]: [ 342 / 355 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))>
13.405 * * * * [progress]: [ 343 / 355 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
13.405 * * * * [progress]: [ 344 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))))))>
13.405 * * * * [progress]: [ 345 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))))>
13.405 * * * * [progress]: [ 346 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))>
13.405 * * * * [progress]: [ 347 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))>
13.405 * * * * [progress]: [ 348 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))>
13.405 * * * * [progress]: [ 349 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))>
13.405 * * * * [progress]: [ 350 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI)))))))))))))>
13.405 * * * * [progress]: [ 351 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))))))))))>
13.405 * * * * [progress]: [ 352 / 355 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))))>
13.405 * * * * [progress]: [ 353 / 355 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))>
13.405 * * * * [progress]: [ 354 / 355 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
13.406 * * * * [progress]: [ 355 / 355 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
13.418 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (log (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (exp (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (- (sqrt k))
  (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))
  (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2))
  (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))
  (/ (cbrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)
  (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (* (cbrt k) (cbrt k))) 1)
  (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) 1)
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt 1) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt 1) 1)
  (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) 1)
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ 1 (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ 1 (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ 1 (pow n (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ 1 (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 1)
  (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))
  (/ (sqrt k) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt k) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) 1)
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ (sqrt k) (pow (* n (* 2 PI)) 1/2))
  (real->posit16 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (- 1)
  (- (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))))
  (- (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))))
  (- (- (log (sqrt k)) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))))
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  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt 1) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt 1) 1))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2)))))
  (/ 1 (/ 1 (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2)))))
  (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ 1 1))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 1)
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (sqrt k))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (pow (* n (* 2 PI)) (/ k 2)))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1)
  (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt 1) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt 1) 1))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) 1/2)))
  (/ 1 (/ 1 (pow n (- 1/2 (/ k 2)))))
  (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))
  (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (/ 1 (/ 1 1))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))))
  (/ 1 1)
  (/ 1 (sqrt k))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) 1/2)))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt 1))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1)
  (/ 1 (sqrt k))
  (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI)))))))))))
  (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))))))))
  (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
  (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
13.435 * * [simplify]: iteration 1: (532 enodes)
13.722 * * [simplify]: iteration 2: (1425 enodes)
14.638 * * [simplify]: Extracting #0: cost 162 inf + 0
14.642 * * [simplify]: Extracting #1: cost 806 inf + 2
14.649 * * [simplify]: Extracting #2: cost 1129 inf + 5964
14.660 * * [simplify]: Extracting #3: cost 1079 inf + 52086
14.685 * * [simplify]: Extracting #4: cost 759 inf + 178242
14.761 * * [simplify]: Extracting #5: cost 332 inf + 353923
14.899 * * [simplify]: Extracting #6: cost 118 inf + 448450
15.024 * * [simplify]: Extracting #7: cost 32 inf + 487613
15.147 * * [simplify]: Extracting #8: cost 0 inf + 505298
15.273 * * [simplify]: Extracting #9: cost 0 inf + 504778
15.425 * * [simplify]: Extracting #10: cost 0 inf + 504618
15.598 * [simplify]: Simplified to:
  (* (log (* (* n PI) 2)) (- 1/2 (/ k 2)))
  (* (log (* (* n PI) 2)) (- 1/2 (/ k 2)))
  (* (log (* (* n PI) 2)) (- 1/2 (/ k 2)))
  (* (log (* (* n PI) 2)) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* n PI) 2))
  (pow (* (* n PI) 2) (/ k 2))
  (pow (* (* n PI) 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n PI) 2) (sqrt (- 1/2 (/ k 2))))
  (* (* n PI) 2)
  (pow (* (* n PI) 2) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n PI) 2) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* n PI) 2)
  (sqrt (* (* n PI) 2))
  (pow (* (* n PI) 2) (- (/ k 2)))
  (sqrt (* (* n PI) 2))
  (pow (* (* n PI) 2) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (log (* (* n PI) 2)) (- 1/2 (/ k 2)))
  (exp (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (pow (* (* n PI) 2) (- 1/4 (/ k 4)))
  (pow (* (* n PI) 2) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (* (* n PI) 2)
  (* (* n PI) 2)
  (log (* (* n PI) 2))
  (log (* (* n PI) 2))
  (log (* (* n PI) 2))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* (* n (* n n)) 8) PI) (* PI PI))
  (* 2 (* (* PI n) (* 4 (* (* PI n) (* PI n)))))
  (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2)))
  (cbrt (* (* n PI) 2))
  (* 2 (* (* PI n) (* 4 (* (* PI n) (* PI n)))))
  (sqrt (* (* n PI) 2))
  (sqrt (* (* n PI) 2))
  (* n 2)
  (* 2 (* PI (cbrt n)))
  (* (sqrt n) (* PI 2))
  (* (* n PI) 2)
  (real->posit16 (* (* n PI) 2))
  (- (log (sqrt k)) (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))))
  (- (log (sqrt k)) (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))))
  (exp (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (* (/ k (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))
  (* (cbrt (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))
  (cbrt (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (* (* (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (sqrt (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (sqrt (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (- (sqrt k))
  (- (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n PI) 2)))
  (/ (cbrt (sqrt k)) (pow (* (* n PI) 2) (- (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n PI) 2)))
  (/ (cbrt (sqrt k)) (pow (* (* n PI) 2) (- (/ k 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))
  (/ (cbrt (sqrt k)) (pow (* PI 2) (- 1/2 (/ k 2))))
  (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (/ (cbrt (sqrt k)) (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))
  (/ (cbrt (sqrt k)) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (* (cbrt (sqrt k)) (cbrt (sqrt k)))
  (/ (cbrt (sqrt k)) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (* (/ (cbrt (sqrt k)) (pow (* (* n PI) 2) (- 1/4 (/ k 4)))) (cbrt (sqrt k)))
  (/ (cbrt (sqrt k)) (pow (* (* n PI) 2) (- 1/4 (/ k 4))))
  (/ (fabs (cbrt k)) (sqrt (* (* n PI) 2)))
  (/ (sqrt (cbrt k)) (pow (* (* n PI) 2) (- (/ k 2))))
  (/ (fabs (cbrt k)) (sqrt (* (* n PI) 2)))
  (/ (sqrt (cbrt k)) (pow (* (* n PI) 2) (- (/ k 2))))
  (/ (fabs (cbrt k)) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt (cbrt k)) (pow (* PI 2) (- 1/2 (/ k 2))))
  (/ (fabs (cbrt k)) (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (/ (fabs (cbrt k)) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (/ (sqrt (cbrt k)) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (fabs (cbrt k))
  (/ (sqrt (cbrt k)) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (/ (fabs (cbrt k)) (pow (* (* n PI) 2) (- 1/4 (/ k 4))))
  (/ (sqrt (cbrt k)) (pow (* (* n PI) 2) (- 1/4 (/ k 4))))
  (/ (sqrt (sqrt k)) (sqrt (* (* n PI) 2)))
  (/ (sqrt (sqrt k)) (pow (* (* n PI) 2) (- (/ k 2))))
  (/ (sqrt (sqrt k)) (sqrt (* (* n PI) 2)))
  (/ (sqrt (sqrt k)) (pow (* (* n PI) 2) (- (/ k 2))))
  (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* PI 2) (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (sqrt (sqrt k))
  (/ (sqrt (sqrt k)) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (/ (sqrt (sqrt k)) (pow (* (* n PI) 2) (- 1/4 (/ k 4))))
  (/ (sqrt (sqrt k)) (pow (* (* n PI) 2) (- 1/4 (/ k 4))))
  (/ 1 (sqrt (* (* n PI) 2)))
  (/ (sqrt k) (pow (* (* n PI) 2) (- (/ k 2))))
  (/ 1 (sqrt (* (* n PI) 2)))
  (/ (sqrt k) (pow (* (* n PI) 2) (- (/ k 2))))
  (/ 1 (pow n (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* PI 2) (- 1/2 (/ k 2))))
  (/ 1 (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))
  (/ (sqrt k) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (/ 1 (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  1
  (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (/ 1 (pow (* (* n PI) 2) (- 1/4 (/ k 4))))
  (/ (sqrt k) (pow (* (* n PI) 2) (- 1/4 (/ k 4))))
  (/ (sqrt (sqrt k)) (sqrt (* (* n PI) 2)))
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  (* (* (/ 1 (fabs (cbrt k))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt (cbrt k))))
  (* (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ 1 (fabs (cbrt k))))
  (/ (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (* (/ 1 (fabs (cbrt k))) (pow (* (* n PI) 2) (- 1/4 (/ k 4))))
  (* (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (/ 1 (sqrt (cbrt k))))
  (/ (* 1 (sqrt (* (* n PI) 2))) (sqrt (sqrt k)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* (* n PI) 2) (- (/ k 2)))))
  (/ (* 1 (sqrt (* (* n PI) 2))) (sqrt (sqrt k)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* (* n PI) 2) (- (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2)))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* PI 2) (- 1/2 (/ k 2))))
  (* (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ 1 (sqrt (sqrt k))))
  (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))
  (* (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt (sqrt k))))
  (* (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (/ (* 1 (pow (* (* n PI) 2) (- 1/4 (/ k 4)))) (sqrt (sqrt k)))
  (/ (* 1 (pow (* (* n PI) 2) (- 1/4 (/ k 4)))) (sqrt (sqrt k)))
  (sqrt (* (* n PI) 2))
  (/ (* 1 (pow (* (* n PI) 2) (- (/ k 2)))) (sqrt k))
  (sqrt (* (* n PI) 2))
  (/ (* 1 (pow (* (* n PI) 2) (- (/ k 2)))) (sqrt k))
  (pow n (- 1/2 (/ k 2)))
  (* (/ 1 (sqrt k)) (pow (* PI 2) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)))
  (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (/ 1 (/ (sqrt k) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))
  1
  (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
  (pow (* (* n PI) 2) (- 1/4 (/ k 4)))
  (* (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (/ 1 (sqrt k)))
  (/ (* 1 (sqrt (* (* n PI) 2))) (sqrt (sqrt k)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* (* n PI) 2) (- (/ k 2)))))
  (/ (* 1 (sqrt (* (* n PI) 2))) (sqrt (sqrt k)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* (* n PI) 2) (- (/ k 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2)))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* PI 2) (- 1/2 (/ k 2))))
  (* (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ 1 (sqrt (sqrt k))))
  (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))
  (* (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt (sqrt k))))
  (* (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (/ (* 1 (pow (* (* n PI) 2) (- 1/4 (/ k 4)))) (sqrt (sqrt k)))
  (/ (* 1 (pow (* (* n PI) 2) (- 1/4 (/ k 4)))) (sqrt (sqrt k)))
  (sqrt (* (* n PI) 2))
  (/ (* 1 (pow (* (* n PI) 2) (- (/ k 2)))) (sqrt k))
  (sqrt (* (* n PI) 2))
  (/ (* 1 (pow (* (* n PI) 2) (- (/ k 2)))) (sqrt k))
  (pow n (- 1/2 (/ k 2)))
  (* (/ 1 (sqrt k)) (pow (* PI 2) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)))
  (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (/ 1 (/ (sqrt k) (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))
  1
  (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
  (pow (* (* n PI) 2) (- 1/4 (/ k 4)))
  (* (pow (* (* n PI) 2) (- 1/4 (/ k 4))) (/ 1 (sqrt k)))
  1
  (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
  (/ 1 (sqrt k))
  (pow (* (* n PI) 2) (- 1/2 (/ k 2)))
  (* (/ 1 (sqrt k)) (sqrt (* (* n PI) 2)))
  (/ 1 (pow (* (* n PI) 2) (/ k 2)))
  (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))
  (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (/ 1 (* (cbrt (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))))
  (/ 1 (sqrt (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))
  (/ (* 1 (sqrt (* (* n PI) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* 1 (sqrt (* (* n PI) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (pow n (- 1/2 (/ k 2))))
  (/ 1 (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))))
  (* (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (pow (* (* n PI) 2) (- 1/4 (/ k 4))))
  (/ (sqrt (* (* n PI) 2)) (fabs (cbrt k)))
  (/ (sqrt (* (* n PI) 2)) (fabs (cbrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (* (* (/ 1 (fabs (cbrt k))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (* (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ 1 (fabs (cbrt k))))
  (/ 1 (fabs (cbrt k)))
  (* (/ 1 (fabs (cbrt k))) (pow (* (* n PI) 2) (- 1/4 (/ k 4))))
  (/ (* 1 (sqrt (* (* n PI) 2))) (sqrt (sqrt k)))
  (/ (* 1 (sqrt (* (* n PI) 2))) (sqrt (sqrt k)))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2)))))
  (* (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ 1 (sqrt (sqrt k))))
  (* (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ (* 1 (pow (* (* n PI) 2) (- 1/4 (/ k 4)))) (sqrt (sqrt k)))
  (sqrt (* (* n PI) 2))
  (sqrt (* (* n PI) 2))
  (pow n (- 1/2 (/ k 2)))
  (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  1
  (pow (* (* n PI) 2) (- 1/4 (/ k 4)))
  (/ (* 1 (sqrt (* (* n PI) 2))) (sqrt (sqrt k)))
  (/ (* 1 (sqrt (* (* n PI) 2))) (sqrt (sqrt k)))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2)))))
  (* (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ 1 (sqrt (sqrt k))))
  (* (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ (* 1 (pow (* (* n PI) 2) (- 1/4 (/ k 4)))) (sqrt (sqrt k)))
  (sqrt (* (* n PI) 2))
  (sqrt (* (* n PI) 2))
  (pow n (- 1/2 (/ k 2)))
  (* (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  1
  (pow (* (* n PI) 2) (- 1/4 (/ k 4)))
  1
  (/ 1 (sqrt k))
  (* (/ 1 (sqrt k)) (sqrt (* (* n PI) 2)))
  (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* (* n PI) 2) (- 1/2 (/ k 2))))
  (/ 1 (sqrt k))
  (real->posit16 (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))
  (+ (+ (* (* 1/8 (* (sqrt (* (* n PI) 2)) (* k k))) (* (log (* PI 2)) (log (* PI 2)))) (+ (sqrt (* (* n PI) 2)) (* (* (* (log n) (log n)) (sqrt (* (* n PI) 2))) (* (* k k) 1/8)))) (+ (* (* (log (* PI 2)) (sqrt (* (* n PI) 2))) (* (* (* k k) (log n)) 1/4)) (* -1/2 (* k (+ (* (sqrt (* (* n PI) 2)) (log n)) (* (log (* PI 2)) (sqrt (* (* n PI) 2))))))))
  (exp (* (- 1/2 (* k 1/2)) (log (* (* n PI) 2))))
  (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))
  (* (* n PI) 2)
  (* (* n PI) 2)
  (* (* n PI) 2)
  (+ (/ (- (* +nan.0 (* (* (* (log (* PI 2)) 1/2) (* k k)) (sqrt 2)))) PI) (+ (- (* +nan.0 (/ (* (sqrt 1/2) (* k k)) PI)) (* (/ (* (* n k) (sqrt 1/2)) (* PI PI)) +nan.0)) (* +nan.0 (- (/ (* (log n) (* (* (sqrt 2) (* k k)) 1/2)) PI) (* (/ (sqrt 1/2) PI) k)))))
  (- (+ (- (/ +nan.0 (* (exp (* (- 1/2 (* k 1/2)) (log (* (* n PI) 2)))) k)) (/ +nan.0 (* (* k k) (exp (* (- 1/2 (* k 1/2)) (log (* (* n PI) 2))))))) (/ +nan.0 (exp (* (- 1/2 (* k 1/2)) (log (* (* n PI) 2)))))))
  (- (- (/ (/ +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))) (* k k)) (- (/ (/ +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))) k) (/ +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))))))
  (+ (* (* (sqrt 2) +nan.0) (- (* (* n PI) k))) (- (* (* PI n) (* (sqrt 2) +nan.0)) (- (* (* (sqrt 2) (* (* n PI) k)) (* +nan.0 (log (* PI 2)))) (* (* (sqrt 2) +nan.0) (- (* (* (* (log n) k) PI) n) (* (* n PI) (* n PI)))))))
  (- (- (* (/ +nan.0 k) (/ (/ (exp (* (- 1/2 (* k 1/2)) (log (* (* n PI) 2)))) k) k)) (* +nan.0 (- (/ (exp (* (- 1/2 (* k 1/2)) (log (* (* n PI) 2)))) k) (/ (/ (exp (* (- 1/2 (* k 1/2)) (log (* (* n PI) 2)))) k) k)))))
  (+ (* (- +nan.0) (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))) k)) (* +nan.0 (- (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k)) (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))))))
15.673 * * * [progress]: adding candidates to table
19.806 * * [progress]: iteration 3 / 4
19.806 * * * [progress]: picking best candidate
19.848 * * * * [pick]: Picked  #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
19.848 * * * [progress]: localizing error
19.888 * * * [progress]: generating rewritten candidates
19.888 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 2)
19.917 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 2 1)
19.934 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1)
19.936 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1)
19.938 * * * [progress]: generating series expansions
19.938 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 2)
19.939 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
19.939 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
19.939 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
19.939 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
19.939 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
19.939 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
19.939 * [taylor]: Taking taylor expansion of 1/2 in k
19.939 * [backup-simplify]: Simplify 1/2 into 1/2
19.939 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
19.939 * [taylor]: Taking taylor expansion of 1/2 in k
19.939 * [backup-simplify]: Simplify 1/2 into 1/2
19.939 * [taylor]: Taking taylor expansion of k in k
19.939 * [backup-simplify]: Simplify 0 into 0
19.939 * [backup-simplify]: Simplify 1 into 1
19.939 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
19.939 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
19.939 * [taylor]: Taking taylor expansion of 2 in k
19.939 * [backup-simplify]: Simplify 2 into 2
19.939 * [taylor]: Taking taylor expansion of (* n PI) in k
19.939 * [taylor]: Taking taylor expansion of n in k
19.939 * [backup-simplify]: Simplify n into n
19.939 * [taylor]: Taking taylor expansion of PI in k
19.939 * [backup-simplify]: Simplify PI into PI
19.939 * [backup-simplify]: Simplify (* n PI) into (* n PI)
19.939 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
19.939 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
19.940 * [backup-simplify]: Simplify (* 1/2 0) into 0
19.940 * [backup-simplify]: Simplify (- 0) into 0
19.940 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.940 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
19.940 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
19.940 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
19.940 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
19.940 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
19.940 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
19.940 * [taylor]: Taking taylor expansion of 1/2 in n
19.940 * [backup-simplify]: Simplify 1/2 into 1/2
19.940 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
19.940 * [taylor]: Taking taylor expansion of 1/2 in n
19.940 * [backup-simplify]: Simplify 1/2 into 1/2
19.940 * [taylor]: Taking taylor expansion of k in n
19.940 * [backup-simplify]: Simplify k into k
19.940 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
19.940 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
19.941 * [taylor]: Taking taylor expansion of 2 in n
19.941 * [backup-simplify]: Simplify 2 into 2
19.941 * [taylor]: Taking taylor expansion of (* n PI) in n
19.941 * [taylor]: Taking taylor expansion of n in n
19.941 * [backup-simplify]: Simplify 0 into 0
19.941 * [backup-simplify]: Simplify 1 into 1
19.941 * [taylor]: Taking taylor expansion of PI in n
19.941 * [backup-simplify]: Simplify PI into PI
19.941 * [backup-simplify]: Simplify (* 0 PI) into 0
19.941 * [backup-simplify]: Simplify (* 2 0) into 0
19.942 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.943 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
19.944 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.944 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
19.944 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
19.944 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
19.945 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.945 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
19.946 * [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)))))
19.946 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
19.946 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
19.946 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
19.946 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
19.946 * [taylor]: Taking taylor expansion of 1/2 in n
19.946 * [backup-simplify]: Simplify 1/2 into 1/2
19.946 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
19.946 * [taylor]: Taking taylor expansion of 1/2 in n
19.946 * [backup-simplify]: Simplify 1/2 into 1/2
19.946 * [taylor]: Taking taylor expansion of k in n
19.946 * [backup-simplify]: Simplify k into k
19.946 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
19.946 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
19.946 * [taylor]: Taking taylor expansion of 2 in n
19.946 * [backup-simplify]: Simplify 2 into 2
19.946 * [taylor]: Taking taylor expansion of (* n PI) in n
19.946 * [taylor]: Taking taylor expansion of n in n
19.946 * [backup-simplify]: Simplify 0 into 0
19.946 * [backup-simplify]: Simplify 1 into 1
19.946 * [taylor]: Taking taylor expansion of PI in n
19.947 * [backup-simplify]: Simplify PI into PI
19.947 * [backup-simplify]: Simplify (* 0 PI) into 0
19.947 * [backup-simplify]: Simplify (* 2 0) into 0
19.952 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.953 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
19.954 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.954 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
19.954 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
19.954 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
19.955 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.956 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
19.957 * [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)))))
19.957 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
19.957 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
19.957 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
19.957 * [taylor]: Taking taylor expansion of 1/2 in k
19.957 * [backup-simplify]: Simplify 1/2 into 1/2
19.957 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
19.957 * [taylor]: Taking taylor expansion of 1/2 in k
19.957 * [backup-simplify]: Simplify 1/2 into 1/2
19.957 * [taylor]: Taking taylor expansion of k in k
19.957 * [backup-simplify]: Simplify 0 into 0
19.957 * [backup-simplify]: Simplify 1 into 1
19.957 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
19.957 * [taylor]: Taking taylor expansion of (log n) in k
19.957 * [taylor]: Taking taylor expansion of n in k
19.957 * [backup-simplify]: Simplify n into n
19.958 * [backup-simplify]: Simplify (log n) into (log n)
19.958 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
19.958 * [taylor]: Taking taylor expansion of (* 2 PI) in k
19.958 * [taylor]: Taking taylor expansion of 2 in k
19.958 * [backup-simplify]: Simplify 2 into 2
19.958 * [taylor]: Taking taylor expansion of PI in k
19.958 * [backup-simplify]: Simplify PI into PI
19.958 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
19.959 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
19.959 * [backup-simplify]: Simplify (* 1/2 0) into 0
19.960 * [backup-simplify]: Simplify (- 0) into 0
19.960 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
19.961 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.962 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
19.963 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
19.964 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
19.965 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
19.966 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
19.968 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
19.969 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
19.969 * [backup-simplify]: Simplify (- 0) into 0
19.969 * [backup-simplify]: Simplify (+ 0 0) into 0
19.971 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.972 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
19.974 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.974 * [taylor]: Taking taylor expansion of 0 in k
19.974 * [backup-simplify]: Simplify 0 into 0
19.974 * [backup-simplify]: Simplify 0 into 0
19.974 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
19.975 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
19.977 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
19.977 * [backup-simplify]: Simplify (+ 0 0) into 0
19.978 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
19.979 * [backup-simplify]: Simplify (- 1/2) into -1/2
19.979 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
19.981 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
19.983 * [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)))))))
19.987 * [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)))))))
19.988 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
19.989 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
19.992 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
19.993 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
19.994 * [backup-simplify]: Simplify (- 0) into 0
19.994 * [backup-simplify]: Simplify (+ 0 0) into 0
19.996 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
19.997 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
19.999 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.000 * [taylor]: Taking taylor expansion of 0 in k
20.000 * [backup-simplify]: Simplify 0 into 0
20.000 * [backup-simplify]: Simplify 0 into 0
20.000 * [backup-simplify]: Simplify 0 into 0
20.001 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
20.002 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
20.006 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
20.007 * [backup-simplify]: Simplify (+ 0 0) into 0
20.008 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
20.008 * [backup-simplify]: Simplify (- 0) into 0
20.009 * [backup-simplify]: Simplify (+ 0 0) into 0
20.010 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
20.014 * [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)))))
20.018 * [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)))))
20.027 * [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)))))
20.028 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
20.028 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
20.028 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
20.028 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
20.028 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
20.028 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
20.028 * [taylor]: Taking taylor expansion of 1/2 in k
20.028 * [backup-simplify]: Simplify 1/2 into 1/2
20.028 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
20.028 * [taylor]: Taking taylor expansion of 1/2 in k
20.028 * [backup-simplify]: Simplify 1/2 into 1/2
20.028 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.028 * [taylor]: Taking taylor expansion of k in k
20.028 * [backup-simplify]: Simplify 0 into 0
20.028 * [backup-simplify]: Simplify 1 into 1
20.028 * [backup-simplify]: Simplify (/ 1 1) into 1
20.028 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
20.028 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
20.028 * [taylor]: Taking taylor expansion of 2 in k
20.028 * [backup-simplify]: Simplify 2 into 2
20.028 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.028 * [taylor]: Taking taylor expansion of PI in k
20.028 * [backup-simplify]: Simplify PI into PI
20.028 * [taylor]: Taking taylor expansion of n in k
20.028 * [backup-simplify]: Simplify n into n
20.029 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.029 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
20.029 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
20.029 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
20.029 * [backup-simplify]: Simplify (- 1/2) into -1/2
20.030 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
20.030 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
20.030 * [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))))
20.030 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
20.030 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
20.030 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
20.030 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
20.030 * [taylor]: Taking taylor expansion of 1/2 in n
20.030 * [backup-simplify]: Simplify 1/2 into 1/2
20.030 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
20.030 * [taylor]: Taking taylor expansion of 1/2 in n
20.030 * [backup-simplify]: Simplify 1/2 into 1/2
20.030 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.030 * [taylor]: Taking taylor expansion of k in n
20.030 * [backup-simplify]: Simplify k into k
20.031 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.031 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
20.031 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
20.031 * [taylor]: Taking taylor expansion of 2 in n
20.031 * [backup-simplify]: Simplify 2 into 2
20.031 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.031 * [taylor]: Taking taylor expansion of PI in n
20.031 * [backup-simplify]: Simplify PI into PI
20.031 * [taylor]: Taking taylor expansion of n in n
20.031 * [backup-simplify]: Simplify 0 into 0
20.031 * [backup-simplify]: Simplify 1 into 1
20.031 * [backup-simplify]: Simplify (/ PI 1) into PI
20.032 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.033 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.033 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
20.033 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
20.033 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
20.034 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.035 * [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)))
20.036 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
20.036 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
20.036 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
20.036 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
20.036 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
20.036 * [taylor]: Taking taylor expansion of 1/2 in n
20.036 * [backup-simplify]: Simplify 1/2 into 1/2
20.036 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
20.036 * [taylor]: Taking taylor expansion of 1/2 in n
20.036 * [backup-simplify]: Simplify 1/2 into 1/2
20.036 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.036 * [taylor]: Taking taylor expansion of k in n
20.037 * [backup-simplify]: Simplify k into k
20.037 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.037 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
20.037 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
20.037 * [taylor]: Taking taylor expansion of 2 in n
20.037 * [backup-simplify]: Simplify 2 into 2
20.037 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.037 * [taylor]: Taking taylor expansion of PI in n
20.037 * [backup-simplify]: Simplify PI into PI
20.037 * [taylor]: Taking taylor expansion of n in n
20.037 * [backup-simplify]: Simplify 0 into 0
20.037 * [backup-simplify]: Simplify 1 into 1
20.037 * [backup-simplify]: Simplify (/ PI 1) into PI
20.038 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.039 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.039 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
20.039 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
20.039 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
20.040 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.041 * [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)))
20.042 * [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))))
20.042 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
20.042 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
20.042 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
20.042 * [taylor]: Taking taylor expansion of 1/2 in k
20.042 * [backup-simplify]: Simplify 1/2 into 1/2
20.042 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
20.042 * [taylor]: Taking taylor expansion of 1/2 in k
20.042 * [backup-simplify]: Simplify 1/2 into 1/2
20.042 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.043 * [taylor]: Taking taylor expansion of k in k
20.043 * [backup-simplify]: Simplify 0 into 0
20.043 * [backup-simplify]: Simplify 1 into 1
20.043 * [backup-simplify]: Simplify (/ 1 1) into 1
20.043 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
20.043 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
20.043 * [taylor]: Taking taylor expansion of (* 2 PI) in k
20.043 * [taylor]: Taking taylor expansion of 2 in k
20.043 * [backup-simplify]: Simplify 2 into 2
20.043 * [taylor]: Taking taylor expansion of PI in k
20.043 * [backup-simplify]: Simplify PI into PI
20.044 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.045 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.045 * [taylor]: Taking taylor expansion of (log n) in k
20.045 * [taylor]: Taking taylor expansion of n in k
20.045 * [backup-simplify]: Simplify n into n
20.045 * [backup-simplify]: Simplify (log n) into (log n)
20.045 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
20.046 * [backup-simplify]: Simplify (- 1/2) into -1/2
20.046 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
20.046 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
20.047 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
20.048 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
20.049 * [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))))
20.051 * [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))))
20.052 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.052 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
20.055 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
20.055 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.055 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
20.056 * [backup-simplify]: Simplify (- 0) into 0
20.056 * [backup-simplify]: Simplify (+ 0 0) into 0
20.058 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.059 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
20.061 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
20.061 * [taylor]: Taking taylor expansion of 0 in k
20.061 * [backup-simplify]: Simplify 0 into 0
20.061 * [backup-simplify]: Simplify 0 into 0
20.061 * [backup-simplify]: Simplify 0 into 0
20.062 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.063 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
20.066 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
20.067 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.068 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
20.068 * [backup-simplify]: Simplify (- 0) into 0
20.068 * [backup-simplify]: Simplify (+ 0 0) into 0
20.070 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.072 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
20.074 * [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
20.074 * [taylor]: Taking taylor expansion of 0 in k
20.074 * [backup-simplify]: Simplify 0 into 0
20.074 * [backup-simplify]: Simplify 0 into 0
20.074 * [backup-simplify]: Simplify 0 into 0
20.074 * [backup-simplify]: Simplify 0 into 0
20.076 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.077 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.083 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
20.083 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.084 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
20.085 * [backup-simplify]: Simplify (- 0) into 0
20.085 * [backup-simplify]: Simplify (+ 0 0) into 0
20.087 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.091 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
20.094 * [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
20.094 * [taylor]: Taking taylor expansion of 0 in k
20.094 * [backup-simplify]: Simplify 0 into 0
20.094 * [backup-simplify]: Simplify 0 into 0
20.095 * [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)))))
20.096 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
20.096 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
20.096 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
20.096 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
20.096 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
20.096 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
20.096 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
20.096 * [taylor]: Taking taylor expansion of 1/2 in k
20.096 * [backup-simplify]: Simplify 1/2 into 1/2
20.096 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.096 * [taylor]: Taking taylor expansion of k in k
20.096 * [backup-simplify]: Simplify 0 into 0
20.096 * [backup-simplify]: Simplify 1 into 1
20.096 * [backup-simplify]: Simplify (/ 1 1) into 1
20.096 * [taylor]: Taking taylor expansion of 1/2 in k
20.096 * [backup-simplify]: Simplify 1/2 into 1/2
20.096 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
20.096 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
20.096 * [taylor]: Taking taylor expansion of -2 in k
20.097 * [backup-simplify]: Simplify -2 into -2
20.097 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.097 * [taylor]: Taking taylor expansion of PI in k
20.097 * [backup-simplify]: Simplify PI into PI
20.097 * [taylor]: Taking taylor expansion of n in k
20.097 * [backup-simplify]: Simplify n into n
20.097 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.097 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
20.097 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
20.097 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
20.098 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
20.098 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
20.098 * [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)))
20.098 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
20.098 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
20.098 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
20.098 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
20.098 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
20.098 * [taylor]: Taking taylor expansion of 1/2 in n
20.098 * [backup-simplify]: Simplify 1/2 into 1/2
20.098 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.098 * [taylor]: Taking taylor expansion of k in n
20.098 * [backup-simplify]: Simplify k into k
20.098 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.098 * [taylor]: Taking taylor expansion of 1/2 in n
20.098 * [backup-simplify]: Simplify 1/2 into 1/2
20.098 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
20.098 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
20.098 * [taylor]: Taking taylor expansion of -2 in n
20.098 * [backup-simplify]: Simplify -2 into -2
20.098 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.098 * [taylor]: Taking taylor expansion of PI in n
20.099 * [backup-simplify]: Simplify PI into PI
20.099 * [taylor]: Taking taylor expansion of n in n
20.099 * [backup-simplify]: Simplify 0 into 0
20.099 * [backup-simplify]: Simplify 1 into 1
20.099 * [backup-simplify]: Simplify (/ PI 1) into PI
20.099 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.100 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
20.100 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
20.101 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
20.102 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.103 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
20.104 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
20.105 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
20.105 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
20.105 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
20.105 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
20.105 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
20.105 * [taylor]: Taking taylor expansion of 1/2 in n
20.105 * [backup-simplify]: Simplify 1/2 into 1/2
20.105 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.105 * [taylor]: Taking taylor expansion of k in n
20.105 * [backup-simplify]: Simplify k into k
20.105 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.105 * [taylor]: Taking taylor expansion of 1/2 in n
20.105 * [backup-simplify]: Simplify 1/2 into 1/2
20.105 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
20.105 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
20.105 * [taylor]: Taking taylor expansion of -2 in n
20.105 * [backup-simplify]: Simplify -2 into -2
20.105 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.105 * [taylor]: Taking taylor expansion of PI in n
20.105 * [backup-simplify]: Simplify PI into PI
20.105 * [taylor]: Taking taylor expansion of n in n
20.105 * [backup-simplify]: Simplify 0 into 0
20.105 * [backup-simplify]: Simplify 1 into 1
20.106 * [backup-simplify]: Simplify (/ PI 1) into PI
20.106 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.107 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
20.107 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
20.107 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
20.109 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.110 * [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)))
20.112 * [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))))
20.112 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
20.112 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
20.112 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
20.112 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
20.112 * [taylor]: Taking taylor expansion of 1/2 in k
20.112 * [backup-simplify]: Simplify 1/2 into 1/2
20.112 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.112 * [taylor]: Taking taylor expansion of k in k
20.112 * [backup-simplify]: Simplify 0 into 0
20.112 * [backup-simplify]: Simplify 1 into 1
20.112 * [backup-simplify]: Simplify (/ 1 1) into 1
20.112 * [taylor]: Taking taylor expansion of 1/2 in k
20.112 * [backup-simplify]: Simplify 1/2 into 1/2
20.112 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
20.112 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
20.113 * [taylor]: Taking taylor expansion of (* -2 PI) in k
20.113 * [taylor]: Taking taylor expansion of -2 in k
20.113 * [backup-simplify]: Simplify -2 into -2
20.113 * [taylor]: Taking taylor expansion of PI in k
20.113 * [backup-simplify]: Simplify PI into PI
20.113 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.114 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
20.114 * [taylor]: Taking taylor expansion of (log n) in k
20.115 * [taylor]: Taking taylor expansion of n in k
20.115 * [backup-simplify]: Simplify n into n
20.115 * [backup-simplify]: Simplify (log n) into (log n)
20.115 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
20.115 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
20.116 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
20.117 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
20.118 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
20.119 * [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))))
20.120 * [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))))
20.121 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.121 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
20.123 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
20.123 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.124 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
20.124 * [backup-simplify]: Simplify (+ 0 0) into 0
20.126 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.127 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
20.129 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
20.129 * [taylor]: Taking taylor expansion of 0 in k
20.129 * [backup-simplify]: Simplify 0 into 0
20.129 * [backup-simplify]: Simplify 0 into 0
20.129 * [backup-simplify]: Simplify 0 into 0
20.130 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.131 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
20.134 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
20.135 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.135 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
20.136 * [backup-simplify]: Simplify (+ 0 0) into 0
20.137 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.139 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
20.141 * [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
20.141 * [taylor]: Taking taylor expansion of 0 in k
20.141 * [backup-simplify]: Simplify 0 into 0
20.141 * [backup-simplify]: Simplify 0 into 0
20.141 * [backup-simplify]: Simplify 0 into 0
20.141 * [backup-simplify]: Simplify 0 into 0
20.142 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.143 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.150 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
20.150 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.151 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
20.152 * [backup-simplify]: Simplify (+ 0 0) into 0
20.153 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.155 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
20.158 * [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
20.158 * [taylor]: Taking taylor expansion of 0 in k
20.158 * [backup-simplify]: Simplify 0 into 0
20.158 * [backup-simplify]: Simplify 0 into 0
20.159 * [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)))))
20.159 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 2 1)
20.160 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
20.160 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
20.160 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
20.160 * [taylor]: Taking taylor expansion of 2 in n
20.160 * [backup-simplify]: Simplify 2 into 2
20.160 * [taylor]: Taking taylor expansion of (* n PI) in n
20.160 * [taylor]: Taking taylor expansion of n in n
20.160 * [backup-simplify]: Simplify 0 into 0
20.160 * [backup-simplify]: Simplify 1 into 1
20.160 * [taylor]: Taking taylor expansion of PI in n
20.160 * [backup-simplify]: Simplify PI into PI
20.160 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
20.160 * [taylor]: Taking taylor expansion of 2 in n
20.160 * [backup-simplify]: Simplify 2 into 2
20.160 * [taylor]: Taking taylor expansion of (* n PI) in n
20.160 * [taylor]: Taking taylor expansion of n in n
20.160 * [backup-simplify]: Simplify 0 into 0
20.160 * [backup-simplify]: Simplify 1 into 1
20.160 * [taylor]: Taking taylor expansion of PI in n
20.160 * [backup-simplify]: Simplify PI into PI
20.161 * [backup-simplify]: Simplify (* 0 PI) into 0
20.161 * [backup-simplify]: Simplify (* 2 0) into 0
20.161 * [backup-simplify]: Simplify 0 into 0
20.163 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.164 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
20.165 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.166 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
20.167 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
20.167 * [backup-simplify]: Simplify 0 into 0
20.168 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
20.169 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
20.169 * [backup-simplify]: Simplify 0 into 0
20.171 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.172 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
20.172 * [backup-simplify]: Simplify 0 into 0
20.174 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.176 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
20.176 * [backup-simplify]: Simplify 0 into 0
20.178 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.179 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
20.179 * [backup-simplify]: Simplify 0 into 0
20.181 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
20.183 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
20.183 * [backup-simplify]: Simplify 0 into 0
20.184 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
20.185 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
20.185 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
20.185 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
20.185 * [taylor]: Taking taylor expansion of 2 in n
20.185 * [backup-simplify]: Simplify 2 into 2
20.185 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.185 * [taylor]: Taking taylor expansion of PI in n
20.185 * [backup-simplify]: Simplify PI into PI
20.185 * [taylor]: Taking taylor expansion of n in n
20.185 * [backup-simplify]: Simplify 0 into 0
20.185 * [backup-simplify]: Simplify 1 into 1
20.186 * [backup-simplify]: Simplify (/ PI 1) into PI
20.186 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
20.186 * [taylor]: Taking taylor expansion of 2 in n
20.186 * [backup-simplify]: Simplify 2 into 2
20.186 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.186 * [taylor]: Taking taylor expansion of PI in n
20.186 * [backup-simplify]: Simplify PI into PI
20.186 * [taylor]: Taking taylor expansion of n in n
20.186 * [backup-simplify]: Simplify 0 into 0
20.186 * [backup-simplify]: Simplify 1 into 1
20.186 * [backup-simplify]: Simplify (/ PI 1) into PI
20.187 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.187 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.188 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.189 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
20.189 * [backup-simplify]: Simplify 0 into 0
20.190 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.191 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
20.191 * [backup-simplify]: Simplify 0 into 0
20.192 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.193 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.193 * [backup-simplify]: Simplify 0 into 0
20.195 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.196 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.196 * [backup-simplify]: Simplify 0 into 0
20.197 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.199 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.199 * [backup-simplify]: Simplify 0 into 0
20.200 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.201 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.201 * [backup-simplify]: Simplify 0 into 0
20.202 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
20.203 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
20.203 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
20.203 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
20.203 * [taylor]: Taking taylor expansion of -2 in n
20.203 * [backup-simplify]: Simplify -2 into -2
20.203 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.203 * [taylor]: Taking taylor expansion of PI in n
20.203 * [backup-simplify]: Simplify PI into PI
20.203 * [taylor]: Taking taylor expansion of n in n
20.203 * [backup-simplify]: Simplify 0 into 0
20.203 * [backup-simplify]: Simplify 1 into 1
20.203 * [backup-simplify]: Simplify (/ PI 1) into PI
20.203 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
20.203 * [taylor]: Taking taylor expansion of -2 in n
20.203 * [backup-simplify]: Simplify -2 into -2
20.203 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.203 * [taylor]: Taking taylor expansion of PI in n
20.203 * [backup-simplify]: Simplify PI into PI
20.203 * [taylor]: Taking taylor expansion of n in n
20.203 * [backup-simplify]: Simplify 0 into 0
20.203 * [backup-simplify]: Simplify 1 into 1
20.204 * [backup-simplify]: Simplify (/ PI 1) into PI
20.204 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.204 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.205 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.205 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
20.205 * [backup-simplify]: Simplify 0 into 0
20.206 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.206 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
20.206 * [backup-simplify]: Simplify 0 into 0
20.207 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.208 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.208 * [backup-simplify]: Simplify 0 into 0
20.208 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.209 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.209 * [backup-simplify]: Simplify 0 into 0
20.210 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.211 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.211 * [backup-simplify]: Simplify 0 into 0
20.211 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.212 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.212 * [backup-simplify]: Simplify 0 into 0
20.213 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
20.213 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1)
20.213 * [backup-simplify]: Simplify (sqrt (sqrt k)) into (pow k 1/4)
20.213 * [approximate]: Taking taylor expansion of (pow k 1/4) in (k) around 0
20.213 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
20.213 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
20.213 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
20.213 * [taylor]: Taking taylor expansion of 1/4 in k
20.213 * [backup-simplify]: Simplify 1/4 into 1/4
20.213 * [taylor]: Taking taylor expansion of (log k) in k
20.213 * [taylor]: Taking taylor expansion of k in k
20.213 * [backup-simplify]: Simplify 0 into 0
20.213 * [backup-simplify]: Simplify 1 into 1
20.213 * [backup-simplify]: Simplify (log 1) into 0
20.213 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.214 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
20.214 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
20.214 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
20.214 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
20.214 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
20.214 * [taylor]: Taking taylor expansion of 1/4 in k
20.214 * [backup-simplify]: Simplify 1/4 into 1/4
20.214 * [taylor]: Taking taylor expansion of (log k) in k
20.214 * [taylor]: Taking taylor expansion of k in k
20.214 * [backup-simplify]: Simplify 0 into 0
20.214 * [backup-simplify]: Simplify 1 into 1
20.214 * [backup-simplify]: Simplify (log 1) into 0
20.214 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.214 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
20.214 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
20.214 * [backup-simplify]: Simplify (pow k 1/4) into (pow k 1/4)
20.215 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
20.216 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.216 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0
20.216 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
20.216 * [backup-simplify]: Simplify 0 into 0
20.218 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
20.218 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.219 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0
20.220 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.220 * [backup-simplify]: Simplify 0 into 0
20.223 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
20.223 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.224 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0
20.226 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
20.227 * [backup-simplify]: Simplify 0 into 0
20.236 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
20.237 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.239 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0
20.241 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.241 * [backup-simplify]: Simplify 0 into 0
20.258 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
20.259 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.261 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0
20.264 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
20.264 * [backup-simplify]: Simplify 0 into 0
20.281 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
20.281 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.282 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0
20.286 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.286 * [backup-simplify]: Simplify 0 into 0
20.286 * [backup-simplify]: Simplify (pow k 1/4) into (pow k 1/4)
20.286 * [backup-simplify]: Simplify (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4)
20.286 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/4) in (k) around 0
20.286 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
20.286 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
20.286 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
20.286 * [taylor]: Taking taylor expansion of 1/4 in k
20.286 * [backup-simplify]: Simplify 1/4 into 1/4
20.286 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
20.286 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.286 * [taylor]: Taking taylor expansion of k in k
20.286 * [backup-simplify]: Simplify 0 into 0
20.286 * [backup-simplify]: Simplify 1 into 1
20.286 * [backup-simplify]: Simplify (/ 1 1) into 1
20.286 * [backup-simplify]: Simplify (log 1) into 0
20.287 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.287 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
20.287 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
20.287 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
20.287 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
20.287 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
20.287 * [taylor]: Taking taylor expansion of 1/4 in k
20.287 * [backup-simplify]: Simplify 1/4 into 1/4
20.287 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
20.287 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.287 * [taylor]: Taking taylor expansion of k in k
20.287 * [backup-simplify]: Simplify 0 into 0
20.287 * [backup-simplify]: Simplify 1 into 1
20.287 * [backup-simplify]: Simplify (/ 1 1) into 1
20.287 * [backup-simplify]: Simplify (log 1) into 0
20.288 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.288 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
20.288 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
20.288 * [backup-simplify]: Simplify (pow k -1/4) into (pow k -1/4)
20.288 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
20.289 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
20.289 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.290 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0
20.290 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
20.290 * [backup-simplify]: Simplify 0 into 0
20.291 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.292 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
20.293 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.293 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0
20.294 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.294 * [backup-simplify]: Simplify 0 into 0
20.294 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.299 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
20.299 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.301 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0
20.302 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
20.302 * [backup-simplify]: Simplify 0 into 0
20.303 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.314 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
20.315 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.317 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0
20.319 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.319 * [backup-simplify]: Simplify 0 into 0
20.320 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.338 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
20.338 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.340 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0
20.343 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
20.343 * [backup-simplify]: Simplify 0 into 0
20.344 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.361 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
20.361 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.362 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0
20.366 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.366 * [backup-simplify]: Simplify 0 into 0
20.366 * [backup-simplify]: Simplify (pow (/ 1 k) -1/4) into (pow (/ 1 k) -1/4)
20.366 * [backup-simplify]: Simplify (sqrt (sqrt (/ 1 (- k)))) into (sqrt (sqrt (/ -1 k)))
20.366 * [approximate]: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in (k) around 0
20.366 * [taylor]: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in k
20.366 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
20.366 * [taylor]: Taking taylor expansion of (/ -1 k) in k
20.366 * [taylor]: Taking taylor expansion of -1 in k
20.366 * [backup-simplify]: Simplify -1 into -1
20.366 * [taylor]: Taking taylor expansion of k in k
20.366 * [backup-simplify]: Simplify 0 into 0
20.366 * [backup-simplify]: Simplify 1 into 1
20.366 * [backup-simplify]: Simplify (/ -1 1) into -1
20.367 * [backup-simplify]: Simplify (sqrt 0) into 0
20.368 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
20.368 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
20.368 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
20.370 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.371 * [backup-simplify]: Simplify (/ +nan.0 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
20.371 * [taylor]: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in k
20.371 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
20.371 * [taylor]: Taking taylor expansion of (/ -1 k) in k
20.371 * [taylor]: Taking taylor expansion of -1 in k
20.371 * [backup-simplify]: Simplify -1 into -1
20.371 * [taylor]: Taking taylor expansion of k in k
20.371 * [backup-simplify]: Simplify 0 into 0
20.371 * [backup-simplify]: Simplify 1 into 1
20.372 * [backup-simplify]: Simplify (/ -1 1) into -1
20.372 * [backup-simplify]: Simplify (sqrt 0) into 0
20.373 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
20.374 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
20.375 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
20.377 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.379 * [backup-simplify]: Simplify (/ +nan.0 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
20.379 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
20.380 * [backup-simplify]: Simplify (/ +nan.0 (sqrt +nan.0)) into (/ +nan.0 (sqrt +nan.0))
20.381 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.384 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
20.389 * [backup-simplify]: Simplify (/ (- +nan.0 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
20.395 * [backup-simplify]: Simplify (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) into (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
20.404 * [backup-simplify]: Simplify (+ (* (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (pow (/ 1 (- k)) 2)) (+ (* (/ +nan.0 (sqrt +nan.0)) (/ 1 (- k))) (sqrt +nan.0))) into (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))))))))
20.404 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1)
20.404 * [backup-simplify]: Simplify (sqrt (sqrt k)) into (pow k 1/4)
20.404 * [approximate]: Taking taylor expansion of (pow k 1/4) in (k) around 0
20.404 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
20.404 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
20.404 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
20.404 * [taylor]: Taking taylor expansion of 1/4 in k
20.404 * [backup-simplify]: Simplify 1/4 into 1/4
20.404 * [taylor]: Taking taylor expansion of (log k) in k
20.404 * [taylor]: Taking taylor expansion of k in k
20.404 * [backup-simplify]: Simplify 0 into 0
20.404 * [backup-simplify]: Simplify 1 into 1
20.405 * [backup-simplify]: Simplify (log 1) into 0
20.405 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.405 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
20.405 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
20.405 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
20.405 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
20.405 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
20.405 * [taylor]: Taking taylor expansion of 1/4 in k
20.405 * [backup-simplify]: Simplify 1/4 into 1/4
20.405 * [taylor]: Taking taylor expansion of (log k) in k
20.405 * [taylor]: Taking taylor expansion of k in k
20.405 * [backup-simplify]: Simplify 0 into 0
20.405 * [backup-simplify]: Simplify 1 into 1
20.406 * [backup-simplify]: Simplify (log 1) into 0
20.406 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.406 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
20.406 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
20.406 * [backup-simplify]: Simplify (pow k 1/4) into (pow k 1/4)
20.408 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
20.408 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.408 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0
20.409 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
20.409 * [backup-simplify]: Simplify 0 into 0
20.412 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
20.413 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.413 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0
20.415 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.415 * [backup-simplify]: Simplify 0 into 0
20.419 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
20.420 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.421 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0
20.422 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
20.422 * [backup-simplify]: Simplify 0 into 0
20.432 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
20.433 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.434 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0
20.436 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.437 * [backup-simplify]: Simplify 0 into 0
20.452 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
20.453 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.455 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0
20.460 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
20.460 * [backup-simplify]: Simplify 0 into 0
20.489 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
20.490 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
20.492 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0
20.497 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.497 * [backup-simplify]: Simplify 0 into 0
20.497 * [backup-simplify]: Simplify (pow k 1/4) into (pow k 1/4)
20.497 * [backup-simplify]: Simplify (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4)
20.497 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/4) in (k) around 0
20.497 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
20.497 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
20.497 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
20.497 * [taylor]: Taking taylor expansion of 1/4 in k
20.497 * [backup-simplify]: Simplify 1/4 into 1/4
20.498 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
20.498 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.498 * [taylor]: Taking taylor expansion of k in k
20.498 * [backup-simplify]: Simplify 0 into 0
20.498 * [backup-simplify]: Simplify 1 into 1
20.498 * [backup-simplify]: Simplify (/ 1 1) into 1
20.498 * [backup-simplify]: Simplify (log 1) into 0
20.499 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.499 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
20.499 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
20.499 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
20.499 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
20.499 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
20.499 * [taylor]: Taking taylor expansion of 1/4 in k
20.499 * [backup-simplify]: Simplify 1/4 into 1/4
20.499 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
20.499 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.499 * [taylor]: Taking taylor expansion of k in k
20.499 * [backup-simplify]: Simplify 0 into 0
20.499 * [backup-simplify]: Simplify 1 into 1
20.500 * [backup-simplify]: Simplify (/ 1 1) into 1
20.500 * [backup-simplify]: Simplify (log 1) into 0
20.500 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.501 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
20.501 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
20.501 * [backup-simplify]: Simplify (pow k -1/4) into (pow k -1/4)
20.501 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
20.503 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
20.503 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.504 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0
20.504 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
20.504 * [backup-simplify]: Simplify 0 into 0
20.505 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.508 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
20.509 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.509 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0
20.510 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.511 * [backup-simplify]: Simplify 0 into 0
20.511 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.515 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
20.516 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.517 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0
20.518 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
20.519 * [backup-simplify]: Simplify 0 into 0
20.519 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.529 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
20.529 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.531 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0
20.533 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.533 * [backup-simplify]: Simplify 0 into 0
20.534 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.549 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
20.550 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.552 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0
20.556 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
20.556 * [backup-simplify]: Simplify 0 into 0
20.557 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.588 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
20.589 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
20.591 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0
20.599 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.599 * [backup-simplify]: Simplify 0 into 0
20.599 * [backup-simplify]: Simplify (pow (/ 1 k) -1/4) into (pow (/ 1 k) -1/4)
20.600 * [backup-simplify]: Simplify (sqrt (sqrt (/ 1 (- k)))) into (sqrt (sqrt (/ -1 k)))
20.600 * [approximate]: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in (k) around 0
20.600 * [taylor]: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in k
20.600 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
20.600 * [taylor]: Taking taylor expansion of (/ -1 k) in k
20.600 * [taylor]: Taking taylor expansion of -1 in k
20.600 * [backup-simplify]: Simplify -1 into -1
20.600 * [taylor]: Taking taylor expansion of k in k
20.600 * [backup-simplify]: Simplify 0 into 0
20.600 * [backup-simplify]: Simplify 1 into 1
20.601 * [backup-simplify]: Simplify (/ -1 1) into -1
20.601 * [backup-simplify]: Simplify (sqrt 0) into 0
20.603 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
20.603 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
20.604 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
20.609 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.610 * [backup-simplify]: Simplify (/ +nan.0 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
20.610 * [taylor]: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in k
20.610 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
20.610 * [taylor]: Taking taylor expansion of (/ -1 k) in k
20.610 * [taylor]: Taking taylor expansion of -1 in k
20.610 * [backup-simplify]: Simplify -1 into -1
20.610 * [taylor]: Taking taylor expansion of k in k
20.610 * [backup-simplify]: Simplify 0 into 0
20.610 * [backup-simplify]: Simplify 1 into 1
20.611 * [backup-simplify]: Simplify (/ -1 1) into -1
20.611 * [backup-simplify]: Simplify (sqrt 0) into 0
20.613 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
20.613 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
20.614 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
20.617 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.619 * [backup-simplify]: Simplify (/ +nan.0 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
20.620 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
20.620 * [backup-simplify]: Simplify (/ +nan.0 (sqrt +nan.0)) into (/ +nan.0 (sqrt +nan.0))
20.621 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.626 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
20.631 * [backup-simplify]: Simplify (/ (- +nan.0 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
20.638 * [backup-simplify]: Simplify (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) into (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
20.647 * [backup-simplify]: Simplify (+ (* (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (pow (/ 1 (- k)) 2)) (+ (* (/ +nan.0 (sqrt +nan.0)) (/ 1 (- k))) (sqrt +nan.0))) into (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))))))))
20.648 * * * [progress]: simplifying candidates
20.648 * * * * [progress]: [ 1 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))))))))>
20.648 * * * * [progress]: [ 2 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))))))))>
20.648 * * * * [progress]: [ 3 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))))))>
20.648 * * * * [progress]: [ 4 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))))))>
20.648 * * * * [progress]: [ 5 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))))))>
20.648 * * * * [progress]: [ 6 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))))))>
20.648 * * * * [progress]: [ 7 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))))))>
20.648 * * * * [progress]: [ 8 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)))))))>
20.648 * * * * [progress]: [ 9 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))))))>
20.648 * * * * [progress]: [ 10 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))))))>
20.648 * * * * [progress]: [ 11 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))))))>
20.649 * * * * [progress]: [ 12 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2))))))))>
20.649 * * * * [progress]: [ 13 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))))))))>
20.649 * * * * [progress]: [ 14 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))))))>
20.649 * * * * [progress]: [ 15 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))))))))>
20.649 * * * * [progress]: [ 16 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))))))))>
20.649 * * * * [progress]: [ 17 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
20.649 * * * * [progress]: [ 18 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1)))))>
20.649 * * * * [progress]: [ 19 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))))>
20.649 * * * * [progress]: [ 20 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))))>
20.649 * * * * [progress]: [ 21 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))))>
20.649 * * * * [progress]: [ 22 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))))>
20.649 * * * * [progress]: [ 23 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))))>
20.649 * * * * [progress]: [ 24 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
20.649 * * * * [progress]: [ 25 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))))>
20.650 * * * * [progress]: [ 26 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))))>
20.650 * * * * [progress]: [ 27 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))))))>
20.650 * * * * [progress]: [ 28 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))))))>
20.650 * * * * [progress]: [ 29 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))))))>
20.650 * * * * [progress]: [ 30 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2)))))))>
20.650 * * * * [progress]: [ 31 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2)))))))>
20.650 * * * * [progress]: [ 32 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2)))))))>
20.650 * * * * [progress]: [ 33 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2)))))))>
20.650 * * * * [progress]: [ 34 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2)))))))>
20.650 * * * * [progress]: [ 35 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2)))))))>
20.650 * * * * [progress]: [ 36 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2)))))))>
20.650 * * * * [progress]: [ 37 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2)))))))>
20.650 * * * * [progress]: [ 38 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 39 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 40 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 41 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 42 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 43 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 44 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 45 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 46 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (pow (sqrt k) 1/2) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 47 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (pow (sqrt (sqrt k)) 1) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 48 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (exp (log (sqrt (sqrt k)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 49 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (log (exp (sqrt (sqrt k)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 50 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (* (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 51 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (cbrt (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.651 * * * * [progress]: [ 52 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (* (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 53 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (* (sqrt (sqrt (* (cbrt k) (cbrt k)))) (sqrt (sqrt (cbrt k)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 54 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 55 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (* (sqrt (sqrt 1)) (sqrt (sqrt k))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 56 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 57 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (* (sqrt 1) (sqrt (sqrt k))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 58 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (pow k (/ 1/2 2)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 59 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (pow (sqrt k) (/ 1 2)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 60 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (pow k (/ (/ 1 2) 2)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 61 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 62 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (fabs (sqrt (sqrt k))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 63 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (fabs (sqrt (sqrt k))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 64 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (* 1 (sqrt (sqrt k))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 65 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (posit16->real (real->posit16 (sqrt (sqrt k)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.652 * * * * [progress]: [ 66 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (pow (sqrt k) 1/2) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 67 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (pow (sqrt (sqrt k)) 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 68 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (exp (log (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 69 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (log (exp (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 70 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 71 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (cbrt (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 72 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 73 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (sqrt (sqrt (* (cbrt k) (cbrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 74 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 75 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (sqrt (sqrt 1)) (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 76 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 77 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (sqrt 1) (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 78 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (pow k (/ 1/2 2)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 79 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (pow (sqrt k) (/ 1 2)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.653 * * * * [progress]: [ 80 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (pow k (/ (/ 1 2) 2)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.654 * * * * [progress]: [ 81 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.654 * * * * [progress]: [ 82 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (fabs (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.654 * * * * [progress]: [ 83 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (fabs (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.654 * * * * [progress]: [ 84 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.654 * * * * [progress]: [ 85 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (posit16->real (real->posit16 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.654 * * * * [progress]: [ 86 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (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)))))))))>
20.654 * * * * [progress]: [ 87 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))>
20.654 * * * * [progress]: [ 88 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))>
20.654 * * * * [progress]: [ 89 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))>
20.654 * * * * [progress]: [ 90 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))>
20.654 * * * * [progress]: [ 91 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))>
20.654 * * * * [progress]: [ 92 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (pow k 1/4) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.654 * * * * [progress]: [ 93 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (pow (/ 1 k) -1/4) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.654 * * * * [progress]: [ 94 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))))))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.655 * * * * [progress]: [ 95 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (pow k 1/4) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.655 * * * * [progress]: [ 96 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (pow (/ 1 k) -1/4) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.655 * * * * [progress]: [ 97 / 97 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))))))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
20.656 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (log (sqrt (sqrt k)))
  (exp (sqrt (sqrt k)))
  (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (cbrt (sqrt (sqrt k)))
  (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))
  (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (sqrt (cbrt (sqrt k)))
  (sqrt (sqrt (* (cbrt k) (cbrt k))))
  (sqrt (sqrt (cbrt k)))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt 1))
  (sqrt (sqrt k))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  (sqrt 1)
  (sqrt (sqrt k))
  (/ 1/2 2)
  (/ 1 2)
  (/ (/ 1 2) 2)
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  (real->posit16 (sqrt (sqrt k)))
  (log (sqrt (sqrt k)))
  (exp (sqrt (sqrt k)))
  (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (cbrt (sqrt (sqrt k)))
  (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))
  (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (sqrt (cbrt (sqrt k)))
  (sqrt (sqrt (* (cbrt k) (cbrt k))))
  (sqrt (sqrt (cbrt k)))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt 1))
  (sqrt (sqrt k))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  (sqrt 1)
  (sqrt (sqrt k))
  (/ 1/2 2)
  (/ 1 2)
  (/ (/ 1 2) 2)
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  (real->posit16 (sqrt (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))
  (pow k 1/4)
  (pow (/ 1 k) -1/4)
  (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))))))))
  (pow k 1/4)
  (pow (/ 1 k) -1/4)
  (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))))))))
20.659 * * [simplify]: iteration 1: (169 enodes)
20.737 * * [simplify]: iteration 2: (431 enodes)
21.200 * * [simplify]: iteration 3: (1320 enodes)
23.314 * * [simplify]: Extracting #0: cost 49 inf + 0
23.315 * * [simplify]: Extracting #1: cost 381 inf + 3
23.329 * * [simplify]: Extracting #2: cost 830 inf + 19200
23.365 * * [simplify]: Extracting #3: cost 854 inf + 85933
23.437 * * [simplify]: Extracting #4: cost 367 inf + 235853
23.534 * * [simplify]: Extracting #5: cost 106 inf + 330702
23.623 * * [simplify]: Extracting #6: cost 14 inf + 364281
23.731 * * [simplify]: Extracting #7: cost 0 inf + 370845
23.825 * * [simplify]: Extracting #8: cost 0 inf + 370805
23.937 * [simplify]: Simplified to:
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2))))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* PI 2) n) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* PI 2) n)
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (- (/ k 2)))
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* PI n) (* 8 (* (* PI n) (* PI n))))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* (* (cbrt n) PI) 2)
  (* (sqrt n) (* PI 2))
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (log (sqrt (sqrt k)))
  (exp (sqrt (sqrt k)))
  (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (cbrt (sqrt (sqrt k)))
  (* (sqrt k) (sqrt (sqrt k)))
  (fabs (cbrt (sqrt k)))
  (sqrt (cbrt (sqrt k)))
  (sqrt (fabs (cbrt k)))
  (sqrt (sqrt (cbrt k)))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  1
  (sqrt (sqrt k))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  1
  (sqrt (sqrt k))
  1/4
  1/2
  1/4
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  (real->posit16 (sqrt (sqrt k)))
  (log (sqrt (sqrt k)))
  (exp (sqrt (sqrt k)))
  (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (cbrt (sqrt (sqrt k)))
  (* (sqrt k) (sqrt (sqrt k)))
  (fabs (cbrt (sqrt k)))
  (sqrt (cbrt (sqrt k)))
  (sqrt (fabs (cbrt k)))
  (sqrt (sqrt (cbrt k)))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  1
  (sqrt (sqrt k))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  1
  (sqrt (sqrt k))
  1/4
  1/2
  1/4
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  (real->posit16 (sqrt (sqrt k)))
  (+ (* (* (* (log (* PI 2)) (* k (* k (sqrt (* (* PI 2) n))))) (log n)) 1/4) (+ (sqrt (* (* PI 2) n)) (+ (* (* k (* k 1/8)) (+ (* (sqrt (* (* PI 2) n)) (* (log (* PI 2)) (log (* PI 2)))) (* (log n) (* (log n) (sqrt (* (* PI 2) n)))))) (* -1/2 (* (* k (sqrt (* (* PI 2) n))) (log (* (* PI 2) n)))))))
  (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2))))
  (exp (* (- 1/2 (* k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
  (pow k 1/4)
  (pow (/ 1 k) -1/4)
  (- (- (sqrt +nan.0) (- (/ (/ +nan.0 k) (sqrt +nan.0)) (/ (/ (/ +nan.0 k) k) (* (sqrt +nan.0) +nan.0)))) (/ (/ (/ +nan.0 k) (sqrt +nan.0)) k))
  (pow k 1/4)
  (pow (/ 1 k) -1/4)
  (- (- (sqrt +nan.0) (- (/ (/ +nan.0 k) (sqrt +nan.0)) (/ (/ (/ +nan.0 k) k) (* (sqrt +nan.0) +nan.0)))) (/ (/ (/ +nan.0 k) (sqrt +nan.0)) k))
23.944 * * * [progress]: adding candidates to table
25.210 * * [progress]: iteration 4 / 4
25.210 * * * [progress]: picking best candidate
25.239 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.239 * * * [progress]: localizing error
25.277 * * * [progress]: generating rewritten candidates
25.277 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1)
25.298 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1)
25.304 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1)
25.316 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2)
25.319 * * * [progress]: generating series expansions
25.319 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1)
25.320 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
25.320 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
25.320 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
25.320 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
25.320 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
25.320 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
25.320 * [taylor]: Taking taylor expansion of 1/2 in k
25.320 * [backup-simplify]: Simplify 1/2 into 1/2
25.320 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
25.320 * [taylor]: Taking taylor expansion of 1/2 in k
25.320 * [backup-simplify]: Simplify 1/2 into 1/2
25.320 * [taylor]: Taking taylor expansion of k in k
25.320 * [backup-simplify]: Simplify 0 into 0
25.320 * [backup-simplify]: Simplify 1 into 1
25.320 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
25.320 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
25.320 * [taylor]: Taking taylor expansion of 2 in k
25.320 * [backup-simplify]: Simplify 2 into 2
25.320 * [taylor]: Taking taylor expansion of (* n PI) in k
25.320 * [taylor]: Taking taylor expansion of n in k
25.320 * [backup-simplify]: Simplify n into n
25.320 * [taylor]: Taking taylor expansion of PI in k
25.320 * [backup-simplify]: Simplify PI into PI
25.320 * [backup-simplify]: Simplify (* n PI) into (* n PI)
25.320 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
25.321 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
25.321 * [backup-simplify]: Simplify (* 1/2 0) into 0
25.321 * [backup-simplify]: Simplify (- 0) into 0
25.321 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
25.321 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
25.321 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
25.322 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
25.322 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
25.322 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
25.322 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
25.322 * [taylor]: Taking taylor expansion of 1/2 in n
25.322 * [backup-simplify]: Simplify 1/2 into 1/2
25.322 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
25.322 * [taylor]: Taking taylor expansion of 1/2 in n
25.322 * [backup-simplify]: Simplify 1/2 into 1/2
25.322 * [taylor]: Taking taylor expansion of k in n
25.322 * [backup-simplify]: Simplify k into k
25.322 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
25.322 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
25.322 * [taylor]: Taking taylor expansion of 2 in n
25.322 * [backup-simplify]: Simplify 2 into 2
25.322 * [taylor]: Taking taylor expansion of (* n PI) in n
25.322 * [taylor]: Taking taylor expansion of n in n
25.322 * [backup-simplify]: Simplify 0 into 0
25.322 * [backup-simplify]: Simplify 1 into 1
25.322 * [taylor]: Taking taylor expansion of PI in n
25.322 * [backup-simplify]: Simplify PI into PI
25.322 * [backup-simplify]: Simplify (* 0 PI) into 0
25.322 * [backup-simplify]: Simplify (* 2 0) into 0
25.330 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
25.331 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
25.332 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.332 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
25.332 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
25.332 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
25.334 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
25.335 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
25.336 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
25.336 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
25.336 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
25.336 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
25.336 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
25.336 * [taylor]: Taking taylor expansion of 1/2 in n
25.336 * [backup-simplify]: Simplify 1/2 into 1/2
25.336 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
25.336 * [taylor]: Taking taylor expansion of 1/2 in n
25.336 * [backup-simplify]: Simplify 1/2 into 1/2
25.336 * [taylor]: Taking taylor expansion of k in n
25.336 * [backup-simplify]: Simplify k into k
25.336 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
25.336 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
25.336 * [taylor]: Taking taylor expansion of 2 in n
25.336 * [backup-simplify]: Simplify 2 into 2
25.336 * [taylor]: Taking taylor expansion of (* n PI) in n
25.336 * [taylor]: Taking taylor expansion of n in n
25.336 * [backup-simplify]: Simplify 0 into 0
25.336 * [backup-simplify]: Simplify 1 into 1
25.336 * [taylor]: Taking taylor expansion of PI in n
25.337 * [backup-simplify]: Simplify PI into PI
25.337 * [backup-simplify]: Simplify (* 0 PI) into 0
25.337 * [backup-simplify]: Simplify (* 2 0) into 0
25.339 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
25.340 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
25.341 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.341 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
25.341 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
25.341 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
25.343 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
25.344 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
25.345 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
25.345 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
25.345 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
25.345 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
25.345 * [taylor]: Taking taylor expansion of 1/2 in k
25.346 * [backup-simplify]: Simplify 1/2 into 1/2
25.346 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
25.346 * [taylor]: Taking taylor expansion of 1/2 in k
25.346 * [backup-simplify]: Simplify 1/2 into 1/2
25.346 * [taylor]: Taking taylor expansion of k in k
25.346 * [backup-simplify]: Simplify 0 into 0
25.346 * [backup-simplify]: Simplify 1 into 1
25.346 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
25.346 * [taylor]: Taking taylor expansion of (log n) in k
25.346 * [taylor]: Taking taylor expansion of n in k
25.346 * [backup-simplify]: Simplify n into n
25.346 * [backup-simplify]: Simplify (log n) into (log n)
25.346 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
25.346 * [taylor]: Taking taylor expansion of (* 2 PI) in k
25.346 * [taylor]: Taking taylor expansion of 2 in k
25.346 * [backup-simplify]: Simplify 2 into 2
25.346 * [taylor]: Taking taylor expansion of PI in k
25.346 * [backup-simplify]: Simplify PI into PI
25.346 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.347 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.348 * [backup-simplify]: Simplify (* 1/2 0) into 0
25.348 * [backup-simplify]: Simplify (- 0) into 0
25.349 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
25.350 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
25.351 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
25.351 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
25.352 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
25.353 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
25.353 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
25.354 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
25.355 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
25.355 * [backup-simplify]: Simplify (- 0) into 0
25.355 * [backup-simplify]: Simplify (+ 0 0) into 0
25.356 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
25.357 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
25.358 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
25.358 * [taylor]: Taking taylor expansion of 0 in k
25.358 * [backup-simplify]: Simplify 0 into 0
25.358 * [backup-simplify]: Simplify 0 into 0
25.358 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
25.359 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
25.360 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
25.360 * [backup-simplify]: Simplify (+ 0 0) into 0
25.360 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
25.361 * [backup-simplify]: Simplify (- 1/2) into -1/2
25.361 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
25.362 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
25.364 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
25.365 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
25.366 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
25.367 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
25.369 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
25.369 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
25.370 * [backup-simplify]: Simplify (- 0) into 0
25.370 * [backup-simplify]: Simplify (+ 0 0) into 0
25.371 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
25.372 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
25.373 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.373 * [taylor]: Taking taylor expansion of 0 in k
25.373 * [backup-simplify]: Simplify 0 into 0
25.373 * [backup-simplify]: Simplify 0 into 0
25.373 * [backup-simplify]: Simplify 0 into 0
25.374 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
25.375 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
25.377 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
25.377 * [backup-simplify]: Simplify (+ 0 0) into 0
25.377 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
25.378 * [backup-simplify]: Simplify (- 0) into 0
25.378 * [backup-simplify]: Simplify (+ 0 0) into 0
25.379 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
25.381 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
25.385 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
25.395 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
25.395 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
25.395 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
25.395 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
25.395 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
25.395 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
25.396 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
25.396 * [taylor]: Taking taylor expansion of 1/2 in k
25.396 * [backup-simplify]: Simplify 1/2 into 1/2
25.396 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
25.396 * [taylor]: Taking taylor expansion of 1/2 in k
25.396 * [backup-simplify]: Simplify 1/2 into 1/2
25.396 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.396 * [taylor]: Taking taylor expansion of k in k
25.396 * [backup-simplify]: Simplify 0 into 0
25.396 * [backup-simplify]: Simplify 1 into 1
25.396 * [backup-simplify]: Simplify (/ 1 1) into 1
25.396 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
25.396 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
25.396 * [taylor]: Taking taylor expansion of 2 in k
25.396 * [backup-simplify]: Simplify 2 into 2
25.396 * [taylor]: Taking taylor expansion of (/ PI n) in k
25.396 * [taylor]: Taking taylor expansion of PI in k
25.396 * [backup-simplify]: Simplify PI into PI
25.396 * [taylor]: Taking taylor expansion of n in k
25.396 * [backup-simplify]: Simplify n into n
25.396 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
25.397 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
25.397 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
25.397 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
25.397 * [backup-simplify]: Simplify (- 1/2) into -1/2
25.398 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
25.398 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
25.398 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
25.398 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
25.398 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
25.398 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
25.398 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
25.398 * [taylor]: Taking taylor expansion of 1/2 in n
25.398 * [backup-simplify]: Simplify 1/2 into 1/2
25.398 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
25.398 * [taylor]: Taking taylor expansion of 1/2 in n
25.398 * [backup-simplify]: Simplify 1/2 into 1/2
25.398 * [taylor]: Taking taylor expansion of (/ 1 k) in n
25.399 * [taylor]: Taking taylor expansion of k in n
25.399 * [backup-simplify]: Simplify k into k
25.399 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
25.399 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
25.399 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
25.399 * [taylor]: Taking taylor expansion of 2 in n
25.399 * [backup-simplify]: Simplify 2 into 2
25.399 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.399 * [taylor]: Taking taylor expansion of PI in n
25.399 * [backup-simplify]: Simplify PI into PI
25.399 * [taylor]: Taking taylor expansion of n in n
25.399 * [backup-simplify]: Simplify 0 into 0
25.399 * [backup-simplify]: Simplify 1 into 1
25.399 * [backup-simplify]: Simplify (/ PI 1) into PI
25.400 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.401 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.401 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
25.401 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
25.401 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
25.403 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.404 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
25.405 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
25.405 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
25.405 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
25.405 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
25.405 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
25.405 * [taylor]: Taking taylor expansion of 1/2 in n
25.405 * [backup-simplify]: Simplify 1/2 into 1/2
25.405 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
25.405 * [taylor]: Taking taylor expansion of 1/2 in n
25.405 * [backup-simplify]: Simplify 1/2 into 1/2
25.405 * [taylor]: Taking taylor expansion of (/ 1 k) in n
25.405 * [taylor]: Taking taylor expansion of k in n
25.405 * [backup-simplify]: Simplify k into k
25.405 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
25.405 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
25.405 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
25.405 * [taylor]: Taking taylor expansion of 2 in n
25.405 * [backup-simplify]: Simplify 2 into 2
25.406 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.406 * [taylor]: Taking taylor expansion of PI in n
25.406 * [backup-simplify]: Simplify PI into PI
25.406 * [taylor]: Taking taylor expansion of n in n
25.406 * [backup-simplify]: Simplify 0 into 0
25.406 * [backup-simplify]: Simplify 1 into 1
25.406 * [backup-simplify]: Simplify (/ PI 1) into PI
25.407 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.408 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.408 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
25.408 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
25.408 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
25.409 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.410 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
25.412 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
25.412 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
25.412 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
25.412 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
25.412 * [taylor]: Taking taylor expansion of 1/2 in k
25.412 * [backup-simplify]: Simplify 1/2 into 1/2
25.412 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
25.412 * [taylor]: Taking taylor expansion of 1/2 in k
25.412 * [backup-simplify]: Simplify 1/2 into 1/2
25.412 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.412 * [taylor]: Taking taylor expansion of k in k
25.412 * [backup-simplify]: Simplify 0 into 0
25.412 * [backup-simplify]: Simplify 1 into 1
25.412 * [backup-simplify]: Simplify (/ 1 1) into 1
25.412 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
25.412 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
25.412 * [taylor]: Taking taylor expansion of (* 2 PI) in k
25.412 * [taylor]: Taking taylor expansion of 2 in k
25.412 * [backup-simplify]: Simplify 2 into 2
25.412 * [taylor]: Taking taylor expansion of PI in k
25.413 * [backup-simplify]: Simplify PI into PI
25.413 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.414 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
25.414 * [taylor]: Taking taylor expansion of (log n) in k
25.414 * [taylor]: Taking taylor expansion of n in k
25.414 * [backup-simplify]: Simplify n into n
25.414 * [backup-simplify]: Simplify (log n) into (log n)
25.415 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
25.415 * [backup-simplify]: Simplify (- 1/2) into -1/2
25.415 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
25.415 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
25.416 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
25.417 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
25.419 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
25.420 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
25.421 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
25.421 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
25.423 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
25.423 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
25.424 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
25.424 * [backup-simplify]: Simplify (- 0) into 0
25.425 * [backup-simplify]: Simplify (+ 0 0) into 0
25.426 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.427 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
25.429 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
25.429 * [taylor]: Taking taylor expansion of 0 in k
25.429 * [backup-simplify]: Simplify 0 into 0
25.429 * [backup-simplify]: Simplify 0 into 0
25.429 * [backup-simplify]: Simplify 0 into 0
25.431 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.432 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
25.435 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
25.435 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
25.436 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
25.437 * [backup-simplify]: Simplify (- 0) into 0
25.437 * [backup-simplify]: Simplify (+ 0 0) into 0
25.439 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.440 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
25.443 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.443 * [taylor]: Taking taylor expansion of 0 in k
25.443 * [backup-simplify]: Simplify 0 into 0
25.443 * [backup-simplify]: Simplify 0 into 0
25.443 * [backup-simplify]: Simplify 0 into 0
25.443 * [backup-simplify]: Simplify 0 into 0
25.444 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.446 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
25.457 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
25.458 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
25.459 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
25.460 * [backup-simplify]: Simplify (- 0) into 0
25.460 * [backup-simplify]: Simplify (+ 0 0) into 0
25.462 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
25.464 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
25.466 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
25.467 * [taylor]: Taking taylor expansion of 0 in k
25.467 * [backup-simplify]: Simplify 0 into 0
25.467 * [backup-simplify]: Simplify 0 into 0
25.468 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
25.469 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
25.469 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
25.469 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
25.469 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
25.469 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
25.469 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
25.469 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
25.469 * [taylor]: Taking taylor expansion of 1/2 in k
25.469 * [backup-simplify]: Simplify 1/2 into 1/2
25.469 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.469 * [taylor]: Taking taylor expansion of k in k
25.469 * [backup-simplify]: Simplify 0 into 0
25.469 * [backup-simplify]: Simplify 1 into 1
25.469 * [backup-simplify]: Simplify (/ 1 1) into 1
25.469 * [taylor]: Taking taylor expansion of 1/2 in k
25.469 * [backup-simplify]: Simplify 1/2 into 1/2
25.469 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
25.469 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
25.469 * [taylor]: Taking taylor expansion of -2 in k
25.470 * [backup-simplify]: Simplify -2 into -2
25.470 * [taylor]: Taking taylor expansion of (/ PI n) in k
25.470 * [taylor]: Taking taylor expansion of PI in k
25.470 * [backup-simplify]: Simplify PI into PI
25.470 * [taylor]: Taking taylor expansion of n in k
25.470 * [backup-simplify]: Simplify n into n
25.470 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
25.470 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
25.470 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
25.470 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
25.471 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
25.471 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
25.471 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
25.471 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
25.471 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
25.471 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
25.471 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
25.471 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
25.471 * [taylor]: Taking taylor expansion of 1/2 in n
25.471 * [backup-simplify]: Simplify 1/2 into 1/2
25.471 * [taylor]: Taking taylor expansion of (/ 1 k) in n
25.471 * [taylor]: Taking taylor expansion of k in n
25.471 * [backup-simplify]: Simplify k into k
25.471 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
25.471 * [taylor]: Taking taylor expansion of 1/2 in n
25.471 * [backup-simplify]: Simplify 1/2 into 1/2
25.472 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
25.472 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
25.472 * [taylor]: Taking taylor expansion of -2 in n
25.472 * [backup-simplify]: Simplify -2 into -2
25.472 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.472 * [taylor]: Taking taylor expansion of PI in n
25.472 * [backup-simplify]: Simplify PI into PI
25.472 * [taylor]: Taking taylor expansion of n in n
25.472 * [backup-simplify]: Simplify 0 into 0
25.472 * [backup-simplify]: Simplify 1 into 1
25.472 * [backup-simplify]: Simplify (/ PI 1) into PI
25.473 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.474 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
25.474 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
25.474 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
25.475 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.477 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
25.478 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
25.478 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
25.478 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
25.478 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
25.478 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
25.478 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
25.478 * [taylor]: Taking taylor expansion of 1/2 in n
25.478 * [backup-simplify]: Simplify 1/2 into 1/2
25.478 * [taylor]: Taking taylor expansion of (/ 1 k) in n
25.478 * [taylor]: Taking taylor expansion of k in n
25.478 * [backup-simplify]: Simplify k into k
25.478 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
25.478 * [taylor]: Taking taylor expansion of 1/2 in n
25.478 * [backup-simplify]: Simplify 1/2 into 1/2
25.478 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
25.478 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
25.478 * [taylor]: Taking taylor expansion of -2 in n
25.478 * [backup-simplify]: Simplify -2 into -2
25.478 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.478 * [taylor]: Taking taylor expansion of PI in n
25.478 * [backup-simplify]: Simplify PI into PI
25.478 * [taylor]: Taking taylor expansion of n in n
25.478 * [backup-simplify]: Simplify 0 into 0
25.478 * [backup-simplify]: Simplify 1 into 1
25.479 * [backup-simplify]: Simplify (/ PI 1) into PI
25.479 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.480 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
25.480 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
25.480 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
25.482 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.483 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
25.484 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
25.484 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
25.484 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
25.484 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
25.484 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
25.484 * [taylor]: Taking taylor expansion of 1/2 in k
25.484 * [backup-simplify]: Simplify 1/2 into 1/2
25.484 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.484 * [taylor]: Taking taylor expansion of k in k
25.484 * [backup-simplify]: Simplify 0 into 0
25.484 * [backup-simplify]: Simplify 1 into 1
25.485 * [backup-simplify]: Simplify (/ 1 1) into 1
25.485 * [taylor]: Taking taylor expansion of 1/2 in k
25.485 * [backup-simplify]: Simplify 1/2 into 1/2
25.485 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
25.485 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
25.485 * [taylor]: Taking taylor expansion of (* -2 PI) in k
25.485 * [taylor]: Taking taylor expansion of -2 in k
25.485 * [backup-simplify]: Simplify -2 into -2
25.485 * [taylor]: Taking taylor expansion of PI in k
25.485 * [backup-simplify]: Simplify PI into PI
25.486 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.487 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
25.487 * [taylor]: Taking taylor expansion of (log n) in k
25.487 * [taylor]: Taking taylor expansion of n in k
25.487 * [backup-simplify]: Simplify n into n
25.487 * [backup-simplify]: Simplify (log n) into (log n)
25.488 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
25.488 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
25.488 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
25.489 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
25.490 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
25.491 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
25.493 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
25.493 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
25.494 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
25.496 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
25.496 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
25.497 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
25.497 * [backup-simplify]: Simplify (+ 0 0) into 0
25.498 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.499 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
25.501 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
25.501 * [taylor]: Taking taylor expansion of 0 in k
25.501 * [backup-simplify]: Simplify 0 into 0
25.501 * [backup-simplify]: Simplify 0 into 0
25.501 * [backup-simplify]: Simplify 0 into 0
25.503 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.504 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
25.507 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
25.507 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
25.508 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
25.509 * [backup-simplify]: Simplify (+ 0 0) into 0
25.510 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.511 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
25.514 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.514 * [taylor]: Taking taylor expansion of 0 in k
25.514 * [backup-simplify]: Simplify 0 into 0
25.514 * [backup-simplify]: Simplify 0 into 0
25.514 * [backup-simplify]: Simplify 0 into 0
25.514 * [backup-simplify]: Simplify 0 into 0
25.515 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.516 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
25.522 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
25.523 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
25.524 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
25.524 * [backup-simplify]: Simplify (+ 0 0) into 0
25.525 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
25.526 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
25.527 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
25.527 * [taylor]: Taking taylor expansion of 0 in k
25.527 * [backup-simplify]: Simplify 0 into 0
25.527 * [backup-simplify]: Simplify 0 into 0
25.528 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
25.528 * * * * [progress]: [ 2 / 4 ] generating series at (2 1)
25.528 * [backup-simplify]: Simplify (/ 1 (sqrt (sqrt k))) into (pow (/ 1 k) 1/4)
25.528 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/4) in (k) around 0
25.528 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
25.528 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
25.528 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
25.528 * [taylor]: Taking taylor expansion of 1/4 in k
25.528 * [backup-simplify]: Simplify 1/4 into 1/4
25.528 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
25.528 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.528 * [taylor]: Taking taylor expansion of k in k
25.529 * [backup-simplify]: Simplify 0 into 0
25.529 * [backup-simplify]: Simplify 1 into 1
25.529 * [backup-simplify]: Simplify (/ 1 1) into 1
25.529 * [backup-simplify]: Simplify (log 1) into 0
25.529 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.529 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
25.529 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
25.530 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
25.530 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
25.530 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
25.530 * [taylor]: Taking taylor expansion of 1/4 in k
25.530 * [backup-simplify]: Simplify 1/4 into 1/4
25.530 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
25.530 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.530 * [taylor]: Taking taylor expansion of k in k
25.530 * [backup-simplify]: Simplify 0 into 0
25.530 * [backup-simplify]: Simplify 1 into 1
25.530 * [backup-simplify]: Simplify (/ 1 1) into 1
25.530 * [backup-simplify]: Simplify (log 1) into 0
25.530 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.530 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
25.531 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
25.531 * [backup-simplify]: Simplify (pow k -1/4) into (pow k -1/4)
25.531 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
25.532 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
25.532 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.532 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0
25.533 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
25.533 * [backup-simplify]: Simplify 0 into 0
25.534 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.535 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
25.535 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.536 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0
25.537 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.537 * [backup-simplify]: Simplify 0 into 0
25.537 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.540 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
25.540 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.541 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0
25.542 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
25.542 * [backup-simplify]: Simplify 0 into 0
25.543 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.549 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
25.549 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.550 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0
25.552 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.552 * [backup-simplify]: Simplify 0 into 0
25.553 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.568 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
25.569 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.571 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0
25.575 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
25.575 * [backup-simplify]: Simplify 0 into 0
25.576 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.604 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
25.604 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.606 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0
25.610 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.610 * [backup-simplify]: Simplify 0 into 0
25.610 * [backup-simplify]: Simplify (pow k -1/4) into (pow k -1/4)
25.610 * [backup-simplify]: Simplify (/ 1 (sqrt (sqrt (/ 1 k)))) into (pow k 1/4)
25.610 * [approximate]: Taking taylor expansion of (pow k 1/4) in (k) around 0
25.610 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
25.610 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
25.610 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
25.610 * [taylor]: Taking taylor expansion of 1/4 in k
25.610 * [backup-simplify]: Simplify 1/4 into 1/4
25.610 * [taylor]: Taking taylor expansion of (log k) in k
25.610 * [taylor]: Taking taylor expansion of k in k
25.610 * [backup-simplify]: Simplify 0 into 0
25.610 * [backup-simplify]: Simplify 1 into 1
25.610 * [backup-simplify]: Simplify (log 1) into 0
25.611 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.611 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
25.611 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
25.611 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
25.611 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
25.611 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
25.611 * [taylor]: Taking taylor expansion of 1/4 in k
25.611 * [backup-simplify]: Simplify 1/4 into 1/4
25.611 * [taylor]: Taking taylor expansion of (log k) in k
25.611 * [taylor]: Taking taylor expansion of k in k
25.611 * [backup-simplify]: Simplify 0 into 0
25.611 * [backup-simplify]: Simplify 1 into 1
25.612 * [backup-simplify]: Simplify (log 1) into 0
25.612 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.612 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
25.612 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
25.612 * [backup-simplify]: Simplify (pow k 1/4) into (pow k 1/4)
25.613 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
25.613 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.614 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0
25.614 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
25.614 * [backup-simplify]: Simplify 0 into 0
25.616 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
25.617 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.618 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0
25.619 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.619 * [backup-simplify]: Simplify 0 into 0
25.625 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
25.626 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.627 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0
25.629 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
25.629 * [backup-simplify]: Simplify 0 into 0
25.640 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
25.641 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.642 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0
25.644 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.644 * [backup-simplify]: Simplify 0 into 0
25.655 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
25.655 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.656 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0
25.658 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
25.659 * [backup-simplify]: Simplify 0 into 0
25.687 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
25.687 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.689 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0
25.692 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.692 * [backup-simplify]: Simplify 0 into 0
25.692 * [backup-simplify]: Simplify (pow (/ 1 k) 1/4) into (pow (/ 1 k) 1/4)
25.692 * [backup-simplify]: Simplify (/ 1 (sqrt (sqrt (/ 1 (- k))))) into (sqrt (/ 1 (sqrt (/ -1 k))))
25.692 * [approximate]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in (k) around 0
25.692 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
25.692 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
25.692 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
25.692 * [taylor]: Taking taylor expansion of (/ -1 k) in k
25.692 * [taylor]: Taking taylor expansion of -1 in k
25.692 * [backup-simplify]: Simplify -1 into -1
25.692 * [taylor]: Taking taylor expansion of k in k
25.692 * [backup-simplify]: Simplify 0 into 0
25.693 * [backup-simplify]: Simplify 1 into 1
25.693 * [backup-simplify]: Simplify (/ -1 1) into -1
25.693 * [backup-simplify]: Simplify (sqrt 0) into 0
25.694 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
25.694 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
25.695 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
25.695 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
25.697 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
25.698 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
25.700 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
25.700 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
25.700 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
25.700 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
25.700 * [taylor]: Taking taylor expansion of (/ -1 k) in k
25.700 * [taylor]: Taking taylor expansion of -1 in k
25.700 * [backup-simplify]: Simplify -1 into -1
25.700 * [taylor]: Taking taylor expansion of k in k
25.700 * [backup-simplify]: Simplify 0 into 0
25.700 * [backup-simplify]: Simplify 1 into 1
25.700 * [backup-simplify]: Simplify (/ -1 1) into -1
25.700 * [backup-simplify]: Simplify (sqrt 0) into 0
25.701 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
25.702 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
25.702 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
25.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
25.709 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
25.710 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
25.711 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
25.712 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
25.712 * [backup-simplify]: Simplify (/ +nan.0 (sqrt +nan.0)) into (/ +nan.0 (sqrt +nan.0))
25.713 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.715 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
25.719 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
25.725 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
25.732 * [backup-simplify]: Simplify (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) into (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
25.741 * [backup-simplify]: Simplify (+ (* (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (pow (/ 1 (- k)) 2)) (+ (* (/ +nan.0 (sqrt +nan.0)) (/ 1 (- k))) (sqrt +nan.0))) into (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))))))))
25.741 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1)
25.742 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
25.742 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
25.742 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
25.742 * [taylor]: Taking taylor expansion of 2 in n
25.742 * [backup-simplify]: Simplify 2 into 2
25.742 * [taylor]: Taking taylor expansion of (* n PI) in n
25.742 * [taylor]: Taking taylor expansion of n in n
25.742 * [backup-simplify]: Simplify 0 into 0
25.742 * [backup-simplify]: Simplify 1 into 1
25.742 * [taylor]: Taking taylor expansion of PI in n
25.742 * [backup-simplify]: Simplify PI into PI
25.742 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
25.742 * [taylor]: Taking taylor expansion of 2 in n
25.742 * [backup-simplify]: Simplify 2 into 2
25.742 * [taylor]: Taking taylor expansion of (* n PI) in n
25.742 * [taylor]: Taking taylor expansion of n in n
25.743 * [backup-simplify]: Simplify 0 into 0
25.743 * [backup-simplify]: Simplify 1 into 1
25.743 * [taylor]: Taking taylor expansion of PI in n
25.743 * [backup-simplify]: Simplify PI into PI
25.743 * [backup-simplify]: Simplify (* 0 PI) into 0
25.744 * [backup-simplify]: Simplify (* 2 0) into 0
25.744 * [backup-simplify]: Simplify 0 into 0
25.745 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
25.747 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
25.747 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.748 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
25.750 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
25.750 * [backup-simplify]: Simplify 0 into 0
25.751 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
25.751 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
25.752 * [backup-simplify]: Simplify 0 into 0
25.752 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
25.753 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
25.753 * [backup-simplify]: Simplify 0 into 0
25.754 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
25.755 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
25.755 * [backup-simplify]: Simplify 0 into 0
25.756 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
25.757 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
25.757 * [backup-simplify]: Simplify 0 into 0
25.758 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
25.759 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
25.759 * [backup-simplify]: Simplify 0 into 0
25.759 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
25.760 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
25.760 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
25.760 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
25.760 * [taylor]: Taking taylor expansion of 2 in n
25.760 * [backup-simplify]: Simplify 2 into 2
25.760 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.760 * [taylor]: Taking taylor expansion of PI in n
25.760 * [backup-simplify]: Simplify PI into PI
25.760 * [taylor]: Taking taylor expansion of n in n
25.760 * [backup-simplify]: Simplify 0 into 0
25.760 * [backup-simplify]: Simplify 1 into 1
25.760 * [backup-simplify]: Simplify (/ PI 1) into PI
25.760 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
25.760 * [taylor]: Taking taylor expansion of 2 in n
25.760 * [backup-simplify]: Simplify 2 into 2
25.760 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.760 * [taylor]: Taking taylor expansion of PI in n
25.760 * [backup-simplify]: Simplify PI into PI
25.760 * [taylor]: Taking taylor expansion of n in n
25.760 * [backup-simplify]: Simplify 0 into 0
25.760 * [backup-simplify]: Simplify 1 into 1
25.760 * [backup-simplify]: Simplify (/ PI 1) into PI
25.761 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.761 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
25.762 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
25.762 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
25.762 * [backup-simplify]: Simplify 0 into 0
25.763 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.763 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
25.763 * [backup-simplify]: Simplify 0 into 0
25.764 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.765 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
25.765 * [backup-simplify]: Simplify 0 into 0
25.765 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.766 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
25.766 * [backup-simplify]: Simplify 0 into 0
25.767 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.768 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
25.768 * [backup-simplify]: Simplify 0 into 0
25.768 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.769 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
25.769 * [backup-simplify]: Simplify 0 into 0
25.770 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
25.770 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
25.770 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
25.770 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
25.770 * [taylor]: Taking taylor expansion of -2 in n
25.770 * [backup-simplify]: Simplify -2 into -2
25.770 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.770 * [taylor]: Taking taylor expansion of PI in n
25.770 * [backup-simplify]: Simplify PI into PI
25.770 * [taylor]: Taking taylor expansion of n in n
25.770 * [backup-simplify]: Simplify 0 into 0
25.770 * [backup-simplify]: Simplify 1 into 1
25.770 * [backup-simplify]: Simplify (/ PI 1) into PI
25.770 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
25.770 * [taylor]: Taking taylor expansion of -2 in n
25.770 * [backup-simplify]: Simplify -2 into -2
25.770 * [taylor]: Taking taylor expansion of (/ PI n) in n
25.770 * [taylor]: Taking taylor expansion of PI in n
25.770 * [backup-simplify]: Simplify PI into PI
25.770 * [taylor]: Taking taylor expansion of n in n
25.770 * [backup-simplify]: Simplify 0 into 0
25.770 * [backup-simplify]: Simplify 1 into 1
25.771 * [backup-simplify]: Simplify (/ PI 1) into PI
25.771 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.771 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
25.772 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
25.772 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
25.772 * [backup-simplify]: Simplify 0 into 0
25.773 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.774 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
25.774 * [backup-simplify]: Simplify 0 into 0
25.774 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.775 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
25.775 * [backup-simplify]: Simplify 0 into 0
25.776 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.776 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
25.776 * [backup-simplify]: Simplify 0 into 0
25.777 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.778 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
25.778 * [backup-simplify]: Simplify 0 into 0
25.778 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.780 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
25.780 * [backup-simplify]: Simplify 0 into 0
25.781 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
25.781 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2)
25.781 * [backup-simplify]: Simplify (sqrt (sqrt k)) into (pow k 1/4)
25.781 * [approximate]: Taking taylor expansion of (pow k 1/4) in (k) around 0
25.781 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
25.781 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
25.781 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
25.781 * [taylor]: Taking taylor expansion of 1/4 in k
25.781 * [backup-simplify]: Simplify 1/4 into 1/4
25.781 * [taylor]: Taking taylor expansion of (log k) in k
25.781 * [taylor]: Taking taylor expansion of k in k
25.781 * [backup-simplify]: Simplify 0 into 0
25.781 * [backup-simplify]: Simplify 1 into 1
25.781 * [backup-simplify]: Simplify (log 1) into 0
25.782 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.782 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
25.782 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
25.782 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
25.782 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
25.782 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
25.782 * [taylor]: Taking taylor expansion of 1/4 in k
25.782 * [backup-simplify]: Simplify 1/4 into 1/4
25.782 * [taylor]: Taking taylor expansion of (log k) in k
25.782 * [taylor]: Taking taylor expansion of k in k
25.782 * [backup-simplify]: Simplify 0 into 0
25.782 * [backup-simplify]: Simplify 1 into 1
25.783 * [backup-simplify]: Simplify (log 1) into 0
25.783 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.783 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
25.783 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
25.783 * [backup-simplify]: Simplify (pow k 1/4) into (pow k 1/4)
25.785 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
25.785 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.786 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0
25.787 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
25.787 * [backup-simplify]: Simplify 0 into 0
25.790 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
25.790 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.791 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0
25.793 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.793 * [backup-simplify]: Simplify 0 into 0
25.797 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
25.797 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.798 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0
25.799 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
25.799 * [backup-simplify]: Simplify 0 into 0
25.805 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
25.806 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.807 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0
25.808 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.808 * [backup-simplify]: Simplify 0 into 0
25.823 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
25.823 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.825 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0
25.829 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
25.829 * [backup-simplify]: Simplify 0 into 0
25.850 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
25.851 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
25.852 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0
25.855 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.855 * [backup-simplify]: Simplify 0 into 0
25.856 * [backup-simplify]: Simplify (pow k 1/4) into (pow k 1/4)
25.856 * [backup-simplify]: Simplify (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4)
25.856 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/4) in (k) around 0
25.856 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
25.856 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
25.856 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
25.856 * [taylor]: Taking taylor expansion of 1/4 in k
25.856 * [backup-simplify]: Simplify 1/4 into 1/4
25.856 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
25.856 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.856 * [taylor]: Taking taylor expansion of k in k
25.856 * [backup-simplify]: Simplify 0 into 0
25.856 * [backup-simplify]: Simplify 1 into 1
25.856 * [backup-simplify]: Simplify (/ 1 1) into 1
25.856 * [backup-simplify]: Simplify (log 1) into 0
25.857 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.857 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
25.857 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
25.857 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
25.857 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
25.857 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
25.857 * [taylor]: Taking taylor expansion of 1/4 in k
25.857 * [backup-simplify]: Simplify 1/4 into 1/4
25.857 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
25.857 * [taylor]: Taking taylor expansion of (/ 1 k) in k
25.857 * [taylor]: Taking taylor expansion of k in k
25.857 * [backup-simplify]: Simplify 0 into 0
25.857 * [backup-simplify]: Simplify 1 into 1
25.857 * [backup-simplify]: Simplify (/ 1 1) into 1
25.857 * [backup-simplify]: Simplify (log 1) into 0
25.858 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.858 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
25.858 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
25.858 * [backup-simplify]: Simplify (pow k -1/4) into (pow k -1/4)
25.859 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
25.859 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
25.860 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.860 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0
25.860 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
25.860 * [backup-simplify]: Simplify 0 into 0
25.861 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.863 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
25.863 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.863 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0
25.864 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.864 * [backup-simplify]: Simplify 0 into 0
25.865 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.868 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
25.869 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.870 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0
25.872 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
25.872 * [backup-simplify]: Simplify 0 into 0
25.873 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.883 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
25.884 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.885 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0
25.886 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.886 * [backup-simplify]: Simplify 0 into 0
25.887 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.896 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
25.897 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.898 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0
25.900 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
25.900 * [backup-simplify]: Simplify 0 into 0
25.901 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.932 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
25.933 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
25.936 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0
25.942 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
25.942 * [backup-simplify]: Simplify 0 into 0
25.942 * [backup-simplify]: Simplify (pow (/ 1 k) -1/4) into (pow (/ 1 k) -1/4)
25.942 * [backup-simplify]: Simplify (sqrt (sqrt (/ 1 (- k)))) into (sqrt (sqrt (/ -1 k)))
25.942 * [approximate]: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in (k) around 0
25.942 * [taylor]: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in k
25.942 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
25.942 * [taylor]: Taking taylor expansion of (/ -1 k) in k
25.942 * [taylor]: Taking taylor expansion of -1 in k
25.942 * [backup-simplify]: Simplify -1 into -1
25.942 * [taylor]: Taking taylor expansion of k in k
25.942 * [backup-simplify]: Simplify 0 into 0
25.942 * [backup-simplify]: Simplify 1 into 1
25.943 * [backup-simplify]: Simplify (/ -1 1) into -1
25.943 * [backup-simplify]: Simplify (sqrt 0) into 0
25.945 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
25.945 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
25.946 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
25.949 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
25.951 * [backup-simplify]: Simplify (/ +nan.0 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
25.951 * [taylor]: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in k
25.951 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
25.951 * [taylor]: Taking taylor expansion of (/ -1 k) in k
25.951 * [taylor]: Taking taylor expansion of -1 in k
25.951 * [backup-simplify]: Simplify -1 into -1
25.951 * [taylor]: Taking taylor expansion of k in k
25.951 * [backup-simplify]: Simplify 0 into 0
25.951 * [backup-simplify]: Simplify 1 into 1
25.952 * [backup-simplify]: Simplify (/ -1 1) into -1
25.952 * [backup-simplify]: Simplify (sqrt 0) into 0
25.953 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
25.954 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
25.955 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
25.958 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
25.959 * [backup-simplify]: Simplify (/ +nan.0 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
25.960 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
25.961 * [backup-simplify]: Simplify (/ +nan.0 (sqrt +nan.0)) into (/ +nan.0 (sqrt +nan.0))
25.962 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
25.966 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
25.971 * [backup-simplify]: Simplify (/ (- +nan.0 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
25.978 * [backup-simplify]: Simplify (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) into (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
25.987 * [backup-simplify]: Simplify (+ (* (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (pow (/ 1 (- k)) 2)) (+ (* (/ +nan.0 (sqrt +nan.0)) (/ 1 (- k))) (sqrt +nan.0))) into (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))))))))
25.987 * * * [progress]: simplifying candidates
25.987 * * * * [progress]: [ 1 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
25.987 * * * * [progress]: [ 2 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
25.987 * * * * [progress]: [ 3 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
25.987 * * * * [progress]: [ 4 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
25.987 * * * * [progress]: [ 5 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
25.987 * * * * [progress]: [ 6 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
25.987 * * * * [progress]: [ 7 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
25.987 * * * * [progress]: [ 8 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2))) (sqrt (sqrt k)))))>
25.987 * * * * [progress]: [ 9 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 10 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 11 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 12 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 13 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 14 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 15 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 16 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 17 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 18 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 19 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 20 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 21 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 22 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 23 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 24 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 25 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 26 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 27 / 137 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt (sqrt k)) -1) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 28 / 137 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) (- 1/2)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 29 / 137 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt (sqrt k)) (- 1)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 30 / 137 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- (/ 1/2 2))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 31 / 137 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) (- (/ 1 2))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 32 / 137 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- (/ (/ 1 2) 2))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 33 / 137 ] simplifiying candidate #<alt (λ (k n) (* (pow (/ 1 (sqrt (sqrt k))) 1) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.988 * * * * [progress]: [ 34 / 137 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 35 / 137 ] simplifiying candidate #<alt (λ (k n) (* (exp (- 0 (log (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 36 / 137 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log 1) (log (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 37 / 137 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 38 / 137 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 39 / 137 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (/ (* (* 1 1) 1) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 40 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (cbrt (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 41 / 137 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 42 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 43 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ (- 1) (- (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 44 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt 1) (cbrt (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 45 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1) (sqrt (cbrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 46 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1) (sqrt (sqrt (cbrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 47 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1) (sqrt (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 48 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt 1))) (/ (cbrt 1) (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 49 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1) (sqrt (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 50 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 51 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1) (sqrt (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 52 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 53 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt 1) (cbrt (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 54 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt 1) (sqrt (cbrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 55 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1) (sqrt (sqrt (cbrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 56 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1) (sqrt (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.989 * * * * [progress]: [ 57 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt 1))) (/ (sqrt 1) (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 58 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1) (sqrt (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 59 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 60 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1) (sqrt (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 61 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 62 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1 (cbrt (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 63 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1 (sqrt (cbrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 64 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ 1 (sqrt (sqrt (cbrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 65 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 66 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt 1))) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 67 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 68 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt 1)) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 69 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 70 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 1) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 71 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 72 / 137 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 73 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 74 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 75 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 76 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (cbrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 77 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 78 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 79 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 80 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt 1)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 81 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.990 * * * * [progress]: [ 82 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 1) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 83 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (cbrt 1))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 84 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt 1))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 85 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 86 / 137 ] simplifiying candidate #<alt (λ (k n) (* (posit16->real (real->posit16 (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 87 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 88 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 89 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 90 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 91 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 92 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 93 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 94 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 95 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 96 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 97 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 98 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 99 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 100 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 101 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 102 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 103 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 104 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 105 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.991 * * * * [progress]: [ 106 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (sqrt k) 1/2))))>
25.991 * * * * [progress]: [ 107 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (sqrt (sqrt k)) 1))))>
25.992 * * * * [progress]: [ 108 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (exp (log (sqrt (sqrt k)))))))>
25.992 * * * * [progress]: [ 109 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (log (exp (sqrt (sqrt k)))))))>
25.992 * * * * [progress]: [ 110 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))))))>
25.992 * * * * [progress]: [ 111 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (cbrt (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))))))>
25.992 * * * * [progress]: [ 112 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k)))))))>
25.992 * * * * [progress]: [ 113 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (sqrt (sqrt (* (cbrt k) (cbrt k)))) (sqrt (sqrt (cbrt k)))))))>
25.992 * * * * [progress]: [ 114 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))))))>
25.992 * * * * [progress]: [ 115 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (sqrt (sqrt 1)) (sqrt (sqrt k))))))>
25.992 * * * * [progress]: [ 116 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))))))>
25.992 * * * * [progress]: [ 117 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (sqrt 1) (sqrt (sqrt k))))))>
25.992 * * * * [progress]: [ 118 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow k (/ 1/2 2)))))>
25.992 * * * * [progress]: [ 119 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (sqrt k) (/ 1 2)))))>
25.992 * * * * [progress]: [ 120 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow k (/ (/ 1 2) 2)))))>
25.992 * * * * [progress]: [ 121 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))))))>
25.992 * * * * [progress]: [ 122 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (fabs (sqrt (sqrt k))))))>
25.992 * * * * [progress]: [ 123 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (fabs (sqrt (sqrt k))))))>
25.992 * * * * [progress]: [ 124 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* 1 (sqrt (sqrt k))))))>
25.992 * * * * [progress]: [ 125 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (posit16->real (real->posit16 (sqrt (sqrt k)))))))>
25.992 * * * * [progress]: [ 126 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (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))))) (sqrt (sqrt k)))))>
25.992 * * * * [progress]: [ 127 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt (sqrt k)))))>
25.992 * * * * [progress]: [ 128 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt (sqrt k)))))>
25.992 * * * * [progress]: [ 129 / 137 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/4) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.992 * * * * [progress]: [ 130 / 137 ] simplifiying candidate #<alt (λ (k n) (* (pow (/ 1 k) 1/4) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.992 * * * * [progress]: [ 131 / 137 ] simplifiying candidate #<alt (λ (k n) (* (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))))))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.993 * * * * [progress]: [ 132 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.993 * * * * [progress]: [ 133 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.993 * * * * [progress]: [ 134 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
25.993 * * * * [progress]: [ 135 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow k 1/4))))>
25.993 * * * * [progress]: [ 136 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (/ 1 k) -1/4))))>
25.993 * * * * [progress]: [ 137 / 137 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))))))))))>
25.994 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (- 1/2)
  (- 1)
  (- (/ 1/2 2))
  (- (/ 1 2))
  (- (/ (/ 1 2) 2))
  (- (log (sqrt (sqrt k))))
  (- 0 (log (sqrt (sqrt k))))
  (- (log 1) (log (sqrt (sqrt k))))
  (log (/ 1 (sqrt (sqrt k))))
  (exp (/ 1 (sqrt (sqrt k))))
  (/ (* (* 1 1) 1) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k)))))
  (cbrt (/ 1 (sqrt (sqrt k))))
  (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))))
  (sqrt (/ 1 (sqrt (sqrt k))))
  (sqrt (/ 1 (sqrt (sqrt k))))
  (- 1)
  (- (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt 1) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (cbrt 1) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (cbrt 1) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt 1)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) 1)
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt 1) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (sqrt 1) (sqrt (cbrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (sqrt 1) (sqrt (sqrt (cbrt k))))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt 1)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt 1))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) 1)
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (cbrt (sqrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) 1)
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ (sqrt (sqrt k)) (cbrt 1))
  (/ (sqrt (sqrt k)) (sqrt 1))
  (/ (sqrt (sqrt k)) 1)
  (real->posit16 (/ 1 (sqrt (sqrt k))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (log (sqrt (sqrt k)))
  (exp (sqrt (sqrt k)))
  (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (cbrt (sqrt (sqrt k)))
  (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))
  (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (sqrt (cbrt (sqrt k)))
  (sqrt (sqrt (* (cbrt k) (cbrt k))))
  (sqrt (sqrt (cbrt k)))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt 1))
  (sqrt (sqrt k))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  (sqrt 1)
  (sqrt (sqrt k))
  (/ 1/2 2)
  (/ 1 2)
  (/ (/ 1 2) 2)
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  (real->posit16 (sqrt (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)))))
  (pow k -1/4)
  (pow (/ 1 k) 1/4)
  (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (pow k 1/4)
  (pow (/ 1 k) -1/4)
  (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))))))))
25.996 * * [simplify]: iteration 1: (232 enodes)
26.069 * * [simplify]: iteration 2: (535 enodes)
26.580 * * [simplify]: iteration 3: (1525 enodes)
28.831 * * [simplify]: Extracting #0: cost 71 inf + 0
28.833 * * [simplify]: Extracting #1: cost 428 inf + 6
28.843 * * [simplify]: Extracting #2: cost 915 inf + 19498
28.878 * * [simplify]: Extracting #3: cost 931 inf + 98098
28.927 * * [simplify]: Extracting #4: cost 392 inf + 264827
29.017 * * [simplify]: Extracting #5: cost 74 inf + 382182
29.160 * * [simplify]: Extracting #6: cost 3 inf + 415898
29.298 * * [simplify]: Extracting #7: cost 0 inf + 416970
29.425 * [simplify]: Simplified to:
  (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))
  (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))
  (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))
  (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (/ k 2))
  (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2))))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* PI (* n 2)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* PI (* n 2))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (- (/ k 2)))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))
  (exp (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (pow (* PI (* n 2)) (- 1/4 (/ k 4)))
  (pow (* PI (* n 2)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  -1/2
  -1
  -1/4
  -1/2
  -1/4
  (- (log (sqrt (sqrt k))))
  (- (log (sqrt (sqrt k))))
  (- (log (sqrt (sqrt k))))
  (- (log (sqrt (sqrt k))))
  (exp (/ 1 (sqrt (sqrt k))))
  (/ (/ 1 (sqrt k)) (sqrt (sqrt k)))
  (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k)))))
  (cbrt (/ 1 (sqrt (sqrt k))))
  (/ (/ 1 (sqrt k)) (sqrt (sqrt k)))
  (sqrt (/ 1 (sqrt (sqrt k))))
  (sqrt (/ 1 (sqrt (sqrt k))))
  -1
  (- (sqrt (sqrt k)))
  (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ 1 (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ 1 (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ 1 (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (sqrt (sqrt k))
  (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (sqrt (sqrt k))
  (sqrt (sqrt k))
  (sqrt (sqrt k))
  (real->posit16 (/ 1 (sqrt (sqrt k))))
  (* PI (* n 2))
  (* PI (* n 2))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* PI (* n 2)) (* PI (* n 2))) (* PI (* n 2)))
  (* (* (* PI (* n 2)) (* PI (* n 2))) (* PI (* n 2)))
  (* (cbrt (* PI (* n 2))) (cbrt (* PI (* n 2))))
  (cbrt (* PI (* n 2)))
  (* (* (* PI (* n 2)) (* PI (* n 2))) (* PI (* n 2)))
  (sqrt (* PI (* n 2)))
  (sqrt (* PI (* n 2)))
  (* n 2)
  (* PI (* 2 (cbrt n)))
  (* (sqrt n) (* PI 2))
  (* PI (* n 2))
  (real->posit16 (* PI (* n 2)))
  (log (sqrt (sqrt k)))
  (exp (sqrt (sqrt k)))
  (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (cbrt (sqrt (sqrt k)))
  (* (sqrt k) (sqrt (sqrt k)))
  (fabs (cbrt (sqrt k)))
  (sqrt (cbrt (sqrt k)))
  (sqrt (fabs (cbrt k)))
  (sqrt (sqrt (cbrt k)))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  1
  (sqrt (sqrt k))
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  1
  (sqrt (sqrt k))
  1/4
  1/2
  1/4
  (sqrt (sqrt (sqrt k)))
  (sqrt (sqrt (sqrt k)))
  (real->posit16 (sqrt (sqrt k)))
  (+ (+ (+ (* (* 1/8 (* (* (log (* PI 2)) k) (* (log (* PI 2)) k))) (sqrt (* PI (* n 2)))) (sqrt (* PI (* n 2)))) (* (* k k) (+ (* (* (log n) (* (log n) (sqrt (* PI (* n 2))))) 1/8) (* (* (* (log (* PI 2)) 1/4) (log n)) (sqrt (* PI (* n 2))))))) (* (* k -1/2) (* (sqrt (* PI (* n 2))) (+ (log n) (log (* PI 2))))))
  (exp (* (log (* PI (* n 2))) (- 1/2 (* k 1/2))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))
  (pow k -1/4)
  (pow (/ 1 k) 1/4)
  (+ (- (sqrt +nan.0) (+ (/ (/ +nan.0 k) (sqrt +nan.0)) (/ +nan.0 (* (* k k) (sqrt +nan.0))))) (/ (/ +nan.0 (* (* k k) +nan.0)) (sqrt +nan.0)))
  (* PI (* n 2))
  (* PI (* n 2))
  (* PI (* n 2))
  (pow k 1/4)
  (pow (/ 1 k) -1/4)
  (+ (- (sqrt +nan.0) (+ (/ (/ +nan.0 k) (sqrt +nan.0)) (/ +nan.0 (* (* k k) (sqrt +nan.0))))) (/ (/ +nan.0 (* (* k k) +nan.0)) (sqrt +nan.0)))
29.437 * * * [progress]: adding candidates to table
31.335 * [progress]: [Phase 3 of 3] Extracting.
31.335 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))> #<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)))))> #<alt (λ (k n) (/ (/ (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))> #<alt (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))))> #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>)
31.336 * * * [regime-changes]: Trying 2 branch expressions: (n k)
31.336 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))> #<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)))))> #<alt (λ (k n) (/ (/ (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))> #<alt (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))))> #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>)
31.392 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))> #<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)))))> #<alt (λ (k n) (/ (/ (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))> #<alt (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))))> #<alt (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>)
31.481 * * * [regime]: Found split indices: #<option (#s(si 6 255))>
31.481 * [simplify]: Simplifying:
  (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))
31.481 * * [simplify]: iteration 1: (16 enodes)
31.484 * * [simplify]: iteration 2: (21 enodes)
31.486 * * [simplify]: Extracting #0: cost 1 inf + 0
31.486 * * [simplify]: Extracting #1: cost 3 inf + 0
31.486 * * [simplify]: Extracting #2: cost 4 inf + 1
31.486 * * [simplify]: Extracting #3: cost 6 inf + 1
31.486 * * [simplify]: Extracting #4: cost 9 inf + 1
31.486 * * [simplify]: Extracting #5: cost 10 inf + 124
31.486 * * [simplify]: Extracting #6: cost 10 inf + 126
31.486 * * [simplify]: Extracting #7: cost 7 inf + 170
31.486 * * [simplify]: Extracting #8: cost 4 inf + 378
31.487 * * [simplify]: Extracting #9: cost 2 inf + 1248
31.487 * * [simplify]: Extracting #10: cost 0 inf + 2359
31.488 * [simplify]: Simplified to:
  (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))))
39.391 * [regime-testing]: Baseline error score: 0.5094319780039045
39.395 * [regime-testing]: Oracle error score: 0.046910149875915345
39.404 * [regime-testing]: End program error score: 0.5094319780039045