33.235 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.249 * * * [progress]: [2/2] Setting up program.
0.252 * [progress]: [Phase 2 of 3] Improving.
0.253 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.253 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.253 * * [simplify]: iteration 1: (13 enodes)
0.256 * * [simplify]: iteration 2: (29 enodes)
0.262 * * [simplify]: iteration 3: (60 enodes)
0.275 * * [simplify]: iteration 4: (123 enodes)
0.377 * * [simplify]: iteration 5: (322 enodes)
0.592 * * [simplify]: iteration 6: (817 enodes)
1.824 * * [simplify]: Extracting #0: cost 1 inf + 0
1.824 * * [simplify]: Extracting #1: cost 58 inf + 0
1.826 * * [simplify]: Extracting #2: cost 198 inf + 1
1.832 * * [simplify]: Extracting #3: cost 265 inf + 46
1.835 * * [simplify]: Extracting #4: cost 245 inf + 1713
1.842 * * [simplify]: Extracting #5: cost 180 inf + 14173
1.881 * * [simplify]: Extracting #6: cost 61 inf + 110645
1.952 * * [simplify]: Extracting #7: cost 0 inf + 167860
2.024 * * [simplify]: Extracting #8: cost 0 inf + 164570
2.073 * [simplify]: Simplified to:
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
2.085 * * [progress]: iteration 1 / 4
2.085 * * * [progress]: picking best candidate
2.090 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.090 * * * [progress]: localizing error
2.112 * * * [progress]: generating rewritten candidates
2.112 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
2.142 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
2.164 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
2.187 * * * [progress]: generating series expansions
2.187 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
2.188 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
2.188 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
2.188 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
2.188 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
2.188 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
2.188 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.188 * [taylor]: Taking taylor expansion of 1/2 in k
2.188 * [backup-simplify]: Simplify 1/2 into 1/2
2.188 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.188 * [taylor]: Taking taylor expansion of 1/2 in k
2.188 * [backup-simplify]: Simplify 1/2 into 1/2
2.188 * [taylor]: Taking taylor expansion of k in k
2.188 * [backup-simplify]: Simplify 0 into 0
2.188 * [backup-simplify]: Simplify 1 into 1
2.188 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
2.188 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
2.188 * [taylor]: Taking taylor expansion of 2 in k
2.188 * [backup-simplify]: Simplify 2 into 2
2.188 * [taylor]: Taking taylor expansion of (* n PI) in k
2.188 * [taylor]: Taking taylor expansion of n in k
2.188 * [backup-simplify]: Simplify n into n
2.188 * [taylor]: Taking taylor expansion of PI in k
2.189 * [backup-simplify]: Simplify PI into PI
2.189 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.189 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
2.189 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
2.189 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.190 * [backup-simplify]: Simplify (- 0) into 0
2.190 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.190 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
2.190 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
2.190 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.191 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.191 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.191 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.191 * [taylor]: Taking taylor expansion of 1/2 in n
2.191 * [backup-simplify]: Simplify 1/2 into 1/2
2.191 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.191 * [taylor]: Taking taylor expansion of 1/2 in n
2.191 * [backup-simplify]: Simplify 1/2 into 1/2
2.191 * [taylor]: Taking taylor expansion of k in n
2.191 * [backup-simplify]: Simplify k into k
2.191 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.191 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.191 * [taylor]: Taking taylor expansion of 2 in n
2.191 * [backup-simplify]: Simplify 2 into 2
2.191 * [taylor]: Taking taylor expansion of (* n PI) in n
2.191 * [taylor]: Taking taylor expansion of n in n
2.191 * [backup-simplify]: Simplify 0 into 0
2.191 * [backup-simplify]: Simplify 1 into 1
2.191 * [taylor]: Taking taylor expansion of PI in n
2.191 * [backup-simplify]: Simplify PI into PI
2.192 * [backup-simplify]: Simplify (* 0 PI) into 0
2.192 * [backup-simplify]: Simplify (* 2 0) into 0
2.194 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.196 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.197 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.197 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.197 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.197 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.199 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.200 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.201 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
2.201 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.201 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.201 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.201 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.201 * [taylor]: Taking taylor expansion of 1/2 in n
2.201 * [backup-simplify]: Simplify 1/2 into 1/2
2.201 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.201 * [taylor]: Taking taylor expansion of 1/2 in n
2.201 * [backup-simplify]: Simplify 1/2 into 1/2
2.201 * [taylor]: Taking taylor expansion of k in n
2.202 * [backup-simplify]: Simplify k into k
2.202 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.202 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.202 * [taylor]: Taking taylor expansion of 2 in n
2.202 * [backup-simplify]: Simplify 2 into 2
2.202 * [taylor]: Taking taylor expansion of (* n PI) in n
2.202 * [taylor]: Taking taylor expansion of n in n
2.202 * [backup-simplify]: Simplify 0 into 0
2.202 * [backup-simplify]: Simplify 1 into 1
2.202 * [taylor]: Taking taylor expansion of PI in n
2.202 * [backup-simplify]: Simplify PI into PI
2.202 * [backup-simplify]: Simplify (* 0 PI) into 0
2.203 * [backup-simplify]: Simplify (* 2 0) into 0
2.204 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.206 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.207 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.207 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.207 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.207 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.209 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.210 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.211 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
2.211 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
2.211 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
2.211 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.212 * [taylor]: Taking taylor expansion of 1/2 in k
2.212 * [backup-simplify]: Simplify 1/2 into 1/2
2.212 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.212 * [taylor]: Taking taylor expansion of 1/2 in k
2.212 * [backup-simplify]: Simplify 1/2 into 1/2
2.212 * [taylor]: Taking taylor expansion of k in k
2.212 * [backup-simplify]: Simplify 0 into 0
2.212 * [backup-simplify]: Simplify 1 into 1
2.212 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
2.212 * [taylor]: Taking taylor expansion of (log n) in k
2.212 * [taylor]: Taking taylor expansion of n in k
2.212 * [backup-simplify]: Simplify n into n
2.212 * [backup-simplify]: Simplify (log n) into (log n)
2.212 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.212 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.212 * [taylor]: Taking taylor expansion of 2 in k
2.212 * [backup-simplify]: Simplify 2 into 2
2.212 * [taylor]: Taking taylor expansion of PI in k
2.212 * [backup-simplify]: Simplify PI into PI
2.212 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.214 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.214 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.214 * [backup-simplify]: Simplify (- 0) into 0
2.215 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.216 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.217 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
2.218 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
2.219 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
2.220 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.221 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.224 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.224 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
2.225 * [backup-simplify]: Simplify (- 0) into 0
2.225 * [backup-simplify]: Simplify (+ 0 0) into 0
2.227 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.228 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
2.230 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.230 * [taylor]: Taking taylor expansion of 0 in k
2.230 * [backup-simplify]: Simplify 0 into 0
2.230 * [backup-simplify]: Simplify 0 into 0
2.231 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
2.232 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.233 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.234 * [backup-simplify]: Simplify (+ 0 0) into 0
2.235 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
2.235 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.235 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.237 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
2.241 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.244 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.245 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.250 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.254 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.255 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
2.255 * [backup-simplify]: Simplify (- 0) into 0
2.256 * [backup-simplify]: Simplify (+ 0 0) into 0
2.257 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.259 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.261 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.262 * [taylor]: Taking taylor expansion of 0 in k
2.262 * [backup-simplify]: Simplify 0 into 0
2.262 * [backup-simplify]: Simplify 0 into 0
2.262 * [backup-simplify]: Simplify 0 into 0
2.263 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
2.264 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.268 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.268 * [backup-simplify]: Simplify (+ 0 0) into 0
2.269 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
2.270 * [backup-simplify]: Simplify (- 0) into 0
2.270 * [backup-simplify]: Simplify (+ 0 0) into 0
2.272 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.276 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
2.281 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
2.291 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
2.292 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
2.292 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
2.292 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
2.292 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
2.292 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
2.292 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.292 * [taylor]: Taking taylor expansion of 1/2 in k
2.293 * [backup-simplify]: Simplify 1/2 into 1/2
2.293 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.293 * [taylor]: Taking taylor expansion of 1/2 in k
2.293 * [backup-simplify]: Simplify 1/2 into 1/2
2.293 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.293 * [taylor]: Taking taylor expansion of k in k
2.293 * [backup-simplify]: Simplify 0 into 0
2.293 * [backup-simplify]: Simplify 1 into 1
2.293 * [backup-simplify]: Simplify (/ 1 1) into 1
2.293 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
2.293 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
2.293 * [taylor]: Taking taylor expansion of 2 in k
2.293 * [backup-simplify]: Simplify 2 into 2
2.293 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.293 * [taylor]: Taking taylor expansion of PI in k
2.293 * [backup-simplify]: Simplify PI into PI
2.293 * [taylor]: Taking taylor expansion of n in k
2.293 * [backup-simplify]: Simplify n into n
2.293 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.293 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
2.293 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
2.294 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.294 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.295 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.295 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
2.295 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
2.295 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.295 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.295 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.295 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.295 * [taylor]: Taking taylor expansion of 1/2 in n
2.295 * [backup-simplify]: Simplify 1/2 into 1/2
2.295 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.295 * [taylor]: Taking taylor expansion of 1/2 in n
2.295 * [backup-simplify]: Simplify 1/2 into 1/2
2.295 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.295 * [taylor]: Taking taylor expansion of k in n
2.295 * [backup-simplify]: Simplify k into k
2.295 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.295 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.296 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.296 * [taylor]: Taking taylor expansion of 2 in n
2.296 * [backup-simplify]: Simplify 2 into 2
2.296 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.296 * [taylor]: Taking taylor expansion of PI in n
2.296 * [backup-simplify]: Simplify PI into PI
2.296 * [taylor]: Taking taylor expansion of n in n
2.296 * [backup-simplify]: Simplify 0 into 0
2.296 * [backup-simplify]: Simplify 1 into 1
2.296 * [backup-simplify]: Simplify (/ PI 1) into PI
2.297 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.298 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.298 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.298 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.298 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.300 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.301 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
2.302 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.302 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.302 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.302 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.303 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.303 * [taylor]: Taking taylor expansion of 1/2 in n
2.303 * [backup-simplify]: Simplify 1/2 into 1/2
2.303 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.303 * [taylor]: Taking taylor expansion of 1/2 in n
2.303 * [backup-simplify]: Simplify 1/2 into 1/2
2.303 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.303 * [taylor]: Taking taylor expansion of k in n
2.303 * [backup-simplify]: Simplify k into k
2.303 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.303 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.303 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.303 * [taylor]: Taking taylor expansion of 2 in n
2.303 * [backup-simplify]: Simplify 2 into 2
2.303 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.303 * [taylor]: Taking taylor expansion of PI in n
2.303 * [backup-simplify]: Simplify PI into PI
2.303 * [taylor]: Taking taylor expansion of n in n
2.303 * [backup-simplify]: Simplify 0 into 0
2.303 * [backup-simplify]: Simplify 1 into 1
2.304 * [backup-simplify]: Simplify (/ PI 1) into PI
2.304 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.305 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.305 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.305 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.305 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.308 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
2.309 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.309 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
2.309 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
2.310 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.310 * [taylor]: Taking taylor expansion of 1/2 in k
2.310 * [backup-simplify]: Simplify 1/2 into 1/2
2.310 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.310 * [taylor]: Taking taylor expansion of 1/2 in k
2.310 * [backup-simplify]: Simplify 1/2 into 1/2
2.310 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.310 * [taylor]: Taking taylor expansion of k in k
2.310 * [backup-simplify]: Simplify 0 into 0
2.310 * [backup-simplify]: Simplify 1 into 1
2.310 * [backup-simplify]: Simplify (/ 1 1) into 1
2.310 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
2.310 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.310 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.310 * [taylor]: Taking taylor expansion of 2 in k
2.310 * [backup-simplify]: Simplify 2 into 2
2.310 * [taylor]: Taking taylor expansion of PI in k
2.310 * [backup-simplify]: Simplify PI into PI
2.311 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.312 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.312 * [taylor]: Taking taylor expansion of (log n) in k
2.312 * [taylor]: Taking taylor expansion of n in k
2.312 * [backup-simplify]: Simplify n into n
2.312 * [backup-simplify]: Simplify (log n) into (log n)
2.313 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.313 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.314 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.314 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.315 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
2.316 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
2.318 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.319 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.320 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.321 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.323 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.324 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.325 * [backup-simplify]: Simplify (- 0) into 0
2.325 * [backup-simplify]: Simplify (+ 0 0) into 0
2.327 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.328 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
2.330 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.330 * [taylor]: Taking taylor expansion of 0 in k
2.330 * [backup-simplify]: Simplify 0 into 0
2.330 * [backup-simplify]: Simplify 0 into 0
2.330 * [backup-simplify]: Simplify 0 into 0
2.331 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.332 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.336 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.336 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.337 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.337 * [backup-simplify]: Simplify (- 0) into 0
2.338 * [backup-simplify]: Simplify (+ 0 0) into 0
2.339 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.341 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
2.343 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.344 * [taylor]: Taking taylor expansion of 0 in k
2.344 * [backup-simplify]: Simplify 0 into 0
2.344 * [backup-simplify]: Simplify 0 into 0
2.344 * [backup-simplify]: Simplify 0 into 0
2.344 * [backup-simplify]: Simplify 0 into 0
2.345 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.346 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.352 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.352 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.353 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
2.354 * [backup-simplify]: Simplify (- 0) into 0
2.354 * [backup-simplify]: Simplify (+ 0 0) into 0
2.356 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.357 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
2.360 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.360 * [taylor]: Taking taylor expansion of 0 in k
2.360 * [backup-simplify]: Simplify 0 into 0
2.360 * [backup-simplify]: Simplify 0 into 0
2.362 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
2.362 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
2.362 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
2.362 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
2.362 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
2.362 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
2.362 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.363 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.363 * [taylor]: Taking taylor expansion of 1/2 in k
2.363 * [backup-simplify]: Simplify 1/2 into 1/2
2.363 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.363 * [taylor]: Taking taylor expansion of k in k
2.363 * [backup-simplify]: Simplify 0 into 0
2.363 * [backup-simplify]: Simplify 1 into 1
2.363 * [backup-simplify]: Simplify (/ 1 1) into 1
2.363 * [taylor]: Taking taylor expansion of 1/2 in k
2.363 * [backup-simplify]: Simplify 1/2 into 1/2
2.363 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
2.363 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
2.363 * [taylor]: Taking taylor expansion of -2 in k
2.363 * [backup-simplify]: Simplify -2 into -2
2.363 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.363 * [taylor]: Taking taylor expansion of PI in k
2.363 * [backup-simplify]: Simplify PI into PI
2.363 * [taylor]: Taking taylor expansion of n in k
2.363 * [backup-simplify]: Simplify n into n
2.363 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.364 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
2.364 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
2.364 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.364 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.365 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
2.365 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
2.365 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.365 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.365 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.365 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.365 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.365 * [taylor]: Taking taylor expansion of 1/2 in n
2.365 * [backup-simplify]: Simplify 1/2 into 1/2
2.365 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.365 * [taylor]: Taking taylor expansion of k in n
2.365 * [backup-simplify]: Simplify k into k
2.365 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.365 * [taylor]: Taking taylor expansion of 1/2 in n
2.365 * [backup-simplify]: Simplify 1/2 into 1/2
2.365 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.366 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.366 * [taylor]: Taking taylor expansion of -2 in n
2.366 * [backup-simplify]: Simplify -2 into -2
2.366 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.366 * [taylor]: Taking taylor expansion of PI in n
2.366 * [backup-simplify]: Simplify PI into PI
2.366 * [taylor]: Taking taylor expansion of n in n
2.366 * [backup-simplify]: Simplify 0 into 0
2.366 * [backup-simplify]: Simplify 1 into 1
2.366 * [backup-simplify]: Simplify (/ PI 1) into PI
2.367 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.368 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.368 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.368 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.369 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.371 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
2.372 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.372 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.372 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.372 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.372 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.372 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.372 * [taylor]: Taking taylor expansion of 1/2 in n
2.372 * [backup-simplify]: Simplify 1/2 into 1/2
2.372 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.372 * [taylor]: Taking taylor expansion of k in n
2.372 * [backup-simplify]: Simplify k into k
2.372 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.372 * [taylor]: Taking taylor expansion of 1/2 in n
2.372 * [backup-simplify]: Simplify 1/2 into 1/2
2.372 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.372 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.372 * [taylor]: Taking taylor expansion of -2 in n
2.372 * [backup-simplify]: Simplify -2 into -2
2.372 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.372 * [taylor]: Taking taylor expansion of PI in n
2.372 * [backup-simplify]: Simplify PI into PI
2.372 * [taylor]: Taking taylor expansion of n in n
2.373 * [backup-simplify]: Simplify 0 into 0
2.373 * [backup-simplify]: Simplify 1 into 1
2.373 * [backup-simplify]: Simplify (/ PI 1) into PI
2.374 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.375 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.375 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.375 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.376 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.377 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
2.379 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.379 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
2.379 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
2.379 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.379 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.379 * [taylor]: Taking taylor expansion of 1/2 in k
2.379 * [backup-simplify]: Simplify 1/2 into 1/2
2.379 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.379 * [taylor]: Taking taylor expansion of k in k
2.379 * [backup-simplify]: Simplify 0 into 0
2.379 * [backup-simplify]: Simplify 1 into 1
2.379 * [backup-simplify]: Simplify (/ 1 1) into 1
2.379 * [taylor]: Taking taylor expansion of 1/2 in k
2.379 * [backup-simplify]: Simplify 1/2 into 1/2
2.379 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
2.379 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
2.380 * [taylor]: Taking taylor expansion of (* -2 PI) in k
2.380 * [taylor]: Taking taylor expansion of -2 in k
2.380 * [backup-simplify]: Simplify -2 into -2
2.380 * [taylor]: Taking taylor expansion of PI in k
2.380 * [backup-simplify]: Simplify PI into PI
2.380 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.381 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.381 * [taylor]: Taking taylor expansion of (log n) in k
2.381 * [taylor]: Taking taylor expansion of n in k
2.381 * [backup-simplify]: Simplify n into n
2.381 * [backup-simplify]: Simplify (log n) into (log n)
2.381 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.381 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.381 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.382 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
2.383 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
2.384 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.384 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.385 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.385 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.386 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
2.386 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.387 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.387 * [backup-simplify]: Simplify (+ 0 0) into 0
2.388 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.389 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
2.392 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.392 * [taylor]: Taking taylor expansion of 0 in k
2.392 * [backup-simplify]: Simplify 0 into 0
2.392 * [backup-simplify]: Simplify 0 into 0
2.392 * [backup-simplify]: Simplify 0 into 0
2.393 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.394 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.396 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
2.396 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.397 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.397 * [backup-simplify]: Simplify (+ 0 0) into 0
2.398 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.399 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
2.400 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.400 * [taylor]: Taking taylor expansion of 0 in k
2.400 * [backup-simplify]: Simplify 0 into 0
2.400 * [backup-simplify]: Simplify 0 into 0
2.400 * [backup-simplify]: Simplify 0 into 0
2.400 * [backup-simplify]: Simplify 0 into 0
2.401 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.402 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.405 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
2.405 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.406 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
2.406 * [backup-simplify]: Simplify (+ 0 0) into 0
2.407 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.408 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
2.410 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.410 * [taylor]: Taking taylor expansion of 0 in k
2.410 * [backup-simplify]: Simplify 0 into 0
2.410 * [backup-simplify]: Simplify 0 into 0
2.411 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
2.411 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
2.411 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
2.411 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
2.411 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.411 * [taylor]: Taking taylor expansion of 2 in n
2.411 * [backup-simplify]: Simplify 2 into 2
2.411 * [taylor]: Taking taylor expansion of (* n PI) in n
2.411 * [taylor]: Taking taylor expansion of n in n
2.411 * [backup-simplify]: Simplify 0 into 0
2.412 * [backup-simplify]: Simplify 1 into 1
2.412 * [taylor]: Taking taylor expansion of PI in n
2.412 * [backup-simplify]: Simplify PI into PI
2.412 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.412 * [taylor]: Taking taylor expansion of 2 in n
2.412 * [backup-simplify]: Simplify 2 into 2
2.412 * [taylor]: Taking taylor expansion of (* n PI) in n
2.412 * [taylor]: Taking taylor expansion of n in n
2.412 * [backup-simplify]: Simplify 0 into 0
2.412 * [backup-simplify]: Simplify 1 into 1
2.412 * [taylor]: Taking taylor expansion of PI in n
2.412 * [backup-simplify]: Simplify PI into PI
2.412 * [backup-simplify]: Simplify (* 0 PI) into 0
2.412 * [backup-simplify]: Simplify (* 2 0) into 0
2.412 * [backup-simplify]: Simplify 0 into 0
2.413 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.414 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.415 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.415 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.416 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.416 * [backup-simplify]: Simplify 0 into 0
2.417 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.418 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.418 * [backup-simplify]: Simplify 0 into 0
2.419 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.421 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.421 * [backup-simplify]: Simplify 0 into 0
2.422 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.424 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
2.424 * [backup-simplify]: Simplify 0 into 0
2.425 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.426 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
2.426 * [backup-simplify]: Simplify 0 into 0
2.427 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
2.428 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
2.428 * [backup-simplify]: Simplify 0 into 0
2.428 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
2.429 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
2.429 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
2.429 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.429 * [taylor]: Taking taylor expansion of 2 in n
2.429 * [backup-simplify]: Simplify 2 into 2
2.429 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.429 * [taylor]: Taking taylor expansion of PI in n
2.429 * [backup-simplify]: Simplify PI into PI
2.429 * [taylor]: Taking taylor expansion of n in n
2.429 * [backup-simplify]: Simplify 0 into 0
2.429 * [backup-simplify]: Simplify 1 into 1
2.429 * [backup-simplify]: Simplify (/ PI 1) into PI
2.429 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.429 * [taylor]: Taking taylor expansion of 2 in n
2.429 * [backup-simplify]: Simplify 2 into 2
2.429 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.429 * [taylor]: Taking taylor expansion of PI in n
2.429 * [backup-simplify]: Simplify PI into PI
2.429 * [taylor]: Taking taylor expansion of n in n
2.429 * [backup-simplify]: Simplify 0 into 0
2.429 * [backup-simplify]: Simplify 1 into 1
2.430 * [backup-simplify]: Simplify (/ PI 1) into PI
2.430 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.430 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.431 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.432 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.432 * [backup-simplify]: Simplify 0 into 0
2.432 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.433 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.433 * [backup-simplify]: Simplify 0 into 0
2.434 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.435 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.435 * [backup-simplify]: Simplify 0 into 0
2.435 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.436 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.436 * [backup-simplify]: Simplify 0 into 0
2.437 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.438 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.438 * [backup-simplify]: Simplify 0 into 0
2.439 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.440 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.440 * [backup-simplify]: Simplify 0 into 0
2.440 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
2.441 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
2.441 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
2.441 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.441 * [taylor]: Taking taylor expansion of -2 in n
2.441 * [backup-simplify]: Simplify -2 into -2
2.441 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.441 * [taylor]: Taking taylor expansion of PI in n
2.441 * [backup-simplify]: Simplify PI into PI
2.441 * [taylor]: Taking taylor expansion of n in n
2.441 * [backup-simplify]: Simplify 0 into 0
2.441 * [backup-simplify]: Simplify 1 into 1
2.441 * [backup-simplify]: Simplify (/ PI 1) into PI
2.441 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.441 * [taylor]: Taking taylor expansion of -2 in n
2.441 * [backup-simplify]: Simplify -2 into -2
2.441 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.441 * [taylor]: Taking taylor expansion of PI in n
2.441 * [backup-simplify]: Simplify PI into PI
2.441 * [taylor]: Taking taylor expansion of n in n
2.441 * [backup-simplify]: Simplify 0 into 0
2.441 * [backup-simplify]: Simplify 1 into 1
2.441 * [backup-simplify]: Simplify (/ PI 1) into PI
2.442 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.442 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.443 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.443 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.443 * [backup-simplify]: Simplify 0 into 0
2.444 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.444 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.444 * [backup-simplify]: Simplify 0 into 0
2.445 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.446 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.446 * [backup-simplify]: Simplify 0 into 0
2.446 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.447 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.447 * [backup-simplify]: Simplify 0 into 0
2.448 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.449 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.449 * [backup-simplify]: Simplify 0 into 0
2.450 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.450 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.451 * [backup-simplify]: Simplify 0 into 0
2.451 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
2.451 * * * * [progress]: [ 3 / 3 ] generating series at (2)
2.451 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))))
2.451 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
2.451 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
2.451 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.451 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.452 * [taylor]: Taking taylor expansion of k in k
2.452 * [backup-simplify]: Simplify 0 into 0
2.452 * [backup-simplify]: Simplify 1 into 1
2.452 * [backup-simplify]: Simplify (/ 1 1) into 1
2.452 * [backup-simplify]: Simplify (sqrt 0) into 0
2.454 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.454 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
2.454 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
2.454 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
2.454 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.454 * [taylor]: Taking taylor expansion of 1/2 in k
2.454 * [backup-simplify]: Simplify 1/2 into 1/2
2.454 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.454 * [taylor]: Taking taylor expansion of 1/2 in k
2.454 * [backup-simplify]: Simplify 1/2 into 1/2
2.454 * [taylor]: Taking taylor expansion of k in k
2.454 * [backup-simplify]: Simplify 0 into 0
2.454 * [backup-simplify]: Simplify 1 into 1
2.454 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
2.454 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
2.454 * [taylor]: Taking taylor expansion of 2 in k
2.454 * [backup-simplify]: Simplify 2 into 2
2.454 * [taylor]: Taking taylor expansion of (* n PI) in k
2.454 * [taylor]: Taking taylor expansion of n in k
2.454 * [backup-simplify]: Simplify n into n
2.454 * [taylor]: Taking taylor expansion of PI in k
2.454 * [backup-simplify]: Simplify PI into PI
2.454 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.454 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
2.455 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
2.455 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.455 * [backup-simplify]: Simplify (- 0) into 0
2.456 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.456 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
2.456 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
2.456 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
2.456 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.456 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.456 * [taylor]: Taking taylor expansion of k in n
2.456 * [backup-simplify]: Simplify k into k
2.456 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.456 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.456 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.456 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.456 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.456 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.456 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.457 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.457 * [taylor]: Taking taylor expansion of 1/2 in n
2.457 * [backup-simplify]: Simplify 1/2 into 1/2
2.457 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.457 * [taylor]: Taking taylor expansion of 1/2 in n
2.457 * [backup-simplify]: Simplify 1/2 into 1/2
2.457 * [taylor]: Taking taylor expansion of k in n
2.457 * [backup-simplify]: Simplify k into k
2.457 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.457 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.457 * [taylor]: Taking taylor expansion of 2 in n
2.457 * [backup-simplify]: Simplify 2 into 2
2.457 * [taylor]: Taking taylor expansion of (* n PI) in n
2.457 * [taylor]: Taking taylor expansion of n in n
2.457 * [backup-simplify]: Simplify 0 into 0
2.457 * [backup-simplify]: Simplify 1 into 1
2.457 * [taylor]: Taking taylor expansion of PI in n
2.457 * [backup-simplify]: Simplify PI into PI
2.457 * [backup-simplify]: Simplify (* 0 PI) into 0
2.458 * [backup-simplify]: Simplify (* 2 0) into 0
2.459 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.461 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.462 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.462 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.462 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.462 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.463 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.464 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.466 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
2.466 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
2.466 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.466 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.466 * [taylor]: Taking taylor expansion of k in n
2.466 * [backup-simplify]: Simplify k into k
2.466 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.466 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.466 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.466 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.466 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.466 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.466 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.466 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.466 * [taylor]: Taking taylor expansion of 1/2 in n
2.466 * [backup-simplify]: Simplify 1/2 into 1/2
2.466 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.466 * [taylor]: Taking taylor expansion of 1/2 in n
2.466 * [backup-simplify]: Simplify 1/2 into 1/2
2.466 * [taylor]: Taking taylor expansion of k in n
2.466 * [backup-simplify]: Simplify k into k
2.466 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.466 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.466 * [taylor]: Taking taylor expansion of 2 in n
2.466 * [backup-simplify]: Simplify 2 into 2
2.466 * [taylor]: Taking taylor expansion of (* n PI) in n
2.466 * [taylor]: Taking taylor expansion of n in n
2.466 * [backup-simplify]: Simplify 0 into 0
2.467 * [backup-simplify]: Simplify 1 into 1
2.467 * [taylor]: Taking taylor expansion of PI in n
2.467 * [backup-simplify]: Simplify PI into PI
2.467 * [backup-simplify]: Simplify (* 0 PI) into 0
2.467 * [backup-simplify]: Simplify (* 2 0) into 0
2.469 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.470 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.471 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.471 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.472 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.472 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.473 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.474 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.475 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
2.477 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k)))
2.477 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
2.477 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
2.477 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
2.477 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.477 * [taylor]: Taking taylor expansion of 1/2 in k
2.477 * [backup-simplify]: Simplify 1/2 into 1/2
2.477 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.477 * [taylor]: Taking taylor expansion of 1/2 in k
2.477 * [backup-simplify]: Simplify 1/2 into 1/2
2.477 * [taylor]: Taking taylor expansion of k in k
2.477 * [backup-simplify]: Simplify 0 into 0
2.477 * [backup-simplify]: Simplify 1 into 1
2.477 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
2.477 * [taylor]: Taking taylor expansion of (log n) in k
2.477 * [taylor]: Taking taylor expansion of n in k
2.477 * [backup-simplify]: Simplify n into n
2.477 * [backup-simplify]: Simplify (log n) into (log n)
2.477 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.477 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.477 * [taylor]: Taking taylor expansion of 2 in k
2.477 * [backup-simplify]: Simplify 2 into 2
2.477 * [taylor]: Taking taylor expansion of PI in k
2.477 * [backup-simplify]: Simplify PI into PI
2.478 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.479 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.479 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.480 * [backup-simplify]: Simplify (- 0) into 0
2.480 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.481 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.482 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
2.484 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
2.484 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.484 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.484 * [taylor]: Taking taylor expansion of k in k
2.484 * [backup-simplify]: Simplify 0 into 0
2.484 * [backup-simplify]: Simplify 1 into 1
2.484 * [backup-simplify]: Simplify (/ 1 1) into 1
2.485 * [backup-simplify]: Simplify (sqrt 0) into 0
2.486 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.487 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
2.487 * [backup-simplify]: Simplify 0 into 0
2.488 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.489 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.491 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.492 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
2.492 * [backup-simplify]: Simplify (- 0) into 0
2.493 * [backup-simplify]: Simplify (+ 0 0) into 0
2.494 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.495 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
2.497 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.498 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
2.498 * [taylor]: Taking taylor expansion of 0 in k
2.499 * [backup-simplify]: Simplify 0 into 0
2.499 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
2.500 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.502 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.503 * [backup-simplify]: Simplify (+ 0 0) into 0
2.504 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
2.508 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.509 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.511 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
2.514 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.518 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.520 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.521 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.522 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.526 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.527 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
2.527 * [backup-simplify]: Simplify (- 0) into 0
2.527 * [backup-simplify]: Simplify (+ 0 0) into 0
2.529 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.530 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.533 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.533 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.534 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
2.536 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
2.536 * [taylor]: Taking taylor expansion of 0 in k
2.536 * [backup-simplify]: Simplify 0 into 0
2.536 * [backup-simplify]: Simplify 0 into 0
2.536 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
2.540 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.541 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
2.542 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.546 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.546 * [backup-simplify]: Simplify (+ 0 0) into 0
2.548 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
2.548 * [backup-simplify]: Simplify (- 0) into 0
2.549 * [backup-simplify]: Simplify (+ 0 0) into 0
2.551 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.556 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
2.565 * [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))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
2.570 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
2.571 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.573 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.578 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.579 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
2.580 * [backup-simplify]: Simplify (- 0) into 0
2.580 * [backup-simplify]: Simplify (+ 0 0) into 0
2.581 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.583 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.586 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.586 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.587 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
2.589 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0
2.589 * [taylor]: Taking taylor expansion of 0 in k
2.589 * [backup-simplify]: Simplify 0 into 0
2.589 * [backup-simplify]: Simplify 0 into 0
2.589 * [backup-simplify]: Simplify 0 into 0
2.590 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.594 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.597 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
2.598 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.604 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.604 * [backup-simplify]: Simplify (+ 0 0) into 0
2.605 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
2.606 * [backup-simplify]: Simplify (- 0) into 0
2.606 * [backup-simplify]: Simplify (+ 0 0) into 0
2.609 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.615 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.632 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
2.644 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
2.662 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
2.662 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
2.662 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
2.662 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
2.662 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.662 * [taylor]: Taking taylor expansion of k in k
2.662 * [backup-simplify]: Simplify 0 into 0
2.662 * [backup-simplify]: Simplify 1 into 1
2.663 * [backup-simplify]: Simplify (sqrt 0) into 0
2.664 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.664 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
2.664 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
2.664 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
2.664 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.664 * [taylor]: Taking taylor expansion of 1/2 in k
2.664 * [backup-simplify]: Simplify 1/2 into 1/2
2.664 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.664 * [taylor]: Taking taylor expansion of 1/2 in k
2.664 * [backup-simplify]: Simplify 1/2 into 1/2
2.664 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.664 * [taylor]: Taking taylor expansion of k in k
2.664 * [backup-simplify]: Simplify 0 into 0
2.664 * [backup-simplify]: Simplify 1 into 1
2.664 * [backup-simplify]: Simplify (/ 1 1) into 1
2.664 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
2.664 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
2.664 * [taylor]: Taking taylor expansion of 2 in k
2.664 * [backup-simplify]: Simplify 2 into 2
2.664 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.664 * [taylor]: Taking taylor expansion of PI in k
2.664 * [backup-simplify]: Simplify PI into PI
2.664 * [taylor]: Taking taylor expansion of n in k
2.664 * [backup-simplify]: Simplify n into n
2.664 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.664 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
2.664 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
2.665 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.665 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.665 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.665 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
2.665 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
2.665 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
2.665 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.665 * [taylor]: Taking taylor expansion of k in n
2.665 * [backup-simplify]: Simplify k into k
2.665 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.665 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.665 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.665 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.666 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.666 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.666 * [taylor]: Taking taylor expansion of 1/2 in n
2.666 * [backup-simplify]: Simplify 1/2 into 1/2
2.666 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.666 * [taylor]: Taking taylor expansion of 1/2 in n
2.666 * [backup-simplify]: Simplify 1/2 into 1/2
2.666 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.666 * [taylor]: Taking taylor expansion of k in n
2.666 * [backup-simplify]: Simplify k into k
2.666 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.666 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.666 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.666 * [taylor]: Taking taylor expansion of 2 in n
2.666 * [backup-simplify]: Simplify 2 into 2
2.666 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.666 * [taylor]: Taking taylor expansion of PI in n
2.666 * [backup-simplify]: Simplify PI into PI
2.666 * [taylor]: Taking taylor expansion of n in n
2.666 * [backup-simplify]: Simplify 0 into 0
2.666 * [backup-simplify]: Simplify 1 into 1
2.666 * [backup-simplify]: Simplify (/ PI 1) into PI
2.666 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.667 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.667 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.667 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.667 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.668 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.669 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
2.670 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.670 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
2.670 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.670 * [taylor]: Taking taylor expansion of k in n
2.670 * [backup-simplify]: Simplify k into k
2.670 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.670 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.670 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.670 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.670 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.670 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.670 * [taylor]: Taking taylor expansion of 1/2 in n
2.670 * [backup-simplify]: Simplify 1/2 into 1/2
2.670 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.670 * [taylor]: Taking taylor expansion of 1/2 in n
2.670 * [backup-simplify]: Simplify 1/2 into 1/2
2.670 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.670 * [taylor]: Taking taylor expansion of k in n
2.670 * [backup-simplify]: Simplify k into k
2.670 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.670 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.670 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.670 * [taylor]: Taking taylor expansion of 2 in n
2.670 * [backup-simplify]: Simplify 2 into 2
2.670 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.670 * [taylor]: Taking taylor expansion of PI in n
2.670 * [backup-simplify]: Simplify PI into PI
2.670 * [taylor]: Taking taylor expansion of n in n
2.670 * [backup-simplify]: Simplify 0 into 0
2.670 * [backup-simplify]: Simplify 1 into 1
2.670 * [backup-simplify]: Simplify (/ PI 1) into PI
2.671 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.671 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.671 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.672 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.672 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.673 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.673 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
2.674 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.675 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
2.675 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
2.675 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
2.675 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
2.675 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.675 * [taylor]: Taking taylor expansion of 1/2 in k
2.675 * [backup-simplify]: Simplify 1/2 into 1/2
2.675 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.675 * [taylor]: Taking taylor expansion of 1/2 in k
2.675 * [backup-simplify]: Simplify 1/2 into 1/2
2.675 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.675 * [taylor]: Taking taylor expansion of k in k
2.675 * [backup-simplify]: Simplify 0 into 0
2.675 * [backup-simplify]: Simplify 1 into 1
2.676 * [backup-simplify]: Simplify (/ 1 1) into 1
2.676 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
2.676 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.676 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.676 * [taylor]: Taking taylor expansion of 2 in k
2.676 * [backup-simplify]: Simplify 2 into 2
2.676 * [taylor]: Taking taylor expansion of PI in k
2.676 * [backup-simplify]: Simplify PI into PI
2.676 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.677 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.677 * [taylor]: Taking taylor expansion of (log n) in k
2.677 * [taylor]: Taking taylor expansion of n in k
2.677 * [backup-simplify]: Simplify n into n
2.677 * [backup-simplify]: Simplify (log n) into (log n)
2.677 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.677 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.677 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.678 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.678 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
2.679 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
2.680 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.680 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.680 * [taylor]: Taking taylor expansion of k in k
2.680 * [backup-simplify]: Simplify 0 into 0
2.680 * [backup-simplify]: Simplify 1 into 1
2.680 * [backup-simplify]: Simplify (sqrt 0) into 0
2.681 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.682 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
2.682 * [backup-simplify]: Simplify 0 into 0
2.682 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.683 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.684 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.684 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.684 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.684 * [backup-simplify]: Simplify (- 0) into 0
2.685 * [backup-simplify]: Simplify (+ 0 0) into 0
2.686 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.686 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
2.687 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.688 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
2.688 * [taylor]: Taking taylor expansion of 0 in k
2.688 * [backup-simplify]: Simplify 0 into 0
2.688 * [backup-simplify]: Simplify 0 into 0
2.689 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.690 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.691 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.691 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.693 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.693 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.694 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.694 * [backup-simplify]: Simplify (- 0) into 0
2.694 * [backup-simplify]: Simplify (+ 0 0) into 0
2.695 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.696 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
2.698 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.699 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
2.700 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
2.700 * [taylor]: Taking taylor expansion of 0 in k
2.700 * [backup-simplify]: Simplify 0 into 0
2.700 * [backup-simplify]: Simplify 0 into 0
2.700 * [backup-simplify]: Simplify 0 into 0
2.701 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.703 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.703 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.704 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.705 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.708 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.708 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.709 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
2.709 * [backup-simplify]: Simplify (- 0) into 0
2.710 * [backup-simplify]: Simplify (+ 0 0) into 0
2.711 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.712 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
2.714 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.714 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
2.716 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0
2.716 * [taylor]: Taking taylor expansion of 0 in k
2.716 * [backup-simplify]: Simplify 0 into 0
2.716 * [backup-simplify]: Simplify 0 into 0
2.716 * [backup-simplify]: Simplify 0 into 0
2.716 * [backup-simplify]: Simplify 0 into 0
2.718 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.719 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.720 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.723 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
2.724 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
2.724 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
2.724 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
2.724 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
2.724 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
2.724 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
2.724 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.724 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.724 * [taylor]: Taking taylor expansion of 1/2 in k
2.724 * [backup-simplify]: Simplify 1/2 into 1/2
2.724 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.724 * [taylor]: Taking taylor expansion of k in k
2.724 * [backup-simplify]: Simplify 0 into 0
2.724 * [backup-simplify]: Simplify 1 into 1
2.725 * [backup-simplify]: Simplify (/ 1 1) into 1
2.725 * [taylor]: Taking taylor expansion of 1/2 in k
2.725 * [backup-simplify]: Simplify 1/2 into 1/2
2.725 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
2.725 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
2.725 * [taylor]: Taking taylor expansion of -2 in k
2.725 * [backup-simplify]: Simplify -2 into -2
2.725 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.725 * [taylor]: Taking taylor expansion of PI in k
2.725 * [backup-simplify]: Simplify PI into PI
2.725 * [taylor]: Taking taylor expansion of n in k
2.725 * [backup-simplify]: Simplify n into n
2.725 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.725 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
2.725 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
2.725 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.725 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.725 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
2.726 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
2.726 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.726 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.726 * [taylor]: Taking taylor expansion of -1 in k
2.726 * [backup-simplify]: Simplify -1 into -1
2.726 * [taylor]: Taking taylor expansion of k in k
2.726 * [backup-simplify]: Simplify 0 into 0
2.726 * [backup-simplify]: Simplify 1 into 1
2.726 * [backup-simplify]: Simplify (/ -1 1) into -1
2.726 * [backup-simplify]: Simplify (sqrt 0) into 0
2.727 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.727 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
2.727 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
2.727 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.727 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.727 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.727 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.727 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.727 * [taylor]: Taking taylor expansion of 1/2 in n
2.727 * [backup-simplify]: Simplify 1/2 into 1/2
2.727 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.727 * [taylor]: Taking taylor expansion of k in n
2.728 * [backup-simplify]: Simplify k into k
2.728 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.728 * [taylor]: Taking taylor expansion of 1/2 in n
2.728 * [backup-simplify]: Simplify 1/2 into 1/2
2.728 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.728 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.728 * [taylor]: Taking taylor expansion of -2 in n
2.728 * [backup-simplify]: Simplify -2 into -2
2.728 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.728 * [taylor]: Taking taylor expansion of PI in n
2.728 * [backup-simplify]: Simplify PI into PI
2.728 * [taylor]: Taking taylor expansion of n in n
2.728 * [backup-simplify]: Simplify 0 into 0
2.728 * [backup-simplify]: Simplify 1 into 1
2.728 * [backup-simplify]: Simplify (/ PI 1) into PI
2.728 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.729 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.729 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.729 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.730 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.731 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
2.732 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.732 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.732 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.732 * [taylor]: Taking taylor expansion of -1 in n
2.732 * [backup-simplify]: Simplify -1 into -1
2.732 * [taylor]: Taking taylor expansion of k in n
2.732 * [backup-simplify]: Simplify k into k
2.732 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.732 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.732 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.732 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.733 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
2.733 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
2.733 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.733 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.733 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.733 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.733 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.733 * [taylor]: Taking taylor expansion of 1/2 in n
2.733 * [backup-simplify]: Simplify 1/2 into 1/2
2.733 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.733 * [taylor]: Taking taylor expansion of k in n
2.733 * [backup-simplify]: Simplify k into k
2.733 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.733 * [taylor]: Taking taylor expansion of 1/2 in n
2.733 * [backup-simplify]: Simplify 1/2 into 1/2
2.733 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.733 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.733 * [taylor]: Taking taylor expansion of -2 in n
2.733 * [backup-simplify]: Simplify -2 into -2
2.733 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.733 * [taylor]: Taking taylor expansion of PI in n
2.733 * [backup-simplify]: Simplify PI into PI
2.733 * [taylor]: Taking taylor expansion of n in n
2.733 * [backup-simplify]: Simplify 0 into 0
2.733 * [backup-simplify]: Simplify 1 into 1
2.733 * [backup-simplify]: Simplify (/ PI 1) into PI
2.734 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.734 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.734 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.734 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.735 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.736 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
2.737 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.737 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.737 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.737 * [taylor]: Taking taylor expansion of -1 in n
2.737 * [backup-simplify]: Simplify -1 into -1
2.737 * [taylor]: Taking taylor expansion of k in n
2.737 * [backup-simplify]: Simplify k into k
2.737 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.737 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.737 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.737 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.740 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
2.740 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
2.740 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
2.740 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
2.740 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.740 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.740 * [taylor]: Taking taylor expansion of 1/2 in k
2.740 * [backup-simplify]: Simplify 1/2 into 1/2
2.740 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.740 * [taylor]: Taking taylor expansion of k in k
2.740 * [backup-simplify]: Simplify 0 into 0
2.740 * [backup-simplify]: Simplify 1 into 1
2.741 * [backup-simplify]: Simplify (/ 1 1) into 1
2.741 * [taylor]: Taking taylor expansion of 1/2 in k
2.741 * [backup-simplify]: Simplify 1/2 into 1/2
2.741 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
2.741 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
2.741 * [taylor]: Taking taylor expansion of (* -2 PI) in k
2.741 * [taylor]: Taking taylor expansion of -2 in k
2.741 * [backup-simplify]: Simplify -2 into -2
2.741 * [taylor]: Taking taylor expansion of PI in k
2.741 * [backup-simplify]: Simplify PI into PI
2.741 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.742 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.742 * [taylor]: Taking taylor expansion of (log n) in k
2.742 * [taylor]: Taking taylor expansion of n in k
2.742 * [backup-simplify]: Simplify n into n
2.742 * [backup-simplify]: Simplify (log n) into (log n)
2.742 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.742 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.742 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.743 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
2.744 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
2.745 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.745 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.745 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.745 * [taylor]: Taking taylor expansion of -1 in k
2.745 * [backup-simplify]: Simplify -1 into -1
2.745 * [taylor]: Taking taylor expansion of k in k
2.745 * [backup-simplify]: Simplify 0 into 0
2.745 * [backup-simplify]: Simplify 1 into 1
2.746 * [backup-simplify]: Simplify (/ -1 1) into -1
2.746 * [backup-simplify]: Simplify (sqrt 0) into 0
2.747 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.749 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
2.750 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
2.751 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.752 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.754 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
2.754 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.755 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.755 * [backup-simplify]: Simplify (+ 0 0) into 0
2.757 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.758 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
2.760 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.761 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
2.761 * [taylor]: Taking taylor expansion of 0 in k
2.761 * [backup-simplify]: Simplify 0 into 0
2.761 * [backup-simplify]: Simplify 0 into 0
2.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
2.763 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.764 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.765 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.766 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.767 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.769 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
2.769 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.769 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.770 * [backup-simplify]: Simplify (+ 0 0) into 0
2.770 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.771 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
2.773 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.773 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.773 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
2.775 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
2.775 * [taylor]: Taking taylor expansion of 0 in k
2.775 * [backup-simplify]: Simplify 0 into 0
2.775 * [backup-simplify]: Simplify 0 into 0
2.775 * [backup-simplify]: Simplify 0 into 0
2.775 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.778 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.780 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.781 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.784 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
2.784 * * * [progress]: simplifying candidates
2.784 * * * * [progress]: [ 1 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.784 * * * * [progress]: [ 2 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.784 * * * * [progress]: [ 3 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.784 * * * * [progress]: [ 4 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.784 * * * * [progress]: [ 5 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.784 * * * * [progress]: [ 6 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.784 * * * * [progress]: [ 7 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.784 * * * * [progress]: [ 8 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))>
2.784 * * * * [progress]: [ 9 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
2.784 * * * * [progress]: [ 10 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
2.784 * * * * [progress]: [ 11 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.784 * * * * [progress]: [ 12 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))>
2.785 * * * * [progress]: [ 13 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))>
2.785 * * * * [progress]: [ 14 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 15 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt k)))>
2.785 * * * * [progress]: [ 16 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt k)))>
2.785 * * * * [progress]: [ 17 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt k)))>
2.785 * * * * [progress]: [ 18 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
2.785 * * * * [progress]: [ 19 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.785 * * * * [progress]: [ 20 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.785 * * * * [progress]: [ 21 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.785 * * * * [progress]: [ 22 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.785 * * * * [progress]: [ 23 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.785 * * * * [progress]: [ 24 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
2.785 * * * * [progress]: [ 25 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 26 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 27 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 28 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 29 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 30 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 31 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 32 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 33 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 34 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 35 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 36 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.785 * * * * [progress]: [ 37 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.786 * * * * [progress]: [ 38 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.786 * * * * [progress]: [ 39 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
2.786 * * * * [progress]: [ 40 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.786 * * * * [progress]: [ 41 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.786 * * * * [progress]: [ 42 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.786 * * * * [progress]: [ 43 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))>
2.786 * * * * [progress]: [ 44 / 124 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) 1))>
2.786 * * * * [progress]: [ 45 / 124 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.786 * * * * [progress]: [ 46 / 124 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.786 * * * * [progress]: [ 47 / 124 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.786 * * * * [progress]: [ 48 / 124 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.786 * * * * [progress]: [ 49 / 124 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
2.786 * * * * [progress]: [ 50 / 124 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.786 * * * * [progress]: [ 51 / 124 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.786 * * * * [progress]: [ 52 / 124 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
2.786 * * * * [progress]: [ 53 / 124 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.786 * * * * [progress]: [ 54 / 124 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.786 * * * * [progress]: [ 55 / 124 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.786 * * * * [progress]: [ 56 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (- (sqrt k))))>
2.786 * * * * [progress]: [ 57 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
2.786 * * * * [progress]: [ 58 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))))>
2.786 * * * * [progress]: [ 59 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.786 * * * * [progress]: [ 60 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1)) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.786 * * * * [progress]: [ 61 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.786 * * * * [progress]: [ 62 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.786 * * * * [progress]: [ 63 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
2.787 * * * * [progress]: [ 64 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))))>
2.787 * * * * [progress]: [ 65 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.787 * * * * [progress]: [ 66 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1)) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.787 * * * * [progress]: [ 67 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.787 * * * * [progress]: [ 68 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.787 * * * * [progress]: [ 69 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
2.787 * * * * [progress]: [ 70 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
2.787 * * * * [progress]: [ 71 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.787 * * * * [progress]: [ 72 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.787 * * * * [progress]: [ 73 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.787 * * * * [progress]: [ 74 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) 1) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.787 * * * * [progress]: [ 75 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
2.787 * * * * [progress]: [ 76 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
2.787 * * * * [progress]: [ 77 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.787 * * * * [progress]: [ 78 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt 1)) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.787 * * * * [progress]: [ 79 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.787 * * * * [progress]: [ 80 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.787 * * * * [progress]: [ 81 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
2.787 * * * * [progress]: [ 82 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
2.787 * * * * [progress]: [ 83 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.787 * * * * [progress]: [ 84 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.787 * * * * [progress]: [ 85 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.787 * * * * [progress]: [ 86 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.787 * * * * [progress]: [ 87 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
2.787 * * * * [progress]: [ 88 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
2.788 * * * * [progress]: [ 89 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.788 * * * * [progress]: [ 90 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
2.788 * * * * [progress]: [ 91 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.788 * * * * [progress]: [ 92 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
2.788 * * * * [progress]: [ 93 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))>
2.788 * * * * [progress]: [ 94 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))>
2.788 * * * * [progress]: [ 95 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
2.788 * * * * [progress]: [ 96 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
2.788 * * * * [progress]: [ 97 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
2.788 * * * * [progress]: [ 98 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
2.788 * * * * [progress]: [ 99 / 124 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
2.788 * * * * [progress]: [ 100 / 124 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
2.788 * * * * [progress]: [ 101 / 124 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
2.788 * * * * [progress]: [ 102 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
2.788 * * * * [progress]: [ 103 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
2.788 * * * * [progress]: [ 104 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.788 * * * * [progress]: [ 105 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k)))>
2.788 * * * * [progress]: [ 106 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.788 * * * * [progress]: [ 107 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
2.788 * * * * [progress]: [ 108 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
2.788 * * * * [progress]: [ 109 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
2.788 * * * * [progress]: [ 110 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
2.788 * * * * [progress]: [ 111 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
2.788 * * * * [progress]: [ 112 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
2.788 * * * * [progress]: [ 113 / 124 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
2.789 * * * * [progress]: [ 114 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
2.789 * * * * [progress]: [ 115 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))>
2.789 * * * * [progress]: [ 116 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
2.789 * * * * [progress]: [ 117 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
2.789 * * * * [progress]: [ 118 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
2.789 * * * * [progress]: [ 119 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.789 * * * * [progress]: [ 120 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.789 * * * * [progress]: [ 121 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.789 * * * * [progress]: [ 122 / 124 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
2.789 * * * * [progress]: [ 123 / 124 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
2.789 * * * * [progress]: [ 124 / 124 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
2.790 * [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))
  (* 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))
  (- (* (+ (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)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
2.793 * * [simplify]: iteration 1: (264 enodes)
2.892 * * [simplify]: iteration 2: (640 enodes)
3.429 * * [simplify]: Extracting #0: cost 94 inf + 0
3.430 * * [simplify]: Extracting #1: cost 362 inf + 1
3.433 * * [simplify]: Extracting #2: cost 548 inf + 5214
3.442 * * [simplify]: Extracting #3: cost 540 inf + 37211
3.455 * * [simplify]: Extracting #4: cost 367 inf + 93605
3.484 * * [simplify]: Extracting #5: cost 170 inf + 181921
3.549 * * [simplify]: Extracting #6: cost 100 inf + 225463
3.596 * * [simplify]: Extracting #7: cost 34 inf + 261579
3.657 * * [simplify]: Extracting #8: cost 4 inf + 286835
3.755 * * [simplify]: Extracting #9: cost 0 inf + 290245
3.808 * * [simplify]: Extracting #10: cost 0 inf + 289445
3.870 * * [simplify]: Extracting #11: cost 0 inf + 289285
3.963 * * [simplify]: Extracting #12: cost 0 inf + 289245
4.059 * [simplify]: Simplified to:
  (* (- 1/2 (/ k 2)) (log (* (* n 2) PI)))
  (* (- 1/2 (/ k 2)) (log (* (* n 2) PI)))
  (* (- 1/2 (/ k 2)) (log (* (* n 2) PI)))
  (* (- 1/2 (/ k 2)) (log (* (* n 2) PI)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* n 2) PI))
  (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))))
  (* (* n 2) PI)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* n 2) PI)
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (- (/ k 2)))
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* (* n 2) PI)))
  (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) (- 1/4 (/ k 4)))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (log (* (* n 2) PI))
  (log (* (* n 2) PI))
  (log (* (* n 2) PI))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* n (* (* n n) 8)) PI) (* PI PI))
  (* (* (* n 2) PI) (* (* (* n 2) PI) (* (* n 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) PI) 2)
  (* (sqrt n) (* PI 2))
  (* (* n 2) PI)
  (- (* (- 1/2 (/ k 2)) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* n 2) PI))) (log (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) 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))
  (/ (/ (sqrt (* (* n 2) PI)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* (* n 2) PI)) (fabs (cbrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* (* n 2) PI)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* n 2) PI))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* n 2) PI)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* n 2) PI))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (/ (sqrt (* (* n 2) PI)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* (* n 2) PI)) (fabs (cbrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* (* n 2) PI)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* n 2) PI))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* n 2) PI)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* n 2) PI))
  (/ (pow (* (* n 2) PI) (- (/ 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 (* (* n 2) PI) (- 1/2 (/ k 2)))) (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 (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (fabs (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)))))
  (/ (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)))))
  (/ (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)))) (fabs (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 (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))))
  (/ (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 (fabs (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
  (/ (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
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (fabs (cbrt k)))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (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))) (fabs (cbrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* (* n 2) PI) (- 1/2 (/ k 2)))
  (/ (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) (- (/ k 2))))
  (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))
  (/ (sqrt k) (pow (* PI 2) (- 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) (- 1/4 (/ k 4))))
  (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))
  (- (+ (+ (sqrt (* (* n 2) PI)) (* (* (* (* k k) (log n)) (log n)) (* 1/8 (sqrt (* (* n 2) PI))))) (+ (* (* (sqrt (* (* n 2) PI)) (* k k)) (* (* (log (* PI 2)) (log (* PI 2))) 1/8)) (* (* (* 1/4 (log (* PI 2))) (sqrt (* (* n 2) PI))) (* (* k k) (log n))))) (* 1/2 (* k (+ (* (log n) (sqrt (* (* n 2) PI))) (* (sqrt (* (* n 2) PI)) (log (* PI 2)))))))
  (exp (* (- 1/2 (* k 1/2)) (log (* (* n 2) PI))))
  (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (* (* n 2) PI)
  (- (+ (- (* (* (* (sqrt (* (* n 2) PI)) (* k k)) (log n)) (* +nan.0 (log (* PI 2)))) (* (* (sqrt (* (* n 2) PI)) (* k k)) (* +nan.0 (log (* PI 2))))) (+ (- (* (* +nan.0 (* (* (log n) k) (* (log n) k))) (sqrt (* (* n 2) PI))) (* +nan.0 (* (sqrt (* (* n 2) PI)) k))) (+ (- (* +nan.0 (sqrt (* (* n 2) PI))) (* (* (* (sqrt (* (* n 2) PI)) (* k k)) (* (log (* PI 2)) (log (* PI 2)))) +nan.0)) (+ (- (* (* +nan.0 (sqrt (* (* n 2) PI))) (* (* k k) (log n))) (* (* (sqrt (* (* n 2) PI)) (* k k)) +nan.0)) (* +nan.0 (- (* (log (* PI 2)) (* (sqrt (* (* n 2) PI)) k)) (* (sqrt (* (* n 2) PI)) (* (log n) k)))))))))
  (- (- (/ (/ (* (exp (* (- 1/2 (* k 1/2)) (log (* (* n 2) PI)))) +nan.0) (* k k)) k) (- (/ (* (exp (* (- 1/2 (* k 1/2)) (log (* (* n 2) PI)))) +nan.0) k) (/ (* (exp (* (- 1/2 (* k 1/2)) (log (* (* n 2) PI)))) +nan.0) (* k k)))))
  (- (- (/ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (/ k +nan.0)) (* +nan.0 (- (/ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* k k)) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2))))))))
4.069 * * * [progress]: adding candidates to table
5.450 * * [progress]: iteration 2 / 4
5.450 * * * [progress]: picking best candidate
5.506 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.506 * * * [progress]: localizing error
5.556 * * * [progress]: generating rewritten candidates
5.556 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
5.582 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1)
5.591 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1)
5.615 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
5.677 * * * [progress]: generating series expansions
5.677 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
5.678 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
5.678 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
5.678 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
5.678 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
5.678 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
5.678 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
5.678 * [taylor]: Taking taylor expansion of 1/2 in k
5.678 * [backup-simplify]: Simplify 1/2 into 1/2
5.678 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.678 * [taylor]: Taking taylor expansion of 1 in k
5.678 * [backup-simplify]: Simplify 1 into 1
5.678 * [taylor]: Taking taylor expansion of k in k
5.678 * [backup-simplify]: Simplify 0 into 0
5.678 * [backup-simplify]: Simplify 1 into 1
5.678 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.678 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.678 * [taylor]: Taking taylor expansion of 2 in k
5.678 * [backup-simplify]: Simplify 2 into 2
5.678 * [taylor]: Taking taylor expansion of (* n PI) in k
5.678 * [taylor]: Taking taylor expansion of n in k
5.678 * [backup-simplify]: Simplify n into n
5.678 * [taylor]: Taking taylor expansion of PI in k
5.678 * [backup-simplify]: Simplify PI into PI
5.678 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.678 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.678 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.679 * [backup-simplify]: Simplify (- 0) into 0
5.679 * [backup-simplify]: Simplify (+ 1 0) into 1
5.680 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.680 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.680 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.680 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.680 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.680 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.680 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.680 * [taylor]: Taking taylor expansion of 1/2 in n
5.680 * [backup-simplify]: Simplify 1/2 into 1/2
5.680 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.680 * [taylor]: Taking taylor expansion of 1 in n
5.680 * [backup-simplify]: Simplify 1 into 1
5.680 * [taylor]: Taking taylor expansion of k in n
5.680 * [backup-simplify]: Simplify k into k
5.680 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.680 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.680 * [taylor]: Taking taylor expansion of 2 in n
5.680 * [backup-simplify]: Simplify 2 into 2
5.680 * [taylor]: Taking taylor expansion of (* n PI) in n
5.680 * [taylor]: Taking taylor expansion of n in n
5.680 * [backup-simplify]: Simplify 0 into 0
5.680 * [backup-simplify]: Simplify 1 into 1
5.680 * [taylor]: Taking taylor expansion of PI in n
5.681 * [backup-simplify]: Simplify PI into PI
5.681 * [backup-simplify]: Simplify (* 0 PI) into 0
5.681 * [backup-simplify]: Simplify (* 2 0) into 0
5.683 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.685 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.686 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.686 * [backup-simplify]: Simplify (- k) into (- k)
5.686 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.686 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.687 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.688 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.690 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.690 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.690 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.690 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.690 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.690 * [taylor]: Taking taylor expansion of 1/2 in n
5.690 * [backup-simplify]: Simplify 1/2 into 1/2
5.690 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.690 * [taylor]: Taking taylor expansion of 1 in n
5.690 * [backup-simplify]: Simplify 1 into 1
5.690 * [taylor]: Taking taylor expansion of k in n
5.690 * [backup-simplify]: Simplify k into k
5.690 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.690 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.690 * [taylor]: Taking taylor expansion of 2 in n
5.690 * [backup-simplify]: Simplify 2 into 2
5.690 * [taylor]: Taking taylor expansion of (* n PI) in n
5.690 * [taylor]: Taking taylor expansion of n in n
5.690 * [backup-simplify]: Simplify 0 into 0
5.690 * [backup-simplify]: Simplify 1 into 1
5.690 * [taylor]: Taking taylor expansion of PI in n
5.690 * [backup-simplify]: Simplify PI into PI
5.691 * [backup-simplify]: Simplify (* 0 PI) into 0
5.691 * [backup-simplify]: Simplify (* 2 0) into 0
5.693 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.694 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.695 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.695 * [backup-simplify]: Simplify (- k) into (- k)
5.695 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.695 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.697 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.698 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.699 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.699 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
5.699 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
5.699 * [taylor]: Taking taylor expansion of 1/2 in k
5.699 * [backup-simplify]: Simplify 1/2 into 1/2
5.699 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
5.699 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.699 * [taylor]: Taking taylor expansion of 1 in k
5.699 * [backup-simplify]: Simplify 1 into 1
5.699 * [taylor]: Taking taylor expansion of k in k
5.699 * [backup-simplify]: Simplify 0 into 0
5.699 * [backup-simplify]: Simplify 1 into 1
5.699 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
5.699 * [taylor]: Taking taylor expansion of (log n) in k
5.699 * [taylor]: Taking taylor expansion of n in k
5.699 * [backup-simplify]: Simplify n into n
5.699 * [backup-simplify]: Simplify (log n) into (log n)
5.699 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.699 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.700 * [taylor]: Taking taylor expansion of 2 in k
5.700 * [backup-simplify]: Simplify 2 into 2
5.700 * [taylor]: Taking taylor expansion of PI in k
5.700 * [backup-simplify]: Simplify PI into PI
5.700 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.701 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.701 * [backup-simplify]: Simplify (- 0) into 0
5.702 * [backup-simplify]: Simplify (+ 1 0) into 1
5.703 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.704 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
5.705 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
5.706 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.708 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.709 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.710 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.712 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.712 * [backup-simplify]: Simplify (- 0) into 0
5.712 * [backup-simplify]: Simplify (+ 0 0) into 0
5.713 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
5.714 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.714 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
5.715 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.715 * [taylor]: Taking taylor expansion of 0 in k
5.716 * [backup-simplify]: Simplify 0 into 0
5.716 * [backup-simplify]: Simplify 0 into 0
5.716 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
5.717 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.718 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.718 * [backup-simplify]: Simplify (+ 0 0) into 0
5.718 * [backup-simplify]: Simplify (- 1) into -1
5.718 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.719 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
5.721 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
5.723 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
5.724 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
5.725 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.726 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.728 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.728 * [backup-simplify]: Simplify (- 0) into 0
5.728 * [backup-simplify]: Simplify (+ 0 0) into 0
5.729 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
5.730 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.731 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.732 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.732 * [taylor]: Taking taylor expansion of 0 in k
5.732 * [backup-simplify]: Simplify 0 into 0
5.732 * [backup-simplify]: Simplify 0 into 0
5.732 * [backup-simplify]: Simplify 0 into 0
5.733 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
5.734 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.736 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.736 * [backup-simplify]: Simplify (+ 0 0) into 0
5.736 * [backup-simplify]: Simplify (- 0) into 0
5.737 * [backup-simplify]: Simplify (+ 0 0) into 0
5.738 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.739 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.747 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
5.752 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
5.761 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
5.762 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
5.762 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
5.762 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
5.762 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.762 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.762 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
5.762 * [taylor]: Taking taylor expansion of 1/2 in k
5.762 * [backup-simplify]: Simplify 1/2 into 1/2
5.762 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.762 * [taylor]: Taking taylor expansion of 1 in k
5.762 * [backup-simplify]: Simplify 1 into 1
5.762 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.762 * [taylor]: Taking taylor expansion of k in k
5.762 * [backup-simplify]: Simplify 0 into 0
5.762 * [backup-simplify]: Simplify 1 into 1
5.762 * [backup-simplify]: Simplify (/ 1 1) into 1
5.762 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.763 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.763 * [taylor]: Taking taylor expansion of 2 in k
5.763 * [backup-simplify]: Simplify 2 into 2
5.763 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.763 * [taylor]: Taking taylor expansion of PI in k
5.763 * [backup-simplify]: Simplify PI into PI
5.763 * [taylor]: Taking taylor expansion of n in k
5.763 * [backup-simplify]: Simplify n into n
5.763 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.763 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.763 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.763 * [backup-simplify]: Simplify (- 1) into -1
5.764 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.764 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
5.764 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.764 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
5.764 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.764 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.765 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.765 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.765 * [taylor]: Taking taylor expansion of 1/2 in n
5.765 * [backup-simplify]: Simplify 1/2 into 1/2
5.765 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.765 * [taylor]: Taking taylor expansion of 1 in n
5.765 * [backup-simplify]: Simplify 1 into 1
5.765 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.765 * [taylor]: Taking taylor expansion of k in n
5.765 * [backup-simplify]: Simplify k into k
5.765 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.765 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.765 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.765 * [taylor]: Taking taylor expansion of 2 in n
5.765 * [backup-simplify]: Simplify 2 into 2
5.765 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.765 * [taylor]: Taking taylor expansion of PI in n
5.765 * [backup-simplify]: Simplify PI into PI
5.765 * [taylor]: Taking taylor expansion of n in n
5.765 * [backup-simplify]: Simplify 0 into 0
5.765 * [backup-simplify]: Simplify 1 into 1
5.766 * [backup-simplify]: Simplify (/ PI 1) into PI
5.766 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.767 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.767 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.767 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.767 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.769 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.770 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.771 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.771 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.771 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.771 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.771 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.771 * [taylor]: Taking taylor expansion of 1/2 in n
5.772 * [backup-simplify]: Simplify 1/2 into 1/2
5.772 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.772 * [taylor]: Taking taylor expansion of 1 in n
5.772 * [backup-simplify]: Simplify 1 into 1
5.772 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.772 * [taylor]: Taking taylor expansion of k in n
5.772 * [backup-simplify]: Simplify k into k
5.772 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.772 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.772 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.772 * [taylor]: Taking taylor expansion of 2 in n
5.772 * [backup-simplify]: Simplify 2 into 2
5.772 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.772 * [taylor]: Taking taylor expansion of PI in n
5.772 * [backup-simplify]: Simplify PI into PI
5.772 * [taylor]: Taking taylor expansion of n in n
5.772 * [backup-simplify]: Simplify 0 into 0
5.772 * [backup-simplify]: Simplify 1 into 1
5.772 * [backup-simplify]: Simplify (/ PI 1) into PI
5.773 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.774 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.774 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.774 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.774 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.776 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.777 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.778 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.778 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
5.778 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
5.778 * [taylor]: Taking taylor expansion of 1/2 in k
5.779 * [backup-simplify]: Simplify 1/2 into 1/2
5.779 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
5.779 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.779 * [taylor]: Taking taylor expansion of 1 in k
5.779 * [backup-simplify]: Simplify 1 into 1
5.779 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.779 * [taylor]: Taking taylor expansion of k in k
5.779 * [backup-simplify]: Simplify 0 into 0
5.779 * [backup-simplify]: Simplify 1 into 1
5.779 * [backup-simplify]: Simplify (/ 1 1) into 1
5.779 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
5.779 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.779 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.779 * [taylor]: Taking taylor expansion of 2 in k
5.779 * [backup-simplify]: Simplify 2 into 2
5.779 * [taylor]: Taking taylor expansion of PI in k
5.779 * [backup-simplify]: Simplify PI into PI
5.780 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.781 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.781 * [taylor]: Taking taylor expansion of (log n) in k
5.781 * [taylor]: Taking taylor expansion of n in k
5.781 * [backup-simplify]: Simplify n into n
5.781 * [backup-simplify]: Simplify (log n) into (log n)
5.781 * [backup-simplify]: Simplify (- 1) into -1
5.782 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.782 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.783 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
5.784 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
5.785 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
5.786 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.787 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.788 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.789 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.790 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.790 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.790 * [backup-simplify]: Simplify (- 0) into 0
5.790 * [backup-simplify]: Simplify (+ 0 0) into 0
5.791 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
5.791 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.792 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.793 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.793 * [taylor]: Taking taylor expansion of 0 in k
5.793 * [backup-simplify]: Simplify 0 into 0
5.793 * [backup-simplify]: Simplify 0 into 0
5.793 * [backup-simplify]: Simplify 0 into 0
5.794 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.795 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.797 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.797 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.797 * [backup-simplify]: Simplify (- 0) into 0
5.797 * [backup-simplify]: Simplify (+ 0 0) into 0
5.798 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
5.799 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.800 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
5.801 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.801 * [taylor]: Taking taylor expansion of 0 in k
5.801 * [backup-simplify]: Simplify 0 into 0
5.801 * [backup-simplify]: Simplify 0 into 0
5.801 * [backup-simplify]: Simplify 0 into 0
5.801 * [backup-simplify]: Simplify 0 into 0
5.802 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.803 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.806 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
5.806 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.806 * [backup-simplify]: Simplify (- 0) into 0
5.807 * [backup-simplify]: Simplify (+ 0 0) into 0
5.807 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
5.808 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.810 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
5.811 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.811 * [taylor]: Taking taylor expansion of 0 in k
5.811 * [backup-simplify]: Simplify 0 into 0
5.812 * [backup-simplify]: Simplify 0 into 0
5.812 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
5.813 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
5.813 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
5.813 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.813 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.813 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.813 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.813 * [taylor]: Taking taylor expansion of 1/2 in k
5.813 * [backup-simplify]: Simplify 1/2 into 1/2
5.813 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.813 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.813 * [taylor]: Taking taylor expansion of k in k
5.813 * [backup-simplify]: Simplify 0 into 0
5.813 * [backup-simplify]: Simplify 1 into 1
5.813 * [backup-simplify]: Simplify (/ 1 1) into 1
5.813 * [taylor]: Taking taylor expansion of 1 in k
5.813 * [backup-simplify]: Simplify 1 into 1
5.813 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.813 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.813 * [taylor]: Taking taylor expansion of -2 in k
5.813 * [backup-simplify]: Simplify -2 into -2
5.813 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.813 * [taylor]: Taking taylor expansion of PI in k
5.813 * [backup-simplify]: Simplify PI into PI
5.813 * [taylor]: Taking taylor expansion of n in k
5.813 * [backup-simplify]: Simplify n into n
5.814 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.814 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.814 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.814 * [backup-simplify]: Simplify (+ 1 0) into 1
5.814 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.814 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.814 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.814 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.815 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.815 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.815 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.815 * [taylor]: Taking taylor expansion of 1/2 in n
5.815 * [backup-simplify]: Simplify 1/2 into 1/2
5.815 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.815 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.815 * [taylor]: Taking taylor expansion of k in n
5.815 * [backup-simplify]: Simplify k into k
5.815 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.815 * [taylor]: Taking taylor expansion of 1 in n
5.815 * [backup-simplify]: Simplify 1 into 1
5.815 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.815 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.815 * [taylor]: Taking taylor expansion of -2 in n
5.815 * [backup-simplify]: Simplify -2 into -2
5.815 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.815 * [taylor]: Taking taylor expansion of PI in n
5.815 * [backup-simplify]: Simplify PI into PI
5.815 * [taylor]: Taking taylor expansion of n in n
5.815 * [backup-simplify]: Simplify 0 into 0
5.815 * [backup-simplify]: Simplify 1 into 1
5.815 * [backup-simplify]: Simplify (/ PI 1) into PI
5.816 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.816 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.816 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.817 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.817 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.818 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.819 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.819 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.819 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.819 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.819 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.819 * [taylor]: Taking taylor expansion of 1/2 in n
5.819 * [backup-simplify]: Simplify 1/2 into 1/2
5.819 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.819 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.819 * [taylor]: Taking taylor expansion of k in n
5.819 * [backup-simplify]: Simplify k into k
5.819 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.819 * [taylor]: Taking taylor expansion of 1 in n
5.819 * [backup-simplify]: Simplify 1 into 1
5.819 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.819 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.819 * [taylor]: Taking taylor expansion of -2 in n
5.819 * [backup-simplify]: Simplify -2 into -2
5.819 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.819 * [taylor]: Taking taylor expansion of PI in n
5.819 * [backup-simplify]: Simplify PI into PI
5.819 * [taylor]: Taking taylor expansion of n in n
5.819 * [backup-simplify]: Simplify 0 into 0
5.819 * [backup-simplify]: Simplify 1 into 1
5.820 * [backup-simplify]: Simplify (/ PI 1) into PI
5.820 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.821 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.821 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.821 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.823 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.824 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.825 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.825 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
5.825 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
5.825 * [taylor]: Taking taylor expansion of 1/2 in k
5.825 * [backup-simplify]: Simplify 1/2 into 1/2
5.825 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
5.825 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.825 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.825 * [taylor]: Taking taylor expansion of k in k
5.825 * [backup-simplify]: Simplify 0 into 0
5.825 * [backup-simplify]: Simplify 1 into 1
5.826 * [backup-simplify]: Simplify (/ 1 1) into 1
5.826 * [taylor]: Taking taylor expansion of 1 in k
5.826 * [backup-simplify]: Simplify 1 into 1
5.826 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
5.826 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
5.826 * [taylor]: Taking taylor expansion of (* -2 PI) in k
5.826 * [taylor]: Taking taylor expansion of -2 in k
5.826 * [backup-simplify]: Simplify -2 into -2
5.826 * [taylor]: Taking taylor expansion of PI in k
5.826 * [backup-simplify]: Simplify PI into PI
5.826 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.827 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.827 * [taylor]: Taking taylor expansion of (log n) in k
5.827 * [taylor]: Taking taylor expansion of n in k
5.827 * [backup-simplify]: Simplify n into n
5.827 * [backup-simplify]: Simplify (log n) into (log n)
5.828 * [backup-simplify]: Simplify (+ 1 0) into 1
5.828 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.829 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
5.830 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
5.831 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
5.833 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.834 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.835 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.836 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.837 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
5.838 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.838 * [backup-simplify]: Simplify (+ 0 0) into 0
5.838 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
5.840 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.841 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
5.842 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.842 * [taylor]: Taking taylor expansion of 0 in k
5.842 * [backup-simplify]: Simplify 0 into 0
5.842 * [backup-simplify]: Simplify 0 into 0
5.842 * [backup-simplify]: Simplify 0 into 0
5.843 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.843 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.845 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
5.845 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.846 * [backup-simplify]: Simplify (+ 0 0) into 0
5.846 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
5.847 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.848 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
5.850 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.850 * [taylor]: Taking taylor expansion of 0 in k
5.850 * [backup-simplify]: Simplify 0 into 0
5.850 * [backup-simplify]: Simplify 0 into 0
5.850 * [backup-simplify]: Simplify 0 into 0
5.850 * [backup-simplify]: Simplify 0 into 0
5.851 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.851 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.855 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
5.855 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.857 * [backup-simplify]: Simplify (+ 0 0) into 0
5.858 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
5.859 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.860 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
5.862 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.862 * [taylor]: Taking taylor expansion of 0 in k
5.862 * [backup-simplify]: Simplify 0 into 0
5.862 * [backup-simplify]: Simplify 0 into 0
5.863 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
5.863 * * * * [progress]: [ 2 / 4 ] generating series at (2 1)
5.863 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
5.863 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0
5.863 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.863 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.863 * [taylor]: Taking taylor expansion of k in k
5.863 * [backup-simplify]: Simplify 0 into 0
5.863 * [backup-simplify]: Simplify 1 into 1
5.864 * [backup-simplify]: Simplify (/ 1 1) into 1
5.864 * [backup-simplify]: Simplify (sqrt 0) into 0
5.865 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.865 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.865 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.865 * [taylor]: Taking taylor expansion of k in k
5.865 * [backup-simplify]: Simplify 0 into 0
5.865 * [backup-simplify]: Simplify 1 into 1
5.865 * [backup-simplify]: Simplify (/ 1 1) into 1
5.865 * [backup-simplify]: Simplify (sqrt 0) into 0
5.866 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.866 * [backup-simplify]: Simplify 0 into 0
5.866 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.867 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.869 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.869 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.870 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.874 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.874 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.874 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
5.874 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
5.874 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0
5.875 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.875 * [taylor]: Taking taylor expansion of k in k
5.875 * [backup-simplify]: Simplify 0 into 0
5.875 * [backup-simplify]: Simplify 1 into 1
5.875 * [backup-simplify]: Simplify (sqrt 0) into 0
5.876 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.877 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.877 * [taylor]: Taking taylor expansion of k in k
5.877 * [backup-simplify]: Simplify 0 into 0
5.877 * [backup-simplify]: Simplify 1 into 1
5.877 * [backup-simplify]: Simplify (sqrt 0) into 0
5.879 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.879 * [backup-simplify]: Simplify 0 into 0
5.879 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.882 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.882 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.886 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.886 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.887 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 k) 3)) (+ (* +nan.0 (pow (/ 1 k) 2)) (* +nan.0 (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
5.887 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k)))
5.887 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0
5.887 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
5.887 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.887 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.887 * [taylor]: Taking taylor expansion of -1 in k
5.887 * [backup-simplify]: Simplify -1 into -1
5.887 * [taylor]: Taking taylor expansion of k in k
5.887 * [backup-simplify]: Simplify 0 into 0
5.887 * [backup-simplify]: Simplify 1 into 1
5.888 * [backup-simplify]: Simplify (/ -1 1) into -1
5.888 * [backup-simplify]: Simplify (sqrt 0) into 0
5.889 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.890 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
5.890 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
5.890 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.890 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.890 * [taylor]: Taking taylor expansion of -1 in k
5.890 * [backup-simplify]: Simplify -1 into -1
5.890 * [taylor]: Taking taylor expansion of k in k
5.890 * [backup-simplify]: Simplify 0 into 0
5.890 * [backup-simplify]: Simplify 1 into 1
5.891 * [backup-simplify]: Simplify (/ -1 1) into -1
5.891 * [backup-simplify]: Simplify (sqrt 0) into 0
5.892 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.893 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
5.893 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.894 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
5.897 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.899 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
5.899 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.900 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.904 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.908 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
5.909 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.910 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
5.910 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1)
5.911 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
5.911 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
5.911 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.911 * [taylor]: Taking taylor expansion of 2 in n
5.911 * [backup-simplify]: Simplify 2 into 2
5.911 * [taylor]: Taking taylor expansion of (* n PI) in n
5.911 * [taylor]: Taking taylor expansion of n in n
5.911 * [backup-simplify]: Simplify 0 into 0
5.911 * [backup-simplify]: Simplify 1 into 1
5.911 * [taylor]: Taking taylor expansion of PI in n
5.911 * [backup-simplify]: Simplify PI into PI
5.911 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.911 * [taylor]: Taking taylor expansion of 2 in n
5.911 * [backup-simplify]: Simplify 2 into 2
5.911 * [taylor]: Taking taylor expansion of (* n PI) in n
5.911 * [taylor]: Taking taylor expansion of n in n
5.911 * [backup-simplify]: Simplify 0 into 0
5.911 * [backup-simplify]: Simplify 1 into 1
5.911 * [taylor]: Taking taylor expansion of PI in n
5.911 * [backup-simplify]: Simplify PI into PI
5.912 * [backup-simplify]: Simplify (* 0 PI) into 0
5.912 * [backup-simplify]: Simplify (* 2 0) into 0
5.912 * [backup-simplify]: Simplify 0 into 0
5.914 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.916 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.916 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.917 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.919 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.919 * [backup-simplify]: Simplify 0 into 0
5.920 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.921 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.921 * [backup-simplify]: Simplify 0 into 0
5.923 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.924 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
5.924 * [backup-simplify]: Simplify 0 into 0
5.926 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.928 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
5.928 * [backup-simplify]: Simplify 0 into 0
5.930 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.932 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
5.932 * [backup-simplify]: Simplify 0 into 0
5.934 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
5.936 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
5.936 * [backup-simplify]: Simplify 0 into 0
5.937 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
5.937 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
5.937 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
5.937 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.937 * [taylor]: Taking taylor expansion of 2 in n
5.937 * [backup-simplify]: Simplify 2 into 2
5.937 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.937 * [taylor]: Taking taylor expansion of PI in n
5.937 * [backup-simplify]: Simplify PI into PI
5.937 * [taylor]: Taking taylor expansion of n in n
5.937 * [backup-simplify]: Simplify 0 into 0
5.938 * [backup-simplify]: Simplify 1 into 1
5.938 * [backup-simplify]: Simplify (/ PI 1) into PI
5.938 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.938 * [taylor]: Taking taylor expansion of 2 in n
5.938 * [backup-simplify]: Simplify 2 into 2
5.938 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.938 * [taylor]: Taking taylor expansion of PI in n
5.938 * [backup-simplify]: Simplify PI into PI
5.938 * [taylor]: Taking taylor expansion of n in n
5.938 * [backup-simplify]: Simplify 0 into 0
5.938 * [backup-simplify]: Simplify 1 into 1
5.939 * [backup-simplify]: Simplify (/ PI 1) into PI
5.939 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.940 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.941 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.942 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.942 * [backup-simplify]: Simplify 0 into 0
5.943 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.944 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.944 * [backup-simplify]: Simplify 0 into 0
5.945 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.946 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.946 * [backup-simplify]: Simplify 0 into 0
5.946 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.948 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.948 * [backup-simplify]: Simplify 0 into 0
5.948 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.949 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.949 * [backup-simplify]: Simplify 0 into 0
5.950 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.951 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.951 * [backup-simplify]: Simplify 0 into 0
5.952 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
5.952 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n))
5.952 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
5.952 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.952 * [taylor]: Taking taylor expansion of -2 in n
5.952 * [backup-simplify]: Simplify -2 into -2
5.952 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.952 * [taylor]: Taking taylor expansion of PI in n
5.952 * [backup-simplify]: Simplify PI into PI
5.952 * [taylor]: Taking taylor expansion of n in n
5.952 * [backup-simplify]: Simplify 0 into 0
5.952 * [backup-simplify]: Simplify 1 into 1
5.953 * [backup-simplify]: Simplify (/ PI 1) into PI
5.953 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.953 * [taylor]: Taking taylor expansion of -2 in n
5.953 * [backup-simplify]: Simplify -2 into -2
5.953 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.953 * [taylor]: Taking taylor expansion of PI in n
5.953 * [backup-simplify]: Simplify PI into PI
5.953 * [taylor]: Taking taylor expansion of n in n
5.953 * [backup-simplify]: Simplify 0 into 0
5.953 * [backup-simplify]: Simplify 1 into 1
5.953 * [backup-simplify]: Simplify (/ PI 1) into PI
5.953 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.954 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.954 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.955 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.955 * [backup-simplify]: Simplify 0 into 0
5.956 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.956 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.956 * [backup-simplify]: Simplify 0 into 0
5.957 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.958 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.958 * [backup-simplify]: Simplify 0 into 0
5.958 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.959 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.959 * [backup-simplify]: Simplify 0 into 0
5.960 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.961 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.961 * [backup-simplify]: Simplify 0 into 0
5.962 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.963 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.963 * [backup-simplify]: Simplify 0 into 0
5.963 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
5.963 * * * * [progress]: [ 4 / 4 ] generating series at (2)
5.964 * [backup-simplify]: Simplify (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
5.964 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0
5.964 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
5.964 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.964 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.964 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.964 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.964 * [taylor]: Taking taylor expansion of 1/2 in n
5.964 * [backup-simplify]: Simplify 1/2 into 1/2
5.964 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.964 * [taylor]: Taking taylor expansion of 1 in n
5.964 * [backup-simplify]: Simplify 1 into 1
5.964 * [taylor]: Taking taylor expansion of k in n
5.964 * [backup-simplify]: Simplify k into k
5.964 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.964 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.964 * [taylor]: Taking taylor expansion of 2 in n
5.964 * [backup-simplify]: Simplify 2 into 2
5.964 * [taylor]: Taking taylor expansion of (* n PI) in n
5.964 * [taylor]: Taking taylor expansion of n in n
5.964 * [backup-simplify]: Simplify 0 into 0
5.964 * [backup-simplify]: Simplify 1 into 1
5.964 * [taylor]: Taking taylor expansion of PI in n
5.964 * [backup-simplify]: Simplify PI into PI
5.964 * [backup-simplify]: Simplify (* 0 PI) into 0
5.965 * [backup-simplify]: Simplify (* 2 0) into 0
5.966 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.967 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.967 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.967 * [backup-simplify]: Simplify (- k) into (- k)
5.967 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.967 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.968 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.969 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.970 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.970 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
5.970 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.970 * [taylor]: Taking taylor expansion of k in n
5.970 * [backup-simplify]: Simplify k into k
5.970 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.970 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
5.970 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.970 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
5.970 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
5.970 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
5.970 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
5.970 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
5.970 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
5.970 * [taylor]: Taking taylor expansion of 1/2 in k
5.970 * [backup-simplify]: Simplify 1/2 into 1/2
5.970 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.970 * [taylor]: Taking taylor expansion of 1 in k
5.970 * [backup-simplify]: Simplify 1 into 1
5.970 * [taylor]: Taking taylor expansion of k in k
5.970 * [backup-simplify]: Simplify 0 into 0
5.970 * [backup-simplify]: Simplify 1 into 1
5.970 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.970 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.970 * [taylor]: Taking taylor expansion of 2 in k
5.970 * [backup-simplify]: Simplify 2 into 2
5.970 * [taylor]: Taking taylor expansion of (* n PI) in k
5.970 * [taylor]: Taking taylor expansion of n in k
5.970 * [backup-simplify]: Simplify n into n
5.970 * [taylor]: Taking taylor expansion of PI in k
5.970 * [backup-simplify]: Simplify PI into PI
5.970 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.970 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.970 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.971 * [backup-simplify]: Simplify (- 0) into 0
5.971 * [backup-simplify]: Simplify (+ 1 0) into 1
5.971 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.971 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.971 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.971 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.971 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.971 * [taylor]: Taking taylor expansion of k in k
5.971 * [backup-simplify]: Simplify 0 into 0
5.972 * [backup-simplify]: Simplify 1 into 1
5.972 * [backup-simplify]: Simplify (/ 1 1) into 1
5.972 * [backup-simplify]: Simplify (sqrt 0) into 0
5.973 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.973 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
5.973 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
5.973 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
5.973 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
5.973 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
5.973 * [taylor]: Taking taylor expansion of 1/2 in k
5.973 * [backup-simplify]: Simplify 1/2 into 1/2
5.973 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.973 * [taylor]: Taking taylor expansion of 1 in k
5.973 * [backup-simplify]: Simplify 1 into 1
5.973 * [taylor]: Taking taylor expansion of k in k
5.973 * [backup-simplify]: Simplify 0 into 0
5.973 * [backup-simplify]: Simplify 1 into 1
5.973 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.973 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.973 * [taylor]: Taking taylor expansion of 2 in k
5.973 * [backup-simplify]: Simplify 2 into 2
5.973 * [taylor]: Taking taylor expansion of (* n PI) in k
5.973 * [taylor]: Taking taylor expansion of n in k
5.973 * [backup-simplify]: Simplify n into n
5.973 * [taylor]: Taking taylor expansion of PI in k
5.973 * [backup-simplify]: Simplify PI into PI
5.973 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.973 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.973 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.974 * [backup-simplify]: Simplify (- 0) into 0
5.974 * [backup-simplify]: Simplify (+ 1 0) into 1
5.974 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.974 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.974 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.974 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.974 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.974 * [taylor]: Taking taylor expansion of k in k
5.974 * [backup-simplify]: Simplify 0 into 0
5.974 * [backup-simplify]: Simplify 1 into 1
5.975 * [backup-simplify]: Simplify (/ 1 1) into 1
5.975 * [backup-simplify]: Simplify (sqrt 0) into 0
5.976 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.976 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0
5.976 * [taylor]: Taking taylor expansion of 0 in n
5.976 * [backup-simplify]: Simplify 0 into 0
5.976 * [backup-simplify]: Simplify 0 into 0
5.976 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
5.977 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
5.978 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
5.978 * [backup-simplify]: Simplify (- 1) into -1
5.978 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.982 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
5.983 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
5.984 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))
5.984 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
5.984 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
5.984 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
5.984 * [taylor]: Taking taylor expansion of +nan.0 in n
5.984 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.984 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
5.984 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.984 * [taylor]: Taking taylor expansion of 2 in n
5.984 * [backup-simplify]: Simplify 2 into 2
5.985 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.985 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.985 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.985 * [taylor]: Taking taylor expansion of (* n PI) in n
5.985 * [taylor]: Taking taylor expansion of n in n
5.985 * [backup-simplify]: Simplify 0 into 0
5.985 * [backup-simplify]: Simplify 1 into 1
5.985 * [taylor]: Taking taylor expansion of PI in n
5.985 * [backup-simplify]: Simplify PI into PI
5.986 * [backup-simplify]: Simplify (* 0 PI) into 0
5.987 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.988 * [backup-simplify]: Simplify (sqrt 0) into 0
5.989 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.989 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
5.990 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.990 * [backup-simplify]: Simplify (- 0) into 0
5.990 * [backup-simplify]: Simplify 0 into 0
5.990 * [backup-simplify]: Simplify 0 into 0
5.991 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.994 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.994 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
5.995 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
5.997 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
5.997 * [backup-simplify]: Simplify (- 0) into 0
5.998 * [backup-simplify]: Simplify (+ 0 0) into 0
5.999 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
6.000 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
6.001 * [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)))
6.001 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))
6.001 * [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
6.001 * [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
6.001 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
6.001 * [taylor]: Taking taylor expansion of +nan.0 in n
6.001 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.001 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
6.002 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
6.002 * [taylor]: Taking taylor expansion of (sqrt 2) in n
6.002 * [taylor]: Taking taylor expansion of 2 in n
6.002 * [backup-simplify]: Simplify 2 into 2
6.002 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
6.003 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
6.003 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
6.003 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.003 * [taylor]: Taking taylor expansion of 2 in n
6.003 * [backup-simplify]: Simplify 2 into 2
6.003 * [taylor]: Taking taylor expansion of (* n PI) in n
6.003 * [taylor]: Taking taylor expansion of n in n
6.003 * [backup-simplify]: Simplify 0 into 0
6.003 * [backup-simplify]: Simplify 1 into 1
6.003 * [taylor]: Taking taylor expansion of PI in n
6.003 * [backup-simplify]: Simplify PI into PI
6.003 * [backup-simplify]: Simplify (* 0 PI) into 0
6.004 * [backup-simplify]: Simplify (* 2 0) into 0
6.005 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.007 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
6.008 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.008 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
6.008 * [taylor]: Taking taylor expansion of (* n PI) in n
6.008 * [taylor]: Taking taylor expansion of n in n
6.008 * [backup-simplify]: Simplify 0 into 0
6.008 * [backup-simplify]: Simplify 1 into 1
6.008 * [taylor]: Taking taylor expansion of PI in n
6.008 * [backup-simplify]: Simplify PI into PI
6.009 * [backup-simplify]: Simplify (* 0 PI) into 0
6.010 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.010 * [backup-simplify]: Simplify (sqrt 0) into 0
6.012 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
6.012 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
6.012 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
6.012 * [taylor]: Taking taylor expansion of +nan.0 in n
6.012 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.012 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
6.012 * [taylor]: Taking taylor expansion of (sqrt 2) in n
6.012 * [taylor]: Taking taylor expansion of 2 in n
6.012 * [backup-simplify]: Simplify 2 into 2
6.013 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
6.013 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
6.013 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
6.013 * [taylor]: Taking taylor expansion of (* n PI) in n
6.013 * [taylor]: Taking taylor expansion of n in n
6.013 * [backup-simplify]: Simplify 0 into 0
6.013 * [backup-simplify]: Simplify 1 into 1
6.013 * [taylor]: Taking taylor expansion of PI in n
6.013 * [backup-simplify]: Simplify PI into PI
6.014 * [backup-simplify]: Simplify (* 0 PI) into 0
6.015 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.016 * [backup-simplify]: Simplify (sqrt 0) into 0
6.017 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
6.019 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.020 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
6.022 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
6.022 * [backup-simplify]: Simplify (* +nan.0 0) into 0
6.023 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
6.023 * [backup-simplify]: Simplify (* +nan.0 0) into 0
6.024 * [backup-simplify]: Simplify (- 0) into 0
6.024 * [backup-simplify]: Simplify (+ 0 0) into 0
6.024 * [backup-simplify]: Simplify (- 0) into 0
6.024 * [backup-simplify]: Simplify 0 into 0
6.028 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
6.033 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
6.035 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
6.037 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
6.037 * [backup-simplify]: Simplify 0 into 0
6.037 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.040 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.040 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.041 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
6.043 * [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
6.043 * [backup-simplify]: Simplify (- 0) into 0
6.043 * [backup-simplify]: Simplify (+ 0 0) into 0
6.044 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
6.045 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
6.046 * [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)))
6.047 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))))
6.047 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n
6.047 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n
6.047 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
6.047 * [taylor]: Taking taylor expansion of +nan.0 in n
6.047 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.047 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
6.047 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
6.047 * [taylor]: Taking taylor expansion of (sqrt 2) in n
6.047 * [taylor]: Taking taylor expansion of 2 in n
6.047 * [backup-simplify]: Simplify 2 into 2
6.047 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
6.048 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
6.048 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
6.048 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.048 * [taylor]: Taking taylor expansion of 2 in n
6.048 * [backup-simplify]: Simplify 2 into 2
6.048 * [taylor]: Taking taylor expansion of (* n PI) in n
6.048 * [taylor]: Taking taylor expansion of n in n
6.048 * [backup-simplify]: Simplify 0 into 0
6.048 * [backup-simplify]: Simplify 1 into 1
6.048 * [taylor]: Taking taylor expansion of PI in n
6.048 * [backup-simplify]: Simplify PI into PI
6.048 * [backup-simplify]: Simplify (* 0 PI) into 0
6.048 * [backup-simplify]: Simplify (* 2 0) into 0
6.049 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.050 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
6.051 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.051 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
6.051 * [taylor]: Taking taylor expansion of (* n PI) in n
6.051 * [taylor]: Taking taylor expansion of n in n
6.051 * [backup-simplify]: Simplify 0 into 0
6.051 * [backup-simplify]: Simplify 1 into 1
6.051 * [taylor]: Taking taylor expansion of PI in n
6.051 * [backup-simplify]: Simplify PI into PI
6.052 * [backup-simplify]: Simplify (* 0 PI) into 0
6.053 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.053 * [backup-simplify]: Simplify (sqrt 0) into 0
6.054 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
6.054 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n
6.054 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n
6.054 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
6.054 * [taylor]: Taking taylor expansion of +nan.0 in n
6.054 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.054 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
6.054 * [taylor]: Taking taylor expansion of (sqrt 2) in n
6.054 * [taylor]: Taking taylor expansion of 2 in n
6.054 * [backup-simplify]: Simplify 2 into 2
6.054 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
6.054 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
6.054 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
6.054 * [taylor]: Taking taylor expansion of (* n PI) in n
6.054 * [taylor]: Taking taylor expansion of n in n
6.054 * [backup-simplify]: Simplify 0 into 0
6.054 * [backup-simplify]: Simplify 1 into 1
6.054 * [taylor]: Taking taylor expansion of PI in n
6.055 * [backup-simplify]: Simplify PI into PI
6.055 * [backup-simplify]: Simplify (* 0 PI) into 0
6.056 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.056 * [backup-simplify]: Simplify (sqrt 0) into 0
6.057 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
6.057 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n
6.057 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
6.057 * [taylor]: Taking taylor expansion of +nan.0 in n
6.058 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.058 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
6.058 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
6.058 * [taylor]: Taking taylor expansion of (sqrt 2) in n
6.058 * [taylor]: Taking taylor expansion of 2 in n
6.058 * [backup-simplify]: Simplify 2 into 2
6.058 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
6.059 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
6.059 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
6.059 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
6.059 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.059 * [taylor]: Taking taylor expansion of 2 in n
6.059 * [backup-simplify]: Simplify 2 into 2
6.059 * [taylor]: Taking taylor expansion of (* n PI) in n
6.059 * [taylor]: Taking taylor expansion of n in n
6.059 * [backup-simplify]: Simplify 0 into 0
6.059 * [backup-simplify]: Simplify 1 into 1
6.059 * [taylor]: Taking taylor expansion of PI in n
6.059 * [backup-simplify]: Simplify PI into PI
6.059 * [backup-simplify]: Simplify (* 0 PI) into 0
6.060 * [backup-simplify]: Simplify (* 2 0) into 0
6.061 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.063 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
6.064 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.066 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.066 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
6.066 * [taylor]: Taking taylor expansion of (* n PI) in n
6.066 * [taylor]: Taking taylor expansion of n in n
6.066 * [backup-simplify]: Simplify 0 into 0
6.066 * [backup-simplify]: Simplify 1 into 1
6.066 * [taylor]: Taking taylor expansion of PI in n
6.066 * [backup-simplify]: Simplify PI into PI
6.066 * [backup-simplify]: Simplify (* 0 PI) into 0
6.068 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.068 * [backup-simplify]: Simplify (sqrt 0) into 0
6.070 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
6.071 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.072 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
6.074 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
6.074 * [backup-simplify]: Simplify (* +nan.0 0) into 0
6.075 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
6.075 * [backup-simplify]: Simplify (* +nan.0 0) into 0
6.077 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.078 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.080 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
6.082 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
6.083 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
6.084 * [backup-simplify]: Simplify (* +nan.0 0) into 0
6.084 * [backup-simplify]: Simplify (- 0) into 0
6.084 * [backup-simplify]: Simplify (+ 0 0) into 0
6.085 * [backup-simplify]: Simplify (- 0) into 0
6.085 * [backup-simplify]: Simplify (+ 0 0) into 0
6.085 * [backup-simplify]: Simplify (- 0) into 0
6.085 * [backup-simplify]: Simplify 0 into 0
6.086 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
6.087 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
6.090 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
6.091 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.093 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
6.095 * [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))))))))
6.102 * [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))))))))
6.108 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
6.114 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
6.118 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
6.128 * [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))))))))))
6.136 * [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)))))))
6.143 * [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)))))))
6.145 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
6.149 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
6.150 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
6.155 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
6.164 * [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))))
6.170 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
6.174 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
6.188 * [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)))))))))))))
6.188 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
6.189 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0
6.189 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
6.189 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
6.189 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
6.189 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
6.189 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
6.189 * [taylor]: Taking taylor expansion of 1/2 in n
6.189 * [backup-simplify]: Simplify 1/2 into 1/2
6.189 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
6.189 * [taylor]: Taking taylor expansion of 1 in n
6.189 * [backup-simplify]: Simplify 1 into 1
6.189 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.189 * [taylor]: Taking taylor expansion of k in n
6.189 * [backup-simplify]: Simplify k into k
6.189 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.189 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
6.189 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.189 * [taylor]: Taking taylor expansion of 2 in n
6.189 * [backup-simplify]: Simplify 2 into 2
6.189 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.189 * [taylor]: Taking taylor expansion of PI in n
6.189 * [backup-simplify]: Simplify PI into PI
6.189 * [taylor]: Taking taylor expansion of n in n
6.189 * [backup-simplify]: Simplify 0 into 0
6.189 * [backup-simplify]: Simplify 1 into 1
6.190 * [backup-simplify]: Simplify (/ PI 1) into PI
6.190 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.191 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.191 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.191 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
6.191 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
6.193 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.194 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
6.195 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
6.195 * [taylor]: Taking taylor expansion of (sqrt k) in n
6.195 * [taylor]: Taking taylor expansion of k in n
6.195 * [backup-simplify]: Simplify k into k
6.195 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
6.195 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
6.195 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
6.195 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
6.195 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
6.195 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
6.195 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
6.196 * [taylor]: Taking taylor expansion of 1/2 in k
6.196 * [backup-simplify]: Simplify 1/2 into 1/2
6.196 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
6.196 * [taylor]: Taking taylor expansion of 1 in k
6.196 * [backup-simplify]: Simplify 1 into 1
6.196 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.196 * [taylor]: Taking taylor expansion of k in k
6.196 * [backup-simplify]: Simplify 0 into 0
6.196 * [backup-simplify]: Simplify 1 into 1
6.196 * [backup-simplify]: Simplify (/ 1 1) into 1
6.196 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
6.196 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
6.196 * [taylor]: Taking taylor expansion of 2 in k
6.196 * [backup-simplify]: Simplify 2 into 2
6.196 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.196 * [taylor]: Taking taylor expansion of PI in k
6.196 * [backup-simplify]: Simplify PI into PI
6.196 * [taylor]: Taking taylor expansion of n in k
6.196 * [backup-simplify]: Simplify n into n
6.196 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.196 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
6.197 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
6.197 * [backup-simplify]: Simplify (- 1) into -1
6.198 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.198 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
6.198 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
6.198 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
6.198 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.198 * [taylor]: Taking taylor expansion of k in k
6.198 * [backup-simplify]: Simplify 0 into 0
6.199 * [backup-simplify]: Simplify 1 into 1
6.199 * [backup-simplify]: Simplify (sqrt 0) into 0
6.200 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.200 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
6.200 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
6.200 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
6.200 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
6.200 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
6.200 * [taylor]: Taking taylor expansion of 1/2 in k
6.200 * [backup-simplify]: Simplify 1/2 into 1/2
6.200 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
6.200 * [taylor]: Taking taylor expansion of 1 in k
6.201 * [backup-simplify]: Simplify 1 into 1
6.201 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.201 * [taylor]: Taking taylor expansion of k in k
6.201 * [backup-simplify]: Simplify 0 into 0
6.201 * [backup-simplify]: Simplify 1 into 1
6.201 * [backup-simplify]: Simplify (/ 1 1) into 1
6.201 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
6.201 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
6.201 * [taylor]: Taking taylor expansion of 2 in k
6.201 * [backup-simplify]: Simplify 2 into 2
6.201 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.201 * [taylor]: Taking taylor expansion of PI in k
6.201 * [backup-simplify]: Simplify PI into PI
6.201 * [taylor]: Taking taylor expansion of n in k
6.201 * [backup-simplify]: Simplify n into n
6.201 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.201 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
6.201 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
6.202 * [backup-simplify]: Simplify (- 1) into -1
6.202 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.203 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
6.203 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
6.203 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
6.203 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.203 * [taylor]: Taking taylor expansion of k in k
6.203 * [backup-simplify]: Simplify 0 into 0
6.203 * [backup-simplify]: Simplify 1 into 1
6.203 * [backup-simplify]: Simplify (sqrt 0) into 0
6.205 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.205 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0
6.205 * [taylor]: Taking taylor expansion of 0 in n
6.205 * [backup-simplify]: Simplify 0 into 0
6.205 * [backup-simplify]: Simplify 0 into 0
6.206 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
6.206 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
6.206 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
6.206 * [taylor]: Taking taylor expansion of +nan.0 in n
6.206 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.206 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
6.206 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
6.206 * [taylor]: Taking taylor expansion of 1/2 in n
6.206 * [backup-simplify]: Simplify 1/2 into 1/2
6.206 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
6.206 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
6.206 * [taylor]: Taking taylor expansion of 1 in n
6.206 * [backup-simplify]: Simplify 1 into 1
6.206 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.206 * [taylor]: Taking taylor expansion of k in n
6.206 * [backup-simplify]: Simplify k into k
6.206 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.206 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
6.206 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.206 * [taylor]: Taking taylor expansion of 2 in n
6.206 * [backup-simplify]: Simplify 2 into 2
6.206 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.206 * [taylor]: Taking taylor expansion of PI in n
6.206 * [backup-simplify]: Simplify PI into PI
6.207 * [taylor]: Taking taylor expansion of n in n
6.207 * [backup-simplify]: Simplify 0 into 0
6.207 * [backup-simplify]: Simplify 1 into 1
6.207 * [backup-simplify]: Simplify (/ PI 1) into PI
6.208 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.209 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.209 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.209 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
6.210 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.211 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
6.212 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
6.213 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
6.214 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
6.214 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
6.215 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
6.215 * [backup-simplify]: Simplify 0 into 0
6.217 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.218 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
6.218 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
6.218 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
6.218 * [taylor]: Taking taylor expansion of +nan.0 in n
6.218 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.218 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
6.218 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
6.218 * [taylor]: Taking taylor expansion of 1/2 in n
6.218 * [backup-simplify]: Simplify 1/2 into 1/2
6.218 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
6.218 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
6.218 * [taylor]: Taking taylor expansion of 1 in n
6.218 * [backup-simplify]: Simplify 1 into 1
6.218 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.218 * [taylor]: Taking taylor expansion of k in n
6.218 * [backup-simplify]: Simplify k into k
6.218 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.218 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
6.218 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.218 * [taylor]: Taking taylor expansion of 2 in n
6.218 * [backup-simplify]: Simplify 2 into 2
6.218 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.218 * [taylor]: Taking taylor expansion of PI in n
6.218 * [backup-simplify]: Simplify PI into PI
6.218 * [taylor]: Taking taylor expansion of n in n
6.218 * [backup-simplify]: Simplify 0 into 0
6.218 * [backup-simplify]: Simplify 1 into 1
6.218 * [backup-simplify]: Simplify (/ PI 1) into PI
6.219 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.219 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.219 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.219 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
6.220 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.221 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
6.222 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
6.223 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
6.223 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
6.224 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
6.225 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
6.226 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.226 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
6.227 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
6.227 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.228 * [backup-simplify]: Simplify (- 0) into 0
6.228 * [backup-simplify]: Simplify (+ 0 0) into 0
6.229 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.229 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
6.230 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
6.232 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.235 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
6.236 * [backup-simplify]: Simplify (- 0) into 0
6.236 * [backup-simplify]: Simplify 0 into 0
6.236 * [backup-simplify]: Simplify 0 into 0
6.238 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.239 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
6.239 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
6.239 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
6.239 * [taylor]: Taking taylor expansion of +nan.0 in n
6.239 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.239 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
6.239 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
6.239 * [taylor]: Taking taylor expansion of 1/2 in n
6.239 * [backup-simplify]: Simplify 1/2 into 1/2
6.239 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
6.239 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
6.239 * [taylor]: Taking taylor expansion of 1 in n
6.239 * [backup-simplify]: Simplify 1 into 1
6.239 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.239 * [taylor]: Taking taylor expansion of k in n
6.239 * [backup-simplify]: Simplify k into k
6.239 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.239 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
6.239 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.239 * [taylor]: Taking taylor expansion of 2 in n
6.239 * [backup-simplify]: Simplify 2 into 2
6.239 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.239 * [taylor]: Taking taylor expansion of PI in n
6.239 * [backup-simplify]: Simplify PI into PI
6.239 * [taylor]: Taking taylor expansion of n in n
6.239 * [backup-simplify]: Simplify 0 into 0
6.239 * [backup-simplify]: Simplify 1 into 1
6.240 * [backup-simplify]: Simplify (/ PI 1) into PI
6.240 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.241 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.241 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.241 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
6.243 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.244 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
6.245 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
6.246 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
6.247 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
6.249 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
6.250 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
6.254 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
6.255 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
6.255 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0
6.255 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
6.255 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
6.255 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
6.255 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
6.255 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
6.255 * [taylor]: Taking taylor expansion of 1/2 in n
6.255 * [backup-simplify]: Simplify 1/2 into 1/2
6.255 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
6.255 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.255 * [taylor]: Taking taylor expansion of k in n
6.255 * [backup-simplify]: Simplify k into k
6.255 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.255 * [taylor]: Taking taylor expansion of 1 in n
6.255 * [backup-simplify]: Simplify 1 into 1
6.255 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.255 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.255 * [taylor]: Taking taylor expansion of -2 in n
6.255 * [backup-simplify]: Simplify -2 into -2
6.255 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.255 * [taylor]: Taking taylor expansion of PI in n
6.256 * [backup-simplify]: Simplify PI into PI
6.256 * [taylor]: Taking taylor expansion of n in n
6.256 * [backup-simplify]: Simplify 0 into 0
6.256 * [backup-simplify]: Simplify 1 into 1
6.256 * [backup-simplify]: Simplify (/ PI 1) into PI
6.257 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.258 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.258 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
6.258 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
6.259 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.260 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
6.262 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
6.262 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
6.262 * [taylor]: Taking taylor expansion of (/ -1 k) in n
6.262 * [taylor]: Taking taylor expansion of -1 in n
6.262 * [backup-simplify]: Simplify -1 into -1
6.262 * [taylor]: Taking taylor expansion of k in n
6.262 * [backup-simplify]: Simplify k into k
6.262 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
6.262 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
6.262 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
6.262 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
6.263 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
6.263 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
6.264 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
6.264 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
6.264 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
6.264 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
6.264 * [taylor]: Taking taylor expansion of 1/2 in k
6.264 * [backup-simplify]: Simplify 1/2 into 1/2
6.264 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
6.264 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.264 * [taylor]: Taking taylor expansion of k in k
6.264 * [backup-simplify]: Simplify 0 into 0
6.264 * [backup-simplify]: Simplify 1 into 1
6.264 * [backup-simplify]: Simplify (/ 1 1) into 1
6.264 * [taylor]: Taking taylor expansion of 1 in k
6.264 * [backup-simplify]: Simplify 1 into 1
6.264 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
6.264 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
6.264 * [taylor]: Taking taylor expansion of -2 in k
6.264 * [backup-simplify]: Simplify -2 into -2
6.264 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.264 * [taylor]: Taking taylor expansion of PI in k
6.264 * [backup-simplify]: Simplify PI into PI
6.264 * [taylor]: Taking taylor expansion of n in k
6.264 * [backup-simplify]: Simplify n into n
6.264 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.265 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
6.265 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
6.265 * [backup-simplify]: Simplify (+ 1 0) into 1
6.266 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
6.266 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
6.266 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
6.266 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.266 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.266 * [taylor]: Taking taylor expansion of -1 in k
6.266 * [backup-simplify]: Simplify -1 into -1
6.266 * [taylor]: Taking taylor expansion of k in k
6.266 * [backup-simplify]: Simplify 0 into 0
6.266 * [backup-simplify]: Simplify 1 into 1
6.266 * [backup-simplify]: Simplify (/ -1 1) into -1
6.267 * [backup-simplify]: Simplify (sqrt 0) into 0
6.268 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.268 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
6.268 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
6.268 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
6.268 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
6.268 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
6.268 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
6.268 * [taylor]: Taking taylor expansion of 1/2 in k
6.268 * [backup-simplify]: Simplify 1/2 into 1/2
6.268 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
6.269 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.269 * [taylor]: Taking taylor expansion of k in k
6.269 * [backup-simplify]: Simplify 0 into 0
6.269 * [backup-simplify]: Simplify 1 into 1
6.269 * [backup-simplify]: Simplify (/ 1 1) into 1
6.269 * [taylor]: Taking taylor expansion of 1 in k
6.269 * [backup-simplify]: Simplify 1 into 1
6.269 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
6.269 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
6.269 * [taylor]: Taking taylor expansion of -2 in k
6.269 * [backup-simplify]: Simplify -2 into -2
6.269 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.269 * [taylor]: Taking taylor expansion of PI in k
6.269 * [backup-simplify]: Simplify PI into PI
6.269 * [taylor]: Taking taylor expansion of n in k
6.269 * [backup-simplify]: Simplify n into n
6.269 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.269 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
6.269 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
6.270 * [backup-simplify]: Simplify (+ 1 0) into 1
6.270 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
6.270 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
6.271 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
6.271 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.271 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.271 * [taylor]: Taking taylor expansion of -1 in k
6.271 * [backup-simplify]: Simplify -1 into -1
6.271 * [taylor]: Taking taylor expansion of k in k
6.271 * [backup-simplify]: Simplify 0 into 0
6.271 * [backup-simplify]: Simplify 1 into 1
6.271 * [backup-simplify]: Simplify (/ -1 1) into -1
6.271 * [backup-simplify]: Simplify (sqrt 0) into 0
6.272 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.273 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
6.273 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
6.273 * [taylor]: Taking taylor expansion of +nan.0 in n
6.273 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.273 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
6.273 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
6.273 * [taylor]: Taking taylor expansion of 1/2 in n
6.273 * [backup-simplify]: Simplify 1/2 into 1/2
6.273 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
6.273 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.273 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.273 * [taylor]: Taking taylor expansion of -2 in n
6.273 * [backup-simplify]: Simplify -2 into -2
6.273 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.273 * [taylor]: Taking taylor expansion of PI in n
6.273 * [backup-simplify]: Simplify PI into PI
6.273 * [taylor]: Taking taylor expansion of n in n
6.273 * [backup-simplify]: Simplify 0 into 0
6.273 * [backup-simplify]: Simplify 1 into 1
6.273 * [backup-simplify]: Simplify (/ PI 1) into PI
6.274 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.274 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.274 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
6.274 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.275 * [taylor]: Taking taylor expansion of k in n
6.275 * [backup-simplify]: Simplify k into k
6.275 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.275 * [taylor]: Taking taylor expansion of 1 in n
6.275 * [backup-simplify]: Simplify 1 into 1
6.275 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.276 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
6.276 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
6.277 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
6.278 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
6.278 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
6.279 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
6.280 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
6.282 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.282 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
6.282 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
6.282 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
6.282 * [taylor]: Taking taylor expansion of +nan.0 in n
6.282 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.282 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
6.282 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
6.282 * [taylor]: Taking taylor expansion of 1/2 in n
6.282 * [backup-simplify]: Simplify 1/2 into 1/2
6.282 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
6.283 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.283 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.283 * [taylor]: Taking taylor expansion of -2 in n
6.283 * [backup-simplify]: Simplify -2 into -2
6.283 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.283 * [taylor]: Taking taylor expansion of PI in n
6.283 * [backup-simplify]: Simplify PI into PI
6.283 * [taylor]: Taking taylor expansion of n in n
6.283 * [backup-simplify]: Simplify 0 into 0
6.283 * [backup-simplify]: Simplify 1 into 1
6.283 * [backup-simplify]: Simplify (/ PI 1) into PI
6.283 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.284 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.284 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
6.284 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.284 * [taylor]: Taking taylor expansion of k in n
6.284 * [backup-simplify]: Simplify k into k
6.284 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.284 * [taylor]: Taking taylor expansion of 1 in n
6.284 * [backup-simplify]: Simplify 1 into 1
6.285 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.285 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
6.286 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
6.287 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
6.288 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
6.289 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
6.290 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
6.290 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
6.291 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.291 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.292 * [backup-simplify]: Simplify (+ 0 0) into 0
6.292 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.293 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
6.294 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
6.295 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
6.296 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
6.297 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.298 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
6.298 * [backup-simplify]: Simplify 0 into 0
6.299 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.302 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.304 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
6.304 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
6.304 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
6.304 * [taylor]: Taking taylor expansion of +nan.0 in n
6.304 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.304 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
6.304 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
6.304 * [taylor]: Taking taylor expansion of 1/2 in n
6.304 * [backup-simplify]: Simplify 1/2 into 1/2
6.304 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
6.304 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.304 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.304 * [taylor]: Taking taylor expansion of -2 in n
6.304 * [backup-simplify]: Simplify -2 into -2
6.304 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.304 * [taylor]: Taking taylor expansion of PI in n
6.304 * [backup-simplify]: Simplify PI into PI
6.304 * [taylor]: Taking taylor expansion of n in n
6.304 * [backup-simplify]: Simplify 0 into 0
6.304 * [backup-simplify]: Simplify 1 into 1
6.305 * [backup-simplify]: Simplify (/ PI 1) into PI
6.305 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.306 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.307 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
6.307 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.307 * [taylor]: Taking taylor expansion of k in n
6.307 * [backup-simplify]: Simplify k into k
6.307 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.307 * [taylor]: Taking taylor expansion of 1 in n
6.307 * [backup-simplify]: Simplify 1 into 1
6.308 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.308 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
6.310 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
6.311 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
6.312 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
6.313 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
6.315 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
6.316 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
6.320 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
6.320 * * * [progress]: simplifying candidates
6.320 * * * * [progress]: [ 1 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
6.320 * * * * [progress]: [ 2 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
6.320 * * * * [progress]: [ 3 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
6.320 * * * * [progress]: [ 4 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
6.321 * * * * [progress]: [ 5 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
6.321 * * * * [progress]: [ 6 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
6.321 * * * * [progress]: [ 7 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
6.321 * * * * [progress]: [ 8 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))>
6.321 * * * * [progress]: [ 9 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2)))))>
6.321 * * * * [progress]: [ 10 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2)))))>
6.321 * * * * [progress]: [ 11 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2)))))>
6.321 * * * * [progress]: [ 12 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2)))))>
6.321 * * * * [progress]: [ 13 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2))))>
6.321 * * * * [progress]: [ 14 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2)))))>
6.321 * * * * [progress]: [ 15 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2)))))>
6.321 * * * * [progress]: [ 16 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2))))>
6.321 * * * * [progress]: [ 17 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
6.321 * * * * [progress]: [ 18 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
6.321 * * * * [progress]: [ 19 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
6.321 * * * * [progress]: [ 20 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2)))))>
6.321 * * * * [progress]: [ 21 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2)))))>
6.322 * * * * [progress]: [ 22 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2))))>
6.322 * * * * [progress]: [ 23 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2)))))>
6.322 * * * * [progress]: [ 24 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2)))))>
6.322 * * * * [progress]: [ 25 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))))>
6.322 * * * * [progress]: [ 26 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
6.322 * * * * [progress]: [ 27 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
6.322 * * * * [progress]: [ 28 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
6.322 * * * * [progress]: [ 29 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
6.322 * * * * [progress]: [ 30 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) (/ 1 2))))>
6.322 * * * * [progress]: [ 31 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))))>
6.322 * * * * [progress]: [ 32 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1)))>
6.322 * * * * [progress]: [ 33 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.322 * * * * [progress]: [ 34 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (log (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.322 * * * * [progress]: [ 35 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.322 * * * * [progress]: [ 36 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (cbrt (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.322 * * * * [progress]: [ 37 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.322 * * * * [progress]: [ 38 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.322 * * * * [progress]: [ 39 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
6.322 * * * * [progress]: [ 40 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.322 * * * * [progress]: [ 41 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.322 * * * * [progress]: [ 42 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) (- 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.322 * * * * [progress]: [ 43 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- (/ 1 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.322 * * * * [progress]: [ 44 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.322 * * * * [progress]: [ 45 / 184 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.322 * * * * [progress]: [ 46 / 184 ] simplifiying candidate #<alt (λ (k n) (* (exp (- 0 (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 47 / 184 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log 1) (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 48 / 184 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 49 / 184 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 50 / 184 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 51 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 52 / 184 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 53 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 54 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (- 1) (- (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 55 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 56 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1) (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 57 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 58 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 59 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 60 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 61 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1) (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 62 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1) (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 63 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 64 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 65 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 66 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 67 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 68 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 69 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 70 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt 1)) (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 71 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.323 * * * * [progress]: [ 72 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 1) (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 73 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 74 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 75 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 76 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 77 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 78 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 79 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt 1)) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 80 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 81 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 82 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (cbrt 1))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 83 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt k) (sqrt 1))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 84 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 85 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 86 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 87 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 88 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (+ (log 2) (log PI)) (log n))) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 89 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (log (* 2 PI)) (log n))) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 90 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (log (* (* 2 PI) n))) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 91 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (log (exp (* (* 2 PI) n))) (/ (- 1 k) 2))))>
6.324 * * * * [progress]: [ 92 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
6.325 * * * * [progress]: [ 93 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
6.325 * * * * [progress]: [ 94 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) (cbrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
6.325 * * * * [progress]: [ 95 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))>
6.325 * * * * [progress]: [ 96 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
6.325 * * * * [progress]: [ 97 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 1 (* (* 2 PI) n)) (/ (- 1 k) 2))))>
6.325 * * * * [progress]: [ 98 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))>
6.325 * * * * [progress]: [ 99 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (- 1 k) 2))))>
6.325 * * * * [progress]: [ 100 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) 1) n) (/ (- 1 k) 2))))>
6.325 * * * * [progress]: [ 101 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))>
6.325 * * * * [progress]: [ 102 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
6.325 * * * * [progress]: [ 103 / 184 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1))>
6.325 * * * * [progress]: [ 104 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
6.325 * * * * [progress]: [ 105 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
6.325 * * * * [progress]: [ 106 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
6.325 * * * * [progress]: [ 107 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
6.325 * * * * [progress]: [ 108 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.325 * * * * [progress]: [ 109 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
6.325 * * * * [progress]: [ 110 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
6.325 * * * * [progress]: [ 111 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
6.325 * * * * [progress]: [ 112 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
6.325 * * * * [progress]: [ 113 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.325 * * * * [progress]: [ 114 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
6.325 * * * * [progress]: [ 115 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
6.325 * * * * [progress]: [ 116 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
6.325 * * * * [progress]: [ 117 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
6.325 * * * * [progress]: [ 118 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 119 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
6.326 * * * * [progress]: [ 120 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
6.326 * * * * [progress]: [ 121 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
6.326 * * * * [progress]: [ 122 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
6.326 * * * * [progress]: [ 123 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 124 / 184 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 125 / 184 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 126 / 184 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 127 / 184 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 128 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 129 / 184 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 130 / 184 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 131 / 184 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))))>
6.326 * * * * [progress]: [ 132 / 184 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.326 * * * * [progress]: [ 133 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 134 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
6.326 * * * * [progress]: [ 135 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 136 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
6.326 * * * * [progress]: [ 137 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 138 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
6.326 * * * * [progress]: [ 139 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 140 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
6.326 * * * * [progress]: [ 141 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
6.326 * * * * [progress]: [ 142 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
6.326 * * * * [progress]: [ 143 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))))>
6.327 * * * * [progress]: [ 144 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 145 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 146 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.327 * * * * [progress]: [ 147 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))>
6.327 * * * * [progress]: [ 148 / 184 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 149 / 184 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 150 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 151 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 152 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 153 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 154 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 155 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) 1) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 156 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 157 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 158 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 159 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt 1)) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 160 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 161 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 162 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 163 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 164 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 165 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 166 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 167 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 168 / 184 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.327 * * * * [progress]: [ 169 / 184 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.328 * * * * [progress]: [ 170 / 184 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* (* 2 PI) n) (/ k 2))))>
6.328 * * * * [progress]: [ 171 / 184 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))>
6.328 * * * * [progress]: [ 172 / 184 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.328 * * * * [progress]: [ 173 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))))>
6.328 * * * * [progress]: [ 174 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))>
6.328 * * * * [progress]: [ 175 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))>
6.328 * * * * [progress]: [ 176 / 184 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.328 * * * * [progress]: [ 177 / 184 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.328 * * * * [progress]: [ 178 / 184 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
6.328 * * * * [progress]: [ 179 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
6.328 * * * * [progress]: [ 180 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
6.328 * * * * [progress]: [ 181 / 184 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
6.328 * * * * [progress]: [ 182 / 184 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))>
6.328 * * * * [progress]: [ 183 / 184 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
6.328 * * * * [progress]: [ 184 / 184 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
6.330 * [simplify]: Simplifying:
  (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2))
  (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))
  (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
  (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* (* 2 PI) n) (/ 1 2))
  (pow (* (* 2 PI) n) (/ k 2))
  (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1))
  (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2 PI) n) (/ 1 1))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1))
  (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2 PI) n) (/ 1 1))
  (pow (* (* 2 PI) n) 1)
  (pow (* (* 2 PI) n) (- 1 k))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
  (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
  (- 1/2)
  (- 1)
  (- (/ 1 2))
  (- (log (sqrt k)))
  (- 0 (log (sqrt k)))
  (- (log 1) (log (sqrt k)))
  (log (/ 1 (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (- 1)
  (- (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1) (cbrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1) (sqrt (cbrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))
  (/ (cbrt 1) (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) 1)
  (/ (cbrt 1) (sqrt k))
  (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1) (cbrt (sqrt k)))
  (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1) (sqrt (cbrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt 1))
  (/ (sqrt 1) (sqrt k))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) 1)
  (/ (sqrt 1) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1)
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ (sqrt k) (cbrt 1))
  (/ (sqrt k) (sqrt 1))
  (/ (sqrt k) 1)
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (+ (+ (log 2) (log PI)) (log n))
  (+ (log (* 2 PI)) (log n))
  (log (* (* 2 PI) n))
  (exp (* (* 2 PI) n))
  (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))
  (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n)))
  (cbrt (* (* 2 PI) n))
  (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (* (* 2 PI) (* (cbrt n) (cbrt n)))
  (* (* 2 PI) (sqrt n))
  (* (* 2 PI) 1)
  (* PI n)
  (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (- (log 1) (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (log (/ 1 (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
  (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* 1 (pow (* (* 2 PI) n) (/ 1 2)))
  (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
  (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt k)) 1)
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2)))
  (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
6.333 * * [simplify]: iteration 1: (341 enodes)
6.527 * * [simplify]: iteration 2: (916 enodes)
7.520 * * [simplify]: Extracting #0: cost 90 inf + 0
7.521 * * [simplify]: Extracting #1: cost 430 inf + 3
7.524 * * [simplify]: Extracting #2: cost 783 inf + 3876
7.534 * * [simplify]: Extracting #3: cost 681 inf + 72515
7.581 * * [simplify]: Extracting #4: cost 353 inf + 199560
7.656 * * [simplify]: Extracting #5: cost 152 inf + 279178
7.749 * * [simplify]: Extracting #6: cost 45 inf + 327363
7.808 * * [simplify]: Extracting #7: cost 12 inf + 341340
7.883 * * [simplify]: Extracting #8: cost 0 inf + 348040
7.979 * * [simplify]: Extracting #9: cost 0 inf + 347560
8.066 * [simplify]: Simplified to:
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt (- 1 k))))
  (pow (* (* PI 2) n) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* (* PI 2) n) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (sqrt (- 1 k)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) 1))
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) 1))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (- 1 k))
  (pow (* PI 2) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) 4))
  (pow (* (* PI 2) n) (/ (- 1 k) 4))
  -1/2
  -1
  -1/2
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ (/ 1 k) (sqrt k))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (/ (/ 1 (sqrt k)) (sqrt k)) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  -1
  (- (sqrt k))
  (* (/ 1 (cbrt (sqrt k))) (/ 1 (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (* (/ 1 (cbrt (sqrt k))) (/ 1 (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (* (/ 1 (cbrt (sqrt k))) (/ 1 (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (sqrt k)
  (* (/ 1 (cbrt (sqrt k))) (/ 1 (cbrt (sqrt k))))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt (sqrt k)))
  1
  (sqrt k)
  (sqrt k)
  (sqrt k)
  (* (* 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))
  (* PI (* 2 (* (cbrt n) (cbrt n))))
  (* (* PI 2) (sqrt n))
  (* PI 2)
  (* PI n)
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (exp (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (/ (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (* (sqrt k) k))
  (* (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (* (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (* (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (* (* PI 2) n))
  (* (sqrt k) (pow (* (* PI 2) n) (/ k 2)))
  (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))
  (* (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k))))
  (* (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k))))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt k))
  (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (/ 1 (sqrt k))))
  (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k))))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (sqrt k))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (- (+ (+ (exp (* 1/2 (log (* (* PI 2) n)))) (+ (* (* (* 1/8 (* (log (* PI 2)) (log (* PI 2)))) (exp (* 1/2 (log (* (* PI 2) n))))) (* k k)) (* (* (exp (* 1/2 (log (* (* PI 2) n)))) (* (log n) (log n))) (* (* k k) 1/8)))) (* (* (* 1/4 (log (* PI 2))) (* (* k k) (log n))) (exp (* 1/2 (log (* (* PI 2) n)))))) (* 1/2 (* k (+ (* (log n) (exp (* 1/2 (log (* (* PI 2) n))))) (* (exp (* 1/2 (log (* (* PI 2) n)))) (log (* PI 2)))))))
  (exp (* (* 1/2 (log (* (* PI 2) n))) (- 1 k)))
  (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n)))))
  (- (* (- +nan.0) (* k k)) (+ (- +nan.0) (* k +nan.0)))
  (+ (- (/ +nan.0 (* k k))) (- (/ +nan.0 k) (/ +nan.0 (* k (* k k)))))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) +nan.0))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
  (+ (* (* (sqrt 2) (* k (* PI n))) (- +nan.0)) (+ (- (* (* +nan.0 (sqrt 2)) (* PI n)) (* (* (sqrt 2) (* k (* PI n))) (* +nan.0 (log (* PI 2))))) (* (* +nan.0 (sqrt 2)) (- (* (* k (log n)) (* PI n)) (* (* n PI) (* n PI))))))
  (- (+ (- (* +nan.0 (/ (exp (* (* 1/2 (log (* (* PI 2) n))) (- 1 k))) k)) (* (/ (exp (* (* 1/2 (log (* (* PI 2) n))) (- 1 k))) (* k k)) +nan.0)) (* (/ +nan.0 k) (/ (exp (* (* 1/2 (log (* (* PI 2) n))) (- 1 k))) (* k k)))))
  (+ (* (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) k) (- +nan.0)) (* +nan.0 (- (/ (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) k) k) (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))))))
8.081 * * * [progress]: adding candidates to table
10.124 * * [progress]: iteration 3 / 4
10.124 * * * [progress]: picking best candidate
10.175 * * * * [pick]: Picked  #<alt (λ (k n) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
10.176 * * * [progress]: localizing error
10.206 * * * [progress]: generating rewritten candidates
10.206 * * * * [progress]: [ 1 / 3 ] rewriting at (2 2)
10.223 * * * * [progress]: [ 2 / 3 ] rewriting at (2 2 1)
10.248 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
10.269 * * * [progress]: generating series expansions
10.269 * * * * [progress]: [ 1 / 3 ] generating series at (2 2)
10.269 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
10.269 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
10.269 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
10.269 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
10.269 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
10.270 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
10.270 * [taylor]: Taking taylor expansion of 1/2 in k
10.270 * [backup-simplify]: Simplify 1/2 into 1/2
10.270 * [taylor]: Taking taylor expansion of (- 1 k) in k
10.270 * [taylor]: Taking taylor expansion of 1 in k
10.270 * [backup-simplify]: Simplify 1 into 1
10.270 * [taylor]: Taking taylor expansion of k in k
10.270 * [backup-simplify]: Simplify 0 into 0
10.270 * [backup-simplify]: Simplify 1 into 1
10.270 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
10.270 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
10.270 * [taylor]: Taking taylor expansion of 2 in k
10.270 * [backup-simplify]: Simplify 2 into 2
10.270 * [taylor]: Taking taylor expansion of (* n PI) in k
10.270 * [taylor]: Taking taylor expansion of n in k
10.270 * [backup-simplify]: Simplify n into n
10.270 * [taylor]: Taking taylor expansion of PI in k
10.270 * [backup-simplify]: Simplify PI into PI
10.270 * [backup-simplify]: Simplify (* n PI) into (* n PI)
10.270 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
10.270 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
10.270 * [backup-simplify]: Simplify (- 0) into 0
10.270 * [backup-simplify]: Simplify (+ 1 0) into 1
10.271 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
10.271 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
10.271 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
10.271 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
10.271 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
10.271 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
10.271 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
10.271 * [taylor]: Taking taylor expansion of 1/2 in n
10.271 * [backup-simplify]: Simplify 1/2 into 1/2
10.271 * [taylor]: Taking taylor expansion of (- 1 k) in n
10.271 * [taylor]: Taking taylor expansion of 1 in n
10.271 * [backup-simplify]: Simplify 1 into 1
10.271 * [taylor]: Taking taylor expansion of k in n
10.271 * [backup-simplify]: Simplify k into k
10.271 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
10.271 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
10.271 * [taylor]: Taking taylor expansion of 2 in n
10.271 * [backup-simplify]: Simplify 2 into 2
10.271 * [taylor]: Taking taylor expansion of (* n PI) in n
10.271 * [taylor]: Taking taylor expansion of n in n
10.271 * [backup-simplify]: Simplify 0 into 0
10.271 * [backup-simplify]: Simplify 1 into 1
10.271 * [taylor]: Taking taylor expansion of PI in n
10.271 * [backup-simplify]: Simplify PI into PI
10.272 * [backup-simplify]: Simplify (* 0 PI) into 0
10.272 * [backup-simplify]: Simplify (* 2 0) into 0
10.273 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.274 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
10.274 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.274 * [backup-simplify]: Simplify (- k) into (- k)
10.274 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
10.275 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
10.275 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.276 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
10.277 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
10.277 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
10.277 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
10.277 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
10.277 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
10.277 * [taylor]: Taking taylor expansion of 1/2 in n
10.277 * [backup-simplify]: Simplify 1/2 into 1/2
10.277 * [taylor]: Taking taylor expansion of (- 1 k) in n
10.277 * [taylor]: Taking taylor expansion of 1 in n
10.277 * [backup-simplify]: Simplify 1 into 1
10.277 * [taylor]: Taking taylor expansion of k in n
10.277 * [backup-simplify]: Simplify k into k
10.277 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
10.277 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
10.277 * [taylor]: Taking taylor expansion of 2 in n
10.277 * [backup-simplify]: Simplify 2 into 2
10.277 * [taylor]: Taking taylor expansion of (* n PI) in n
10.277 * [taylor]: Taking taylor expansion of n in n
10.277 * [backup-simplify]: Simplify 0 into 0
10.277 * [backup-simplify]: Simplify 1 into 1
10.277 * [taylor]: Taking taylor expansion of PI in n
10.277 * [backup-simplify]: Simplify PI into PI
10.278 * [backup-simplify]: Simplify (* 0 PI) into 0
10.278 * [backup-simplify]: Simplify (* 2 0) into 0
10.279 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.280 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
10.281 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.281 * [backup-simplify]: Simplify (- k) into (- k)
10.281 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
10.281 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
10.282 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.282 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
10.283 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
10.283 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
10.283 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
10.283 * [taylor]: Taking taylor expansion of 1/2 in k
10.283 * [backup-simplify]: Simplify 1/2 into 1/2
10.283 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
10.283 * [taylor]: Taking taylor expansion of (- 1 k) in k
10.283 * [taylor]: Taking taylor expansion of 1 in k
10.283 * [backup-simplify]: Simplify 1 into 1
10.284 * [taylor]: Taking taylor expansion of k in k
10.284 * [backup-simplify]: Simplify 0 into 0
10.284 * [backup-simplify]: Simplify 1 into 1
10.284 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
10.284 * [taylor]: Taking taylor expansion of (log n) in k
10.284 * [taylor]: Taking taylor expansion of n in k
10.284 * [backup-simplify]: Simplify n into n
10.284 * [backup-simplify]: Simplify (log n) into (log n)
10.284 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
10.284 * [taylor]: Taking taylor expansion of (* 2 PI) in k
10.284 * [taylor]: Taking taylor expansion of 2 in k
10.284 * [backup-simplify]: Simplify 2 into 2
10.284 * [taylor]: Taking taylor expansion of PI in k
10.284 * [backup-simplify]: Simplify PI into PI
10.284 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.285 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.286 * [backup-simplify]: Simplify (- 0) into 0
10.286 * [backup-simplify]: Simplify (+ 1 0) into 1
10.287 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.292 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
10.293 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
10.294 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
10.295 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
10.296 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
10.297 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
10.299 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
10.300 * [backup-simplify]: Simplify (- 0) into 0
10.300 * [backup-simplify]: Simplify (+ 0 0) into 0
10.301 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
10.302 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.303 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
10.305 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
10.305 * [taylor]: Taking taylor expansion of 0 in k
10.305 * [backup-simplify]: Simplify 0 into 0
10.305 * [backup-simplify]: Simplify 0 into 0
10.306 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
10.307 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
10.309 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
10.309 * [backup-simplify]: Simplify (+ 0 0) into 0
10.309 * [backup-simplify]: Simplify (- 1) into -1
10.310 * [backup-simplify]: Simplify (+ 0 -1) into -1
10.311 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
10.313 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
10.317 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
10.320 * [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)))))))
10.321 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
10.322 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
10.326 * [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
10.326 * [backup-simplify]: Simplify (- 0) into 0
10.327 * [backup-simplify]: Simplify (+ 0 0) into 0
10.327 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
10.329 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.330 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
10.333 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
10.333 * [taylor]: Taking taylor expansion of 0 in k
10.333 * [backup-simplify]: Simplify 0 into 0
10.333 * [backup-simplify]: Simplify 0 into 0
10.333 * [backup-simplify]: Simplify 0 into 0
10.334 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
10.336 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
10.339 * [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
10.340 * [backup-simplify]: Simplify (+ 0 0) into 0
10.340 * [backup-simplify]: Simplify (- 0) into 0
10.341 * [backup-simplify]: Simplify (+ 0 0) into 0
10.343 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
10.345 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
10.350 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
10.355 * [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)))))
10.365 * [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)))))
10.366 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
10.366 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
10.366 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
10.366 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
10.366 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
10.366 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
10.366 * [taylor]: Taking taylor expansion of 1/2 in k
10.367 * [backup-simplify]: Simplify 1/2 into 1/2
10.367 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
10.367 * [taylor]: Taking taylor expansion of 1 in k
10.367 * [backup-simplify]: Simplify 1 into 1
10.367 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.367 * [taylor]: Taking taylor expansion of k in k
10.367 * [backup-simplify]: Simplify 0 into 0
10.367 * [backup-simplify]: Simplify 1 into 1
10.367 * [backup-simplify]: Simplify (/ 1 1) into 1
10.367 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
10.367 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
10.367 * [taylor]: Taking taylor expansion of 2 in k
10.367 * [backup-simplify]: Simplify 2 into 2
10.367 * [taylor]: Taking taylor expansion of (/ PI n) in k
10.367 * [taylor]: Taking taylor expansion of PI in k
10.367 * [backup-simplify]: Simplify PI into PI
10.367 * [taylor]: Taking taylor expansion of n in k
10.367 * [backup-simplify]: Simplify n into n
10.367 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
10.367 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
10.368 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
10.368 * [backup-simplify]: Simplify (- 1) into -1
10.368 * [backup-simplify]: Simplify (+ 0 -1) into -1
10.369 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
10.369 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
10.369 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
10.369 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
10.369 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
10.369 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
10.369 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
10.369 * [taylor]: Taking taylor expansion of 1/2 in n
10.369 * [backup-simplify]: Simplify 1/2 into 1/2
10.369 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
10.369 * [taylor]: Taking taylor expansion of 1 in n
10.369 * [backup-simplify]: Simplify 1 into 1
10.369 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.369 * [taylor]: Taking taylor expansion of k in n
10.369 * [backup-simplify]: Simplify k into k
10.369 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.370 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
10.370 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
10.370 * [taylor]: Taking taylor expansion of 2 in n
10.370 * [backup-simplify]: Simplify 2 into 2
10.370 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.370 * [taylor]: Taking taylor expansion of PI in n
10.370 * [backup-simplify]: Simplify PI into PI
10.370 * [taylor]: Taking taylor expansion of n in n
10.370 * [backup-simplify]: Simplify 0 into 0
10.370 * [backup-simplify]: Simplify 1 into 1
10.370 * [backup-simplify]: Simplify (/ PI 1) into PI
10.371 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.372 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.372 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
10.372 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
10.372 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
10.374 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.375 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
10.376 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
10.376 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
10.376 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
10.376 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
10.376 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
10.376 * [taylor]: Taking taylor expansion of 1/2 in n
10.376 * [backup-simplify]: Simplify 1/2 into 1/2
10.376 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
10.376 * [taylor]: Taking taylor expansion of 1 in n
10.376 * [backup-simplify]: Simplify 1 into 1
10.376 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.376 * [taylor]: Taking taylor expansion of k in n
10.376 * [backup-simplify]: Simplify k into k
10.376 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.376 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
10.376 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
10.376 * [taylor]: Taking taylor expansion of 2 in n
10.377 * [backup-simplify]: Simplify 2 into 2
10.377 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.377 * [taylor]: Taking taylor expansion of PI in n
10.377 * [backup-simplify]: Simplify PI into PI
10.377 * [taylor]: Taking taylor expansion of n in n
10.377 * [backup-simplify]: Simplify 0 into 0
10.377 * [backup-simplify]: Simplify 1 into 1
10.377 * [backup-simplify]: Simplify (/ PI 1) into PI
10.378 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.379 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.379 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
10.379 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
10.379 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
10.380 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.382 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
10.383 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
10.383 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
10.383 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
10.383 * [taylor]: Taking taylor expansion of 1/2 in k
10.383 * [backup-simplify]: Simplify 1/2 into 1/2
10.383 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
10.383 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
10.383 * [taylor]: Taking taylor expansion of 1 in k
10.383 * [backup-simplify]: Simplify 1 into 1
10.383 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.383 * [taylor]: Taking taylor expansion of k in k
10.383 * [backup-simplify]: Simplify 0 into 0
10.383 * [backup-simplify]: Simplify 1 into 1
10.384 * [backup-simplify]: Simplify (/ 1 1) into 1
10.384 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
10.384 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
10.384 * [taylor]: Taking taylor expansion of (* 2 PI) in k
10.384 * [taylor]: Taking taylor expansion of 2 in k
10.384 * [backup-simplify]: Simplify 2 into 2
10.384 * [taylor]: Taking taylor expansion of PI in k
10.384 * [backup-simplify]: Simplify PI into PI
10.384 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.385 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.385 * [taylor]: Taking taylor expansion of (log n) in k
10.385 * [taylor]: Taking taylor expansion of n in k
10.385 * [backup-simplify]: Simplify n into n
10.385 * [backup-simplify]: Simplify (log n) into (log n)
10.386 * [backup-simplify]: Simplify (- 1) into -1
10.386 * [backup-simplify]: Simplify (+ 0 -1) into -1
10.386 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
10.387 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
10.388 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
10.390 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
10.391 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
10.392 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
10.393 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
10.394 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
10.396 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
10.396 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
10.396 * [backup-simplify]: Simplify (- 0) into 0
10.397 * [backup-simplify]: Simplify (+ 0 0) into 0
10.397 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
10.398 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.400 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
10.402 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
10.402 * [taylor]: Taking taylor expansion of 0 in k
10.402 * [backup-simplify]: Simplify 0 into 0
10.402 * [backup-simplify]: Simplify 0 into 0
10.402 * [backup-simplify]: Simplify 0 into 0
10.403 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.405 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
10.408 * [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
10.408 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
10.408 * [backup-simplify]: Simplify (- 0) into 0
10.409 * [backup-simplify]: Simplify (+ 0 0) into 0
10.410 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
10.411 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.413 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
10.415 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
10.415 * [taylor]: Taking taylor expansion of 0 in k
10.415 * [backup-simplify]: Simplify 0 into 0
10.415 * [backup-simplify]: Simplify 0 into 0
10.415 * [backup-simplify]: Simplify 0 into 0
10.416 * [backup-simplify]: Simplify 0 into 0
10.417 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.418 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
10.423 * [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
10.424 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
10.424 * [backup-simplify]: Simplify (- 0) into 0
10.425 * [backup-simplify]: Simplify (+ 0 0) into 0
10.426 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
10.427 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.429 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
10.432 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
10.432 * [taylor]: Taking taylor expansion of 0 in k
10.432 * [backup-simplify]: Simplify 0 into 0
10.432 * [backup-simplify]: Simplify 0 into 0
10.436 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
10.436 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
10.436 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
10.436 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
10.436 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
10.436 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
10.436 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
10.436 * [taylor]: Taking taylor expansion of 1/2 in k
10.436 * [backup-simplify]: Simplify 1/2 into 1/2
10.436 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
10.436 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.436 * [taylor]: Taking taylor expansion of k in k
10.436 * [backup-simplify]: Simplify 0 into 0
10.436 * [backup-simplify]: Simplify 1 into 1
10.436 * [backup-simplify]: Simplify (/ 1 1) into 1
10.436 * [taylor]: Taking taylor expansion of 1 in k
10.437 * [backup-simplify]: Simplify 1 into 1
10.437 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
10.437 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
10.437 * [taylor]: Taking taylor expansion of -2 in k
10.437 * [backup-simplify]: Simplify -2 into -2
10.437 * [taylor]: Taking taylor expansion of (/ PI n) in k
10.437 * [taylor]: Taking taylor expansion of PI in k
10.437 * [backup-simplify]: Simplify PI into PI
10.437 * [taylor]: Taking taylor expansion of n in k
10.437 * [backup-simplify]: Simplify n into n
10.437 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
10.437 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
10.437 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
10.437 * [backup-simplify]: Simplify (+ 1 0) into 1
10.437 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
10.437 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
10.438 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
10.438 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
10.438 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
10.438 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
10.438 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
10.438 * [taylor]: Taking taylor expansion of 1/2 in n
10.438 * [backup-simplify]: Simplify 1/2 into 1/2
10.438 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
10.438 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.438 * [taylor]: Taking taylor expansion of k in n
10.438 * [backup-simplify]: Simplify k into k
10.438 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.438 * [taylor]: Taking taylor expansion of 1 in n
10.438 * [backup-simplify]: Simplify 1 into 1
10.438 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
10.438 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
10.438 * [taylor]: Taking taylor expansion of -2 in n
10.438 * [backup-simplify]: Simplify -2 into -2
10.438 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.438 * [taylor]: Taking taylor expansion of PI in n
10.438 * [backup-simplify]: Simplify PI into PI
10.438 * [taylor]: Taking taylor expansion of n in n
10.438 * [backup-simplify]: Simplify 0 into 0
10.438 * [backup-simplify]: Simplify 1 into 1
10.438 * [backup-simplify]: Simplify (/ PI 1) into PI
10.439 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
10.439 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
10.439 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
10.439 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
10.440 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.441 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
10.442 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
10.442 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
10.442 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
10.442 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
10.442 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
10.442 * [taylor]: Taking taylor expansion of 1/2 in n
10.442 * [backup-simplify]: Simplify 1/2 into 1/2
10.442 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
10.442 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.442 * [taylor]: Taking taylor expansion of k in n
10.442 * [backup-simplify]: Simplify k into k
10.442 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.442 * [taylor]: Taking taylor expansion of 1 in n
10.442 * [backup-simplify]: Simplify 1 into 1
10.442 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
10.442 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
10.442 * [taylor]: Taking taylor expansion of -2 in n
10.442 * [backup-simplify]: Simplify -2 into -2
10.442 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.442 * [taylor]: Taking taylor expansion of PI in n
10.442 * [backup-simplify]: Simplify PI into PI
10.442 * [taylor]: Taking taylor expansion of n in n
10.442 * [backup-simplify]: Simplify 0 into 0
10.442 * [backup-simplify]: Simplify 1 into 1
10.442 * [backup-simplify]: Simplify (/ PI 1) into PI
10.443 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
10.443 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
10.443 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
10.444 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
10.444 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.445 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
10.446 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
10.446 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
10.446 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
10.446 * [taylor]: Taking taylor expansion of 1/2 in k
10.446 * [backup-simplify]: Simplify 1/2 into 1/2
10.446 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
10.446 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
10.446 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.446 * [taylor]: Taking taylor expansion of k in k
10.446 * [backup-simplify]: Simplify 0 into 0
10.446 * [backup-simplify]: Simplify 1 into 1
10.446 * [backup-simplify]: Simplify (/ 1 1) into 1
10.446 * [taylor]: Taking taylor expansion of 1 in k
10.446 * [backup-simplify]: Simplify 1 into 1
10.446 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
10.446 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
10.446 * [taylor]: Taking taylor expansion of (* -2 PI) in k
10.447 * [taylor]: Taking taylor expansion of -2 in k
10.447 * [backup-simplify]: Simplify -2 into -2
10.447 * [taylor]: Taking taylor expansion of PI in k
10.447 * [backup-simplify]: Simplify PI into PI
10.447 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
10.447 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
10.448 * [taylor]: Taking taylor expansion of (log n) in k
10.448 * [taylor]: Taking taylor expansion of n in k
10.448 * [backup-simplify]: Simplify n into n
10.448 * [backup-simplify]: Simplify (log n) into (log n)
10.448 * [backup-simplify]: Simplify (+ 1 0) into 1
10.448 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
10.449 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
10.449 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
10.450 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
10.451 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
10.451 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
10.452 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
10.452 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
10.453 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
10.454 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
10.454 * [backup-simplify]: Simplify (+ 0 0) into 0
10.454 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
10.455 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.456 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
10.457 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
10.457 * [taylor]: Taking taylor expansion of 0 in k
10.457 * [backup-simplify]: Simplify 0 into 0
10.457 * [backup-simplify]: Simplify 0 into 0
10.457 * [backup-simplify]: Simplify 0 into 0
10.458 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.458 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
10.460 * [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
10.460 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
10.461 * [backup-simplify]: Simplify (+ 0 0) into 0
10.461 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
10.462 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.463 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
10.465 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
10.465 * [taylor]: Taking taylor expansion of 0 in k
10.465 * [backup-simplify]: Simplify 0 into 0
10.465 * [backup-simplify]: Simplify 0 into 0
10.465 * [backup-simplify]: Simplify 0 into 0
10.465 * [backup-simplify]: Simplify 0 into 0
10.465 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.466 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
10.469 * [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
10.470 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
10.470 * [backup-simplify]: Simplify (+ 0 0) into 0
10.471 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
10.471 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.473 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
10.474 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
10.474 * [taylor]: Taking taylor expansion of 0 in k
10.474 * [backup-simplify]: Simplify 0 into 0
10.474 * [backup-simplify]: Simplify 0 into 0
10.475 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
10.475 * * * * [progress]: [ 2 / 3 ] generating series at (2 2 1)
10.476 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
10.476 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
10.476 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
10.476 * [taylor]: Taking taylor expansion of 2 in n
10.476 * [backup-simplify]: Simplify 2 into 2
10.476 * [taylor]: Taking taylor expansion of (* n PI) in n
10.476 * [taylor]: Taking taylor expansion of n in n
10.476 * [backup-simplify]: Simplify 0 into 0
10.476 * [backup-simplify]: Simplify 1 into 1
10.476 * [taylor]: Taking taylor expansion of PI in n
10.476 * [backup-simplify]: Simplify PI into PI
10.476 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
10.476 * [taylor]: Taking taylor expansion of 2 in n
10.476 * [backup-simplify]: Simplify 2 into 2
10.476 * [taylor]: Taking taylor expansion of (* n PI) in n
10.476 * [taylor]: Taking taylor expansion of n in n
10.476 * [backup-simplify]: Simplify 0 into 0
10.476 * [backup-simplify]: Simplify 1 into 1
10.476 * [taylor]: Taking taylor expansion of PI in n
10.476 * [backup-simplify]: Simplify PI into PI
10.476 * [backup-simplify]: Simplify (* 0 PI) into 0
10.476 * [backup-simplify]: Simplify (* 2 0) into 0
10.476 * [backup-simplify]: Simplify 0 into 0
10.477 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.478 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
10.479 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.479 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
10.480 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
10.480 * [backup-simplify]: Simplify 0 into 0
10.481 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
10.481 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
10.481 * [backup-simplify]: Simplify 0 into 0
10.482 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
10.483 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
10.483 * [backup-simplify]: Simplify 0 into 0
10.484 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
10.485 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
10.485 * [backup-simplify]: Simplify 0 into 0
10.486 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
10.487 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
10.487 * [backup-simplify]: Simplify 0 into 0
10.488 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
10.490 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
10.490 * [backup-simplify]: Simplify 0 into 0
10.490 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
10.491 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
10.491 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
10.491 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
10.491 * [taylor]: Taking taylor expansion of 2 in n
10.491 * [backup-simplify]: Simplify 2 into 2
10.491 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.491 * [taylor]: Taking taylor expansion of PI in n
10.491 * [backup-simplify]: Simplify PI into PI
10.491 * [taylor]: Taking taylor expansion of n in n
10.491 * [backup-simplify]: Simplify 0 into 0
10.491 * [backup-simplify]: Simplify 1 into 1
10.492 * [backup-simplify]: Simplify (/ PI 1) into PI
10.492 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
10.492 * [taylor]: Taking taylor expansion of 2 in n
10.492 * [backup-simplify]: Simplify 2 into 2
10.492 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.492 * [taylor]: Taking taylor expansion of PI in n
10.492 * [backup-simplify]: Simplify PI into PI
10.492 * [taylor]: Taking taylor expansion of n in n
10.492 * [backup-simplify]: Simplify 0 into 0
10.492 * [backup-simplify]: Simplify 1 into 1
10.492 * [backup-simplify]: Simplify (/ PI 1) into PI
10.493 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.493 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.494 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
10.495 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
10.495 * [backup-simplify]: Simplify 0 into 0
10.496 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.498 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
10.498 * [backup-simplify]: Simplify 0 into 0
10.499 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.500 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
10.500 * [backup-simplify]: Simplify 0 into 0
10.502 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.503 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
10.503 * [backup-simplify]: Simplify 0 into 0
10.505 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.506 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
10.506 * [backup-simplify]: Simplify 0 into 0
10.507 * [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
10.509 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
10.509 * [backup-simplify]: Simplify 0 into 0
10.510 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
10.511 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n))
10.511 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
10.511 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
10.511 * [taylor]: Taking taylor expansion of -2 in n
10.511 * [backup-simplify]: Simplify -2 into -2
10.511 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.511 * [taylor]: Taking taylor expansion of PI in n
10.511 * [backup-simplify]: Simplify PI into PI
10.511 * [taylor]: Taking taylor expansion of n in n
10.511 * [backup-simplify]: Simplify 0 into 0
10.511 * [backup-simplify]: Simplify 1 into 1
10.512 * [backup-simplify]: Simplify (/ PI 1) into PI
10.512 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
10.512 * [taylor]: Taking taylor expansion of -2 in n
10.512 * [backup-simplify]: Simplify -2 into -2
10.512 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.512 * [taylor]: Taking taylor expansion of PI in n
10.512 * [backup-simplify]: Simplify PI into PI
10.512 * [taylor]: Taking taylor expansion of n in n
10.512 * [backup-simplify]: Simplify 0 into 0
10.512 * [backup-simplify]: Simplify 1 into 1
10.512 * [backup-simplify]: Simplify (/ PI 1) into PI
10.513 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
10.513 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
10.514 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
10.515 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
10.515 * [backup-simplify]: Simplify 0 into 0
10.516 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.517 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
10.517 * [backup-simplify]: Simplify 0 into 0
10.519 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.520 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
10.520 * [backup-simplify]: Simplify 0 into 0
10.521 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.523 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
10.523 * [backup-simplify]: Simplify 0 into 0
10.524 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.526 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
10.526 * [backup-simplify]: Simplify 0 into 0
10.527 * [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
10.529 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
10.529 * [backup-simplify]: Simplify 0 into 0
10.529 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
10.529 * * * * [progress]: [ 3 / 3 ] generating series at (2)
10.530 * [backup-simplify]: Simplify (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
10.530 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0
10.530 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
10.530 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
10.530 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
10.530 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
10.530 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
10.530 * [taylor]: Taking taylor expansion of 1/2 in n
10.530 * [backup-simplify]: Simplify 1/2 into 1/2
10.530 * [taylor]: Taking taylor expansion of (- 1 k) in n
10.530 * [taylor]: Taking taylor expansion of 1 in n
10.530 * [backup-simplify]: Simplify 1 into 1
10.530 * [taylor]: Taking taylor expansion of k in n
10.530 * [backup-simplify]: Simplify k into k
10.530 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
10.530 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
10.530 * [taylor]: Taking taylor expansion of 2 in n
10.530 * [backup-simplify]: Simplify 2 into 2
10.530 * [taylor]: Taking taylor expansion of (* n PI) in n
10.530 * [taylor]: Taking taylor expansion of n in n
10.530 * [backup-simplify]: Simplify 0 into 0
10.531 * [backup-simplify]: Simplify 1 into 1
10.531 * [taylor]: Taking taylor expansion of PI in n
10.531 * [backup-simplify]: Simplify PI into PI
10.531 * [backup-simplify]: Simplify (* 0 PI) into 0
10.531 * [backup-simplify]: Simplify (* 2 0) into 0
10.533 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.534 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
10.535 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.535 * [backup-simplify]: Simplify (- k) into (- k)
10.535 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
10.536 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
10.537 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.538 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
10.539 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
10.539 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
10.539 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.539 * [taylor]: Taking taylor expansion of k in n
10.539 * [backup-simplify]: Simplify k into k
10.539 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.539 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
10.539 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
10.539 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
10.540 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
10.540 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
10.540 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
10.540 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
10.540 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
10.540 * [taylor]: Taking taylor expansion of 1/2 in k
10.540 * [backup-simplify]: Simplify 1/2 into 1/2
10.540 * [taylor]: Taking taylor expansion of (- 1 k) in k
10.540 * [taylor]: Taking taylor expansion of 1 in k
10.540 * [backup-simplify]: Simplify 1 into 1
10.540 * [taylor]: Taking taylor expansion of k in k
10.540 * [backup-simplify]: Simplify 0 into 0
10.540 * [backup-simplify]: Simplify 1 into 1
10.540 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
10.540 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
10.540 * [taylor]: Taking taylor expansion of 2 in k
10.540 * [backup-simplify]: Simplify 2 into 2
10.540 * [taylor]: Taking taylor expansion of (* n PI) in k
10.540 * [taylor]: Taking taylor expansion of n in k
10.540 * [backup-simplify]: Simplify n into n
10.540 * [taylor]: Taking taylor expansion of PI in k
10.540 * [backup-simplify]: Simplify PI into PI
10.540 * [backup-simplify]: Simplify (* n PI) into (* n PI)
10.540 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
10.540 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
10.541 * [backup-simplify]: Simplify (- 0) into 0
10.541 * [backup-simplify]: Simplify (+ 1 0) into 1
10.541 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
10.542 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
10.542 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
10.542 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
10.542 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.542 * [taylor]: Taking taylor expansion of k in k
10.542 * [backup-simplify]: Simplify 0 into 0
10.542 * [backup-simplify]: Simplify 1 into 1
10.542 * [backup-simplify]: Simplify (/ 1 1) into 1
10.542 * [backup-simplify]: Simplify (sqrt 0) into 0
10.544 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
10.544 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
10.544 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
10.544 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
10.544 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
10.544 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
10.544 * [taylor]: Taking taylor expansion of 1/2 in k
10.544 * [backup-simplify]: Simplify 1/2 into 1/2
10.544 * [taylor]: Taking taylor expansion of (- 1 k) in k
10.544 * [taylor]: Taking taylor expansion of 1 in k
10.544 * [backup-simplify]: Simplify 1 into 1
10.544 * [taylor]: Taking taylor expansion of k in k
10.544 * [backup-simplify]: Simplify 0 into 0
10.544 * [backup-simplify]: Simplify 1 into 1
10.544 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
10.544 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
10.544 * [taylor]: Taking taylor expansion of 2 in k
10.544 * [backup-simplify]: Simplify 2 into 2
10.544 * [taylor]: Taking taylor expansion of (* n PI) in k
10.544 * [taylor]: Taking taylor expansion of n in k
10.544 * [backup-simplify]: Simplify n into n
10.544 * [taylor]: Taking taylor expansion of PI in k
10.544 * [backup-simplify]: Simplify PI into PI
10.544 * [backup-simplify]: Simplify (* n PI) into (* n PI)
10.545 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
10.545 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
10.545 * [backup-simplify]: Simplify (- 0) into 0
10.545 * [backup-simplify]: Simplify (+ 1 0) into 1
10.546 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
10.546 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
10.546 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
10.546 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
10.546 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.546 * [taylor]: Taking taylor expansion of k in k
10.546 * [backup-simplify]: Simplify 0 into 0
10.546 * [backup-simplify]: Simplify 1 into 1
10.546 * [backup-simplify]: Simplify (/ 1 1) into 1
10.550 * [backup-simplify]: Simplify (sqrt 0) into 0
10.552 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
10.552 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0
10.552 * [taylor]: Taking taylor expansion of 0 in n
10.552 * [backup-simplify]: Simplify 0 into 0
10.552 * [backup-simplify]: Simplify 0 into 0
10.553 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
10.553 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
10.554 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
10.554 * [backup-simplify]: Simplify (- 1) into -1
10.555 * [backup-simplify]: Simplify (+ 0 -1) into -1
10.556 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
10.556 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
10.557 * [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)))))
10.557 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
10.557 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
10.557 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
10.557 * [taylor]: Taking taylor expansion of +nan.0 in n
10.557 * [backup-simplify]: Simplify +nan.0 into +nan.0
10.557 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
10.557 * [taylor]: Taking taylor expansion of (sqrt 2) in n
10.557 * [taylor]: Taking taylor expansion of 2 in n
10.557 * [backup-simplify]: Simplify 2 into 2
10.557 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
10.558 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
10.558 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
10.558 * [taylor]: Taking taylor expansion of (* n PI) in n
10.558 * [taylor]: Taking taylor expansion of n in n
10.558 * [backup-simplify]: Simplify 0 into 0
10.558 * [backup-simplify]: Simplify 1 into 1
10.558 * [taylor]: Taking taylor expansion of PI in n
10.558 * [backup-simplify]: Simplify PI into PI
10.559 * [backup-simplify]: Simplify (* 0 PI) into 0
10.560 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.561 * [backup-simplify]: Simplify (sqrt 0) into 0
10.563 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
10.563 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
10.564 * [backup-simplify]: Simplify (* +nan.0 0) into 0
10.564 * [backup-simplify]: Simplify (- 0) into 0
10.564 * [backup-simplify]: Simplify 0 into 0
10.564 * [backup-simplify]: Simplify 0 into 0
10.565 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
10.568 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
10.568 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
10.569 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
10.571 * [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
10.571 * [backup-simplify]: Simplify (- 0) into 0
10.572 * [backup-simplify]: Simplify (+ 0 0) into 0
10.573 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
10.574 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
10.575 * [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)))
10.575 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))
10.575 * [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
10.575 * [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
10.575 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
10.575 * [taylor]: Taking taylor expansion of +nan.0 in n
10.575 * [backup-simplify]: Simplify +nan.0 into +nan.0
10.576 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
10.576 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
10.576 * [taylor]: Taking taylor expansion of (sqrt 2) in n
10.576 * [taylor]: Taking taylor expansion of 2 in n
10.576 * [backup-simplify]: Simplify 2 into 2
10.576 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
10.577 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
10.577 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
10.577 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
10.577 * [taylor]: Taking taylor expansion of 2 in n
10.577 * [backup-simplify]: Simplify 2 into 2
10.577 * [taylor]: Taking taylor expansion of (* n PI) in n
10.577 * [taylor]: Taking taylor expansion of n in n
10.577 * [backup-simplify]: Simplify 0 into 0
10.577 * [backup-simplify]: Simplify 1 into 1
10.577 * [taylor]: Taking taylor expansion of PI in n
10.577 * [backup-simplify]: Simplify PI into PI
10.577 * [backup-simplify]: Simplify (* 0 PI) into 0
10.578 * [backup-simplify]: Simplify (* 2 0) into 0
10.579 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.581 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
10.582 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.582 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
10.582 * [taylor]: Taking taylor expansion of (* n PI) in n
10.582 * [taylor]: Taking taylor expansion of n in n
10.582 * [backup-simplify]: Simplify 0 into 0
10.582 * [backup-simplify]: Simplify 1 into 1
10.582 * [taylor]: Taking taylor expansion of PI in n
10.582 * [backup-simplify]: Simplify PI into PI
10.583 * [backup-simplify]: Simplify (* 0 PI) into 0
10.584 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.585 * [backup-simplify]: Simplify (sqrt 0) into 0
10.586 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
10.586 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
10.586 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
10.586 * [taylor]: Taking taylor expansion of +nan.0 in n
10.586 * [backup-simplify]: Simplify +nan.0 into +nan.0
10.586 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
10.586 * [taylor]: Taking taylor expansion of (sqrt 2) in n
10.586 * [taylor]: Taking taylor expansion of 2 in n
10.586 * [backup-simplify]: Simplify 2 into 2
10.587 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
10.587 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
10.587 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
10.587 * [taylor]: Taking taylor expansion of (* n PI) in n
10.587 * [taylor]: Taking taylor expansion of n in n
10.587 * [backup-simplify]: Simplify 0 into 0
10.587 * [backup-simplify]: Simplify 1 into 1
10.587 * [taylor]: Taking taylor expansion of PI in n
10.587 * [backup-simplify]: Simplify PI into PI
10.588 * [backup-simplify]: Simplify (* 0 PI) into 0
10.589 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.590 * [backup-simplify]: Simplify (sqrt 0) into 0
10.591 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
10.593 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.594 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
10.596 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
10.596 * [backup-simplify]: Simplify (* +nan.0 0) into 0
10.597 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
10.597 * [backup-simplify]: Simplify (* +nan.0 0) into 0
10.597 * [backup-simplify]: Simplify (- 0) into 0
10.598 * [backup-simplify]: Simplify (+ 0 0) into 0
10.598 * [backup-simplify]: Simplify (- 0) into 0
10.598 * [backup-simplify]: Simplify 0 into 0
10.601 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
10.606 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
10.610 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
10.613 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
10.613 * [backup-simplify]: Simplify 0 into 0
10.614 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.617 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
10.618 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
10.619 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
10.622 * [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
10.623 * [backup-simplify]: Simplify (- 0) into 0
10.623 * [backup-simplify]: Simplify (+ 0 0) into 0
10.624 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
10.626 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
10.627 * [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)))
10.628 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))))
10.628 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n
10.628 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n
10.628 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
10.628 * [taylor]: Taking taylor expansion of +nan.0 in n
10.628 * [backup-simplify]: Simplify +nan.0 into +nan.0
10.628 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
10.628 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
10.628 * [taylor]: Taking taylor expansion of (sqrt 2) in n
10.628 * [taylor]: Taking taylor expansion of 2 in n
10.628 * [backup-simplify]: Simplify 2 into 2
10.629 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
10.629 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
10.629 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
10.629 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
10.629 * [taylor]: Taking taylor expansion of 2 in n
10.629 * [backup-simplify]: Simplify 2 into 2
10.629 * [taylor]: Taking taylor expansion of (* n PI) in n
10.629 * [taylor]: Taking taylor expansion of n in n
10.629 * [backup-simplify]: Simplify 0 into 0
10.629 * [backup-simplify]: Simplify 1 into 1
10.629 * [taylor]: Taking taylor expansion of PI in n
10.629 * [backup-simplify]: Simplify PI into PI
10.630 * [backup-simplify]: Simplify (* 0 PI) into 0
10.630 * [backup-simplify]: Simplify (* 2 0) into 0
10.631 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.632 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
10.632 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.632 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
10.632 * [taylor]: Taking taylor expansion of (* n PI) in n
10.632 * [taylor]: Taking taylor expansion of n in n
10.632 * [backup-simplify]: Simplify 0 into 0
10.632 * [backup-simplify]: Simplify 1 into 1
10.632 * [taylor]: Taking taylor expansion of PI in n
10.632 * [backup-simplify]: Simplify PI into PI
10.633 * [backup-simplify]: Simplify (* 0 PI) into 0
10.634 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.634 * [backup-simplify]: Simplify (sqrt 0) into 0
10.635 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
10.635 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n
10.635 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n
10.635 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
10.635 * [taylor]: Taking taylor expansion of +nan.0 in n
10.635 * [backup-simplify]: Simplify +nan.0 into +nan.0
10.635 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
10.635 * [taylor]: Taking taylor expansion of (sqrt 2) in n
10.635 * [taylor]: Taking taylor expansion of 2 in n
10.635 * [backup-simplify]: Simplify 2 into 2
10.635 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
10.635 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
10.636 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
10.636 * [taylor]: Taking taylor expansion of (* n PI) in n
10.636 * [taylor]: Taking taylor expansion of n in n
10.636 * [backup-simplify]: Simplify 0 into 0
10.636 * [backup-simplify]: Simplify 1 into 1
10.636 * [taylor]: Taking taylor expansion of PI in n
10.636 * [backup-simplify]: Simplify PI into PI
10.636 * [backup-simplify]: Simplify (* 0 PI) into 0
10.637 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.637 * [backup-simplify]: Simplify (sqrt 0) into 0
10.638 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
10.638 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n
10.638 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
10.638 * [taylor]: Taking taylor expansion of +nan.0 in n
10.638 * [backup-simplify]: Simplify +nan.0 into +nan.0
10.638 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
10.638 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
10.638 * [taylor]: Taking taylor expansion of (sqrt 2) in n
10.638 * [taylor]: Taking taylor expansion of 2 in n
10.638 * [backup-simplify]: Simplify 2 into 2
10.638 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
10.639 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
10.639 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
10.639 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
10.639 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
10.639 * [taylor]: Taking taylor expansion of 2 in n
10.639 * [backup-simplify]: Simplify 2 into 2
10.639 * [taylor]: Taking taylor expansion of (* n PI) in n
10.639 * [taylor]: Taking taylor expansion of n in n
10.639 * [backup-simplify]: Simplify 0 into 0
10.639 * [backup-simplify]: Simplify 1 into 1
10.639 * [taylor]: Taking taylor expansion of PI in n
10.639 * [backup-simplify]: Simplify PI into PI
10.639 * [backup-simplify]: Simplify (* 0 PI) into 0
10.639 * [backup-simplify]: Simplify (* 2 0) into 0
10.640 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.641 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
10.642 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.643 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.643 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
10.643 * [taylor]: Taking taylor expansion of (* n PI) in n
10.643 * [taylor]: Taking taylor expansion of n in n
10.643 * [backup-simplify]: Simplify 0 into 0
10.643 * [backup-simplify]: Simplify 1 into 1
10.643 * [taylor]: Taking taylor expansion of PI in n
10.643 * [backup-simplify]: Simplify PI into PI
10.643 * [backup-simplify]: Simplify (* 0 PI) into 0
10.644 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.645 * [backup-simplify]: Simplify (sqrt 0) into 0
10.646 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
10.646 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.647 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
10.648 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
10.649 * [backup-simplify]: Simplify (* +nan.0 0) into 0
10.649 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
10.649 * [backup-simplify]: Simplify (* +nan.0 0) into 0
10.650 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.652 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.653 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
10.654 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
10.655 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
10.655 * [backup-simplify]: Simplify (* +nan.0 0) into 0
10.655 * [backup-simplify]: Simplify (- 0) into 0
10.656 * [backup-simplify]: Simplify (+ 0 0) into 0
10.656 * [backup-simplify]: Simplify (- 0) into 0
10.656 * [backup-simplify]: Simplify (+ 0 0) into 0
10.656 * [backup-simplify]: Simplify (- 0) into 0
10.656 * [backup-simplify]: Simplify 0 into 0
10.657 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
10.658 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
10.659 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
10.659 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.660 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
10.662 * [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))))))))
10.669 * [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))))))))
10.671 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
10.675 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
10.677 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
10.682 * [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))))))))))
10.687 * [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)))))))
10.692 * [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)))))))
10.693 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
10.695 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
10.696 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
10.699 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
10.705 * [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))))
10.709 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
10.713 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
10.721 * [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)))))))))))))
10.722 * [backup-simplify]: Simplify (* (pow (/ 1 k) -1/2) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
10.722 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0
10.722 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
10.722 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
10.722 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
10.722 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
10.722 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
10.722 * [taylor]: Taking taylor expansion of 1/2 in n
10.722 * [backup-simplify]: Simplify 1/2 into 1/2
10.722 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
10.722 * [taylor]: Taking taylor expansion of 1 in n
10.722 * [backup-simplify]: Simplify 1 into 1
10.722 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.722 * [taylor]: Taking taylor expansion of k in n
10.722 * [backup-simplify]: Simplify k into k
10.722 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.722 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
10.722 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
10.722 * [taylor]: Taking taylor expansion of 2 in n
10.722 * [backup-simplify]: Simplify 2 into 2
10.722 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.722 * [taylor]: Taking taylor expansion of PI in n
10.722 * [backup-simplify]: Simplify PI into PI
10.722 * [taylor]: Taking taylor expansion of n in n
10.722 * [backup-simplify]: Simplify 0 into 0
10.722 * [backup-simplify]: Simplify 1 into 1
10.723 * [backup-simplify]: Simplify (/ PI 1) into PI
10.723 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.724 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.724 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
10.724 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
10.724 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
10.725 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.725 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
10.726 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
10.726 * [taylor]: Taking taylor expansion of (sqrt k) in n
10.726 * [taylor]: Taking taylor expansion of k in n
10.726 * [backup-simplify]: Simplify k into k
10.726 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
10.726 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
10.726 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
10.726 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
10.726 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
10.726 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
10.726 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
10.726 * [taylor]: Taking taylor expansion of 1/2 in k
10.726 * [backup-simplify]: Simplify 1/2 into 1/2
10.727 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
10.727 * [taylor]: Taking taylor expansion of 1 in k
10.727 * [backup-simplify]: Simplify 1 into 1
10.727 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.727 * [taylor]: Taking taylor expansion of k in k
10.727 * [backup-simplify]: Simplify 0 into 0
10.727 * [backup-simplify]: Simplify 1 into 1
10.727 * [backup-simplify]: Simplify (/ 1 1) into 1
10.727 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
10.727 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
10.727 * [taylor]: Taking taylor expansion of 2 in k
10.727 * [backup-simplify]: Simplify 2 into 2
10.727 * [taylor]: Taking taylor expansion of (/ PI n) in k
10.727 * [taylor]: Taking taylor expansion of PI in k
10.727 * [backup-simplify]: Simplify PI into PI
10.727 * [taylor]: Taking taylor expansion of n in k
10.727 * [backup-simplify]: Simplify n into n
10.727 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
10.727 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
10.727 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
10.727 * [backup-simplify]: Simplify (- 1) into -1
10.728 * [backup-simplify]: Simplify (+ 0 -1) into -1
10.728 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
10.728 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
10.728 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
10.728 * [taylor]: Taking taylor expansion of (sqrt k) in k
10.728 * [taylor]: Taking taylor expansion of k in k
10.728 * [backup-simplify]: Simplify 0 into 0
10.728 * [backup-simplify]: Simplify 1 into 1
10.728 * [backup-simplify]: Simplify (sqrt 0) into 0
10.729 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
10.729 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
10.729 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
10.729 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
10.729 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
10.729 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
10.729 * [taylor]: Taking taylor expansion of 1/2 in k
10.729 * [backup-simplify]: Simplify 1/2 into 1/2
10.729 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
10.729 * [taylor]: Taking taylor expansion of 1 in k
10.729 * [backup-simplify]: Simplify 1 into 1
10.729 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.730 * [taylor]: Taking taylor expansion of k in k
10.730 * [backup-simplify]: Simplify 0 into 0
10.730 * [backup-simplify]: Simplify 1 into 1
10.730 * [backup-simplify]: Simplify (/ 1 1) into 1
10.730 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
10.730 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
10.730 * [taylor]: Taking taylor expansion of 2 in k
10.730 * [backup-simplify]: Simplify 2 into 2
10.730 * [taylor]: Taking taylor expansion of (/ PI n) in k
10.730 * [taylor]: Taking taylor expansion of PI in k
10.730 * [backup-simplify]: Simplify PI into PI
10.730 * [taylor]: Taking taylor expansion of n in k
10.730 * [backup-simplify]: Simplify n into n
10.730 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
10.730 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
10.730 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
10.730 * [backup-simplify]: Simplify (- 1) into -1
10.731 * [backup-simplify]: Simplify (+ 0 -1) into -1
10.731 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
10.731 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
10.731 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
10.731 * [taylor]: Taking taylor expansion of (sqrt k) in k
10.731 * [taylor]: Taking taylor expansion of k in k
10.731 * [backup-simplify]: Simplify 0 into 0
10.731 * [backup-simplify]: Simplify 1 into 1
10.731 * [backup-simplify]: Simplify (sqrt 0) into 0
10.732 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
10.732 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0
10.732 * [taylor]: Taking taylor expansion of 0 in n
10.732 * [backup-simplify]: Simplify 0 into 0
10.732 * [backup-simplify]: Simplify 0 into 0
10.733 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
10.733 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
10.733 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
10.733 * [taylor]: Taking taylor expansion of +nan.0 in n
10.733 * [backup-simplify]: Simplify +nan.0 into +nan.0
10.733 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
10.733 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
10.733 * [taylor]: Taking taylor expansion of 1/2 in n
10.733 * [backup-simplify]: Simplify 1/2 into 1/2
10.733 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
10.733 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
10.733 * [taylor]: Taking taylor expansion of 1 in n
10.733 * [backup-simplify]: Simplify 1 into 1
10.733 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.733 * [taylor]: Taking taylor expansion of k in n
10.733 * [backup-simplify]: Simplify k into k
10.733 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.733 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
10.733 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
10.733 * [taylor]: Taking taylor expansion of 2 in n
10.733 * [backup-simplify]: Simplify 2 into 2
10.733 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.733 * [taylor]: Taking taylor expansion of PI in n
10.733 * [backup-simplify]: Simplify PI into PI
10.733 * [taylor]: Taking taylor expansion of n in n
10.733 * [backup-simplify]: Simplify 0 into 0
10.733 * [backup-simplify]: Simplify 1 into 1
10.734 * [backup-simplify]: Simplify (/ PI 1) into PI
10.734 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.735 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.735 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
10.735 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
10.736 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.737 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
10.737 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
10.738 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
10.739 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
10.739 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
10.740 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
10.740 * [backup-simplify]: Simplify 0 into 0
10.742 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
10.743 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
10.743 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
10.743 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
10.743 * [taylor]: Taking taylor expansion of +nan.0 in n
10.743 * [backup-simplify]: Simplify +nan.0 into +nan.0
10.743 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
10.743 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
10.743 * [taylor]: Taking taylor expansion of 1/2 in n
10.743 * [backup-simplify]: Simplify 1/2 into 1/2
10.743 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
10.743 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
10.743 * [taylor]: Taking taylor expansion of 1 in n
10.743 * [backup-simplify]: Simplify 1 into 1
10.743 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.743 * [taylor]: Taking taylor expansion of k in n
10.743 * [backup-simplify]: Simplify k into k
10.743 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.743 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
10.743 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
10.743 * [taylor]: Taking taylor expansion of 2 in n
10.743 * [backup-simplify]: Simplify 2 into 2
10.743 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.743 * [taylor]: Taking taylor expansion of PI in n
10.743 * [backup-simplify]: Simplify PI into PI
10.743 * [taylor]: Taking taylor expansion of n in n
10.743 * [backup-simplify]: Simplify 0 into 0
10.743 * [backup-simplify]: Simplify 1 into 1
10.743 * [backup-simplify]: Simplify (/ PI 1) into PI
10.744 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.744 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.744 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
10.745 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
10.745 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.746 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
10.747 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
10.748 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
10.748 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
10.749 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
10.750 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
10.750 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
10.751 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
10.752 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
10.752 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
10.752 * [backup-simplify]: Simplify (- 0) into 0
10.753 * [backup-simplify]: Simplify (+ 0 0) into 0
10.753 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.754 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
10.758 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
10.759 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
10.760 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
10.761 * [backup-simplify]: Simplify (- 0) into 0
10.761 * [backup-simplify]: Simplify 0 into 0
10.761 * [backup-simplify]: Simplify 0 into 0
10.763 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
10.764 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
10.764 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
10.764 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
10.764 * [taylor]: Taking taylor expansion of +nan.0 in n
10.764 * [backup-simplify]: Simplify +nan.0 into +nan.0
10.764 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
10.764 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
10.764 * [taylor]: Taking taylor expansion of 1/2 in n
10.764 * [backup-simplify]: Simplify 1/2 into 1/2
10.764 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
10.764 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
10.764 * [taylor]: Taking taylor expansion of 1 in n
10.764 * [backup-simplify]: Simplify 1 into 1
10.764 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.764 * [taylor]: Taking taylor expansion of k in n
10.764 * [backup-simplify]: Simplify k into k
10.764 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.764 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
10.764 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
10.764 * [taylor]: Taking taylor expansion of 2 in n
10.764 * [backup-simplify]: Simplify 2 into 2
10.764 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.764 * [taylor]: Taking taylor expansion of PI in n
10.764 * [backup-simplify]: Simplify PI into PI
10.764 * [taylor]: Taking taylor expansion of n in n
10.764 * [backup-simplify]: Simplify 0 into 0
10.764 * [backup-simplify]: Simplify 1 into 1
10.765 * [backup-simplify]: Simplify (/ PI 1) into PI
10.765 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.766 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.766 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
10.767 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
10.768 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.769 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
10.770 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
10.771 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
10.772 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
10.774 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
10.775 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
10.778 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
10.779 * [backup-simplify]: Simplify (* (pow (/ 1 (- k)) -1/2) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))))
10.779 * [approximate]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in (k n) around 0
10.779 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in n
10.779 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in n
10.779 * [taylor]: Taking taylor expansion of (/ k -1) in n
10.779 * [taylor]: Taking taylor expansion of k in n
10.779 * [backup-simplify]: Simplify k into k
10.779 * [taylor]: Taking taylor expansion of -1 in n
10.779 * [backup-simplify]: Simplify -1 into -1
10.779 * [backup-simplify]: Simplify (/ k -1) into (* -1 k)
10.779 * [backup-simplify]: Simplify (sqrt (* -1 k)) into (sqrt (* -1 k))
10.780 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* (* -1 k) (/ 0 -1)))) into 0
10.780 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* -1 k)))) into 0
10.780 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
10.780 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
10.780 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
10.780 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
10.780 * [taylor]: Taking taylor expansion of 1/2 in n
10.780 * [backup-simplify]: Simplify 1/2 into 1/2
10.780 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
10.780 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.780 * [taylor]: Taking taylor expansion of k in n
10.780 * [backup-simplify]: Simplify k into k
10.780 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.780 * [taylor]: Taking taylor expansion of 1 in n
10.780 * [backup-simplify]: Simplify 1 into 1
10.780 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
10.780 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
10.780 * [taylor]: Taking taylor expansion of -2 in n
10.780 * [backup-simplify]: Simplify -2 into -2
10.780 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.780 * [taylor]: Taking taylor expansion of PI in n
10.780 * [backup-simplify]: Simplify PI into PI
10.780 * [taylor]: Taking taylor expansion of n in n
10.780 * [backup-simplify]: Simplify 0 into 0
10.780 * [backup-simplify]: Simplify 1 into 1
10.780 * [backup-simplify]: Simplify (/ PI 1) into PI
10.781 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
10.781 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
10.781 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
10.782 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
10.782 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.783 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
10.784 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
10.784 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k
10.784 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in k
10.784 * [taylor]: Taking taylor expansion of (/ k -1) in k
10.784 * [taylor]: Taking taylor expansion of k in k
10.784 * [backup-simplify]: Simplify 0 into 0
10.784 * [backup-simplify]: Simplify 1 into 1
10.784 * [taylor]: Taking taylor expansion of -1 in k
10.784 * [backup-simplify]: Simplify -1 into -1
10.784 * [backup-simplify]: Simplify (/ 1 -1) into -1
10.785 * [backup-simplify]: Simplify (sqrt 0) into 0
10.786 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
10.786 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
10.786 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
10.786 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
10.786 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
10.786 * [taylor]: Taking taylor expansion of 1/2 in k
10.786 * [backup-simplify]: Simplify 1/2 into 1/2
10.786 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
10.786 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.786 * [taylor]: Taking taylor expansion of k in k
10.786 * [backup-simplify]: Simplify 0 into 0
10.786 * [backup-simplify]: Simplify 1 into 1
10.786 * [backup-simplify]: Simplify (/ 1 1) into 1
10.786 * [taylor]: Taking taylor expansion of 1 in k
10.786 * [backup-simplify]: Simplify 1 into 1
10.786 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
10.786 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
10.786 * [taylor]: Taking taylor expansion of -2 in k
10.786 * [backup-simplify]: Simplify -2 into -2
10.786 * [taylor]: Taking taylor expansion of (/ PI n) in k
10.786 * [taylor]: Taking taylor expansion of PI in k
10.786 * [backup-simplify]: Simplify PI into PI
10.786 * [taylor]: Taking taylor expansion of n in k
10.786 * [backup-simplify]: Simplify n into n
10.786 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
10.786 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
10.786 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
10.787 * [backup-simplify]: Simplify (+ 1 0) into 1
10.787 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
10.787 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
10.787 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
10.787 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k
10.787 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in k
10.787 * [taylor]: Taking taylor expansion of (/ k -1) in k
10.787 * [taylor]: Taking taylor expansion of k in k
10.787 * [backup-simplify]: Simplify 0 into 0
10.787 * [backup-simplify]: Simplify 1 into 1
10.787 * [taylor]: Taking taylor expansion of -1 in k
10.787 * [backup-simplify]: Simplify -1 into -1
10.787 * [backup-simplify]: Simplify (/ 1 -1) into -1
10.788 * [backup-simplify]: Simplify (sqrt 0) into 0
10.788 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
10.789 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
10.789 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
10.789 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
10.789 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
10.789 * [taylor]: Taking taylor expansion of 1/2 in k
10.789 * [backup-simplify]: Simplify 1/2 into 1/2
10.789 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
10.789 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.789 * [taylor]: Taking taylor expansion of k in k
10.789 * [backup-simplify]: Simplify 0 into 0
10.789 * [backup-simplify]: Simplify 1 into 1
10.789 * [backup-simplify]: Simplify (/ 1 1) into 1
10.789 * [taylor]: Taking taylor expansion of 1 in k
10.789 * [backup-simplify]: Simplify 1 into 1
10.789 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
10.789 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
10.789 * [taylor]: Taking taylor expansion of -2 in k
10.789 * [backup-simplify]: Simplify -2 into -2
10.789 * [taylor]: Taking taylor expansion of (/ PI n) in k
10.789 * [taylor]: Taking taylor expansion of PI in k
10.789 * [backup-simplify]: Simplify PI into PI
10.789 * [taylor]: Taking taylor expansion of n in k
10.789 * [backup-simplify]: Simplify n into n
10.789 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
10.789 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
10.789 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
10.789 * [backup-simplify]: Simplify (+ 1 0) into 1
10.790 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
10.790 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
10.790 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
10.790 * [backup-simplify]: Simplify (* 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into 0
10.790 * [taylor]: Taking taylor expansion of 0 in n
10.790 * [backup-simplify]: Simplify 0 into 0
10.790 * [backup-simplify]: Simplify 0 into 0
10.791 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
10.791 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
10.791 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
10.791 * [taylor]: Taking taylor expansion of +nan.0 in n
10.791 * [backup-simplify]: Simplify +nan.0 into +nan.0
10.791 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
10.791 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
10.791 * [taylor]: Taking taylor expansion of 1/2 in n
10.791 * [backup-simplify]: Simplify 1/2 into 1/2
10.791 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
10.791 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
10.791 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
10.791 * [taylor]: Taking taylor expansion of -2 in n
10.791 * [backup-simplify]: Simplify -2 into -2
10.791 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.791 * [taylor]: Taking taylor expansion of PI in n
10.791 * [backup-simplify]: Simplify PI into PI
10.791 * [taylor]: Taking taylor expansion of n in n
10.791 * [backup-simplify]: Simplify 0 into 0
10.791 * [backup-simplify]: Simplify 1 into 1
10.791 * [backup-simplify]: Simplify (/ PI 1) into PI
10.792 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
10.792 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
10.792 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
10.792 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.792 * [taylor]: Taking taylor expansion of k in n
10.792 * [backup-simplify]: Simplify k into k
10.792 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.792 * [taylor]: Taking taylor expansion of 1 in n
10.792 * [backup-simplify]: Simplify 1 into 1
10.793 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.793 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
10.794 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
10.795 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
10.796 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
10.797 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
10.798 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
10.799 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
10.799 * [backup-simplify]: Simplify 0 into 0
10.800 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)))) into 0
10.803 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
10.804 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
10.804 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
10.804 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
10.804 * [taylor]: Taking taylor expansion of +nan.0 in n
10.804 * [backup-simplify]: Simplify +nan.0 into +nan.0
10.804 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
10.804 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
10.804 * [taylor]: Taking taylor expansion of 1/2 in n
10.804 * [backup-simplify]: Simplify 1/2 into 1/2
10.804 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
10.804 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
10.804 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
10.804 * [taylor]: Taking taylor expansion of -2 in n
10.804 * [backup-simplify]: Simplify -2 into -2
10.804 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.805 * [taylor]: Taking taylor expansion of PI in n
10.805 * [backup-simplify]: Simplify PI into PI
10.805 * [taylor]: Taking taylor expansion of n in n
10.805 * [backup-simplify]: Simplify 0 into 0
10.805 * [backup-simplify]: Simplify 1 into 1
10.805 * [backup-simplify]: Simplify (/ PI 1) into PI
10.806 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
10.807 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
10.807 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
10.807 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.807 * [taylor]: Taking taylor expansion of k in n
10.807 * [backup-simplify]: Simplify k into k
10.807 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.807 * [taylor]: Taking taylor expansion of 1 in n
10.807 * [backup-simplify]: Simplify 1 into 1
10.808 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.808 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
10.810 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
10.811 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
10.812 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
10.814 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
10.815 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
10.816 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
10.818 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.818 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
10.818 * [backup-simplify]: Simplify (+ 0 0) into 0
10.819 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
10.820 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
10.821 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
10.823 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
10.824 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
10.826 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
10.828 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
10.828 * [backup-simplify]: Simplify (- 0) into 0
10.828 * [backup-simplify]: Simplify 0 into 0
10.828 * [backup-simplify]: Simplify 0 into 0
10.829 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
10.833 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
10.835 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
10.835 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
10.835 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
10.835 * [taylor]: Taking taylor expansion of +nan.0 in n
10.835 * [backup-simplify]: Simplify +nan.0 into +nan.0
10.835 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
10.835 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
10.836 * [taylor]: Taking taylor expansion of 1/2 in n
10.836 * [backup-simplify]: Simplify 1/2 into 1/2
10.836 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
10.836 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
10.836 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
10.836 * [taylor]: Taking taylor expansion of -2 in n
10.836 * [backup-simplify]: Simplify -2 into -2
10.836 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.836 * [taylor]: Taking taylor expansion of PI in n
10.836 * [backup-simplify]: Simplify PI into PI
10.836 * [taylor]: Taking taylor expansion of n in n
10.836 * [backup-simplify]: Simplify 0 into 0
10.836 * [backup-simplify]: Simplify 1 into 1
10.836 * [backup-simplify]: Simplify (/ PI 1) into PI
10.837 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
10.838 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
10.838 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
10.838 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.838 * [taylor]: Taking taylor expansion of k in n
10.838 * [backup-simplify]: Simplify k into k
10.838 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.838 * [taylor]: Taking taylor expansion of 1 in n
10.838 * [backup-simplify]: Simplify 1 into 1
10.840 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.840 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
10.841 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
10.842 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
10.843 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
10.844 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
10.845 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
10.847 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
10.851 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)))))))
10.851 * * * [progress]: simplifying candidates
10.851 * * * * [progress]: [ 1 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (exp (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
10.851 * * * * [progress]: [ 2 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (exp (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
10.851 * * * * [progress]: [ 3 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
10.851 * * * * [progress]: [ 4 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
10.851 * * * * [progress]: [ 5 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
10.852 * * * * [progress]: [ 6 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
10.852 * * * * [progress]: [ 7 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
10.852 * * * * [progress]: [ 8 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))>
10.852 * * * * [progress]: [ 9 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2)))))>
10.852 * * * * [progress]: [ 10 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2)))))>
10.852 * * * * [progress]: [ 11 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2)))))>
10.852 * * * * [progress]: [ 12 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2)))))>
10.852 * * * * [progress]: [ 13 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2))))>
10.852 * * * * [progress]: [ 14 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2)))))>
10.852 * * * * [progress]: [ 15 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2)))))>
10.852 * * * * [progress]: [ 16 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2))))>
10.852 * * * * [progress]: [ 17 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
10.852 * * * * [progress]: [ 18 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
10.852 * * * * [progress]: [ 19 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
10.852 * * * * [progress]: [ 20 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2)))))>
10.853 * * * * [progress]: [ 21 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2)))))>
10.853 * * * * [progress]: [ 22 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2))))>
10.853 * * * * [progress]: [ 23 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2)))))>
10.853 * * * * [progress]: [ 24 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2)))))>
10.853 * * * * [progress]: [ 25 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))))>
10.853 * * * * [progress]: [ 26 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
10.853 * * * * [progress]: [ 27 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
10.853 * * * * [progress]: [ 28 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
10.853 * * * * [progress]: [ 29 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
10.853 * * * * [progress]: [ 30 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (- 1 k)) (/ 1 2))))>
10.853 * * * * [progress]: [ 31 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))))>
10.853 * * * * [progress]: [ 32 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1)))>
10.853 * * * * [progress]: [ 33 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (exp (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.853 * * * * [progress]: [ 34 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (log (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.853 * * * * [progress]: [ 35 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (* (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.853 * * * * [progress]: [ 36 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (cbrt (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.854 * * * * [progress]: [ 37 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.854 * * * * [progress]: [ 38 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
10.854 * * * * [progress]: [ 39 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
10.854 * * * * [progress]: [ 40 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
10.854 * * * * [progress]: [ 41 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
10.854 * * * * [progress]: [ 42 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
10.854 * * * * [progress]: [ 43 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (exp (+ (+ (log 2) (log PI)) (log n))) (/ (- 1 k) 2))))>
10.854 * * * * [progress]: [ 44 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (exp (+ (log (* 2 PI)) (log n))) (/ (- 1 k) 2))))>
10.854 * * * * [progress]: [ 45 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (exp (log (* (* 2 PI) n))) (/ (- 1 k) 2))))>
10.854 * * * * [progress]: [ 46 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (log (exp (* (* 2 PI) n))) (/ (- 1 k) 2))))>
10.854 * * * * [progress]: [ 47 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (cbrt (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
10.854 * * * * [progress]: [ 48 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (cbrt (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
10.854 * * * * [progress]: [ 49 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) (cbrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
10.854 * * * * [progress]: [ 50 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))>
10.855 * * * * [progress]: [ 51 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
10.855 * * * * [progress]: [ 52 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* 1 (* (* 2 PI) n)) (/ (- 1 k) 2))))>
10.855 * * * * [progress]: [ 53 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))>
10.855 * * * * [progress]: [ 54 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (- 1 k) 2))))>
10.855 * * * * [progress]: [ 55 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* (* (* 2 PI) 1) n) (/ (- 1 k) 2))))>
10.855 * * * * [progress]: [ 56 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))>
10.855 * * * * [progress]: [ 57 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
10.855 * * * * [progress]: [ 58 / 109 ] simplifiying candidate #<alt (λ (k n) (pow (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1))>
10.855 * * * * [progress]: [ 59 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log k) -1/2) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
10.855 * * * * [progress]: [ 60 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log k) -1/2) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
10.855 * * * * [progress]: [ 61 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
10.855 * * * * [progress]: [ 62 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
10.855 * * * * [progress]: [ 63 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log k) -1/2) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.855 * * * * [progress]: [ 64 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log k) -1/2) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
10.855 * * * * [progress]: [ 65 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log k) -1/2) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
10.856 * * * * [progress]: [ 66 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
10.856 * * * * [progress]: [ 67 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
10.856 * * * * [progress]: [ 68 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log k) -1/2) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.856 * * * * [progress]: [ 69 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow k -1/2)) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
10.856 * * * * [progress]: [ 70 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow k -1/2)) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
10.856 * * * * [progress]: [ 71 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow k -1/2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
10.856 * * * * [progress]: [ 72 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow k -1/2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
10.856 * * * * [progress]: [ 73 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow k -1/2)) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.856 * * * * [progress]: [ 74 / 109 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.856 * * * * [progress]: [ 75 / 109 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.856 * * * * [progress]: [ 76 / 109 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow k -1/2) (pow k -1/2)) (pow k -1/2)) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.856 * * * * [progress]: [ 77 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.856 * * * * [progress]: [ 78 / 109 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.856 * * * * [progress]: [ 79 / 109 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.856 * * * * [progress]: [ 80 / 109 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
10.857 * * * * [progress]: [ 81 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt k) -1/2) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (pow (sqrt k) -1/2) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.857 * * * * [progress]: [ 82 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt k) -1/2) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (pow (sqrt k) -1/2) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
10.857 * * * * [progress]: [ 83 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow k -1/2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (pow k -1/2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.857 * * * * [progress]: [ 84 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (sqrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
10.857 * * * * [progress]: [ 85 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (pow k (/ -1/2 2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (pow k (/ -1/2 2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
10.857 * * * * [progress]: [ 86 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
10.857 * * * * [progress]: [ 87 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (pow k -1/2) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))))>
10.857 * * * * [progress]: [ 88 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (pow k -1/2) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
10.857 * * * * [progress]: [ 89 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (pow k -1/2) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
10.857 * * * * [progress]: [ 90 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (pow k -1/2) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
10.857 * * * * [progress]: [ 91 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))>
10.857 * * * * [progress]: [ 92 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (cbrt k) (cbrt k)) -1/2) (* (pow (cbrt k) -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
10.857 * * * * [progress]: [ 93 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) -1/2) (* (pow (sqrt k) -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
10.857 * * * * [progress]: [ 94 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow 1 -1/2) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
10.857 * * * * [progress]: [ 95 / 109 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (pow k -1/2)) (cbrt (pow k -1/2))) (* (cbrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
10.857 * * * * [progress]: [ 96 / 109 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (pow k -1/2)) (* (sqrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
10.857 * * * * [progress]: [ 97 / 109 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
10.858 * * * * [progress]: [ 98 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k (/ -1/2 2)) (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
10.858 * * * * [progress]: [ 99 / 109 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow k -1/2) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* (* 2 PI) n) (/ k 2))))>
10.858 * * * * [progress]: [ 100 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow k -1/2)))>
10.858 * * * * [progress]: [ 101 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (- (+ (* 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)))))))>
10.858 * * * * [progress]: [ 102 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))>
10.858 * * * * [progress]: [ 103 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))>
10.858 * * * * [progress]: [ 104 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
10.858 * * * * [progress]: [ 105 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
10.858 * * * * [progress]: [ 106 / 109 ] simplifiying candidate #<alt (λ (k n) (* (pow k -1/2) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
10.858 * * * * [progress]: [ 107 / 109 ] 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))))))))))))))>
10.858 * * * * [progress]: [ 108 / 109 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
10.858 * * * * [progress]: [ 109 / 109 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))))))))>
10.860 * [simplify]: Simplifying:
  (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2))
  (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))
  (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
  (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* (* 2 PI) n) (/ 1 2))
  (pow (* (* 2 PI) n) (/ k 2))
  (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1))
  (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2 PI) n) (/ 1 1))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1))
  (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2 PI) n) (/ 1 1))
  (pow (* (* 2 PI) n) 1)
  (pow (* (* 2 PI) n) (- 1 k))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
  (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (+ (+ (log 2) (log PI)) (log n))
  (+ (log (* 2 PI)) (log n))
  (log (* (* 2 PI) n))
  (exp (* (* 2 PI) n))
  (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))
  (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n)))
  (cbrt (* (* 2 PI) n))
  (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (* (* 2 PI) (* (cbrt n) (cbrt n)))
  (* (* 2 PI) (sqrt n))
  (* (* 2 PI) 1)
  (* PI n)
  (+ (* (log k) -1/2) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (* (log k) -1/2) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (* (log k) -1/2) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (* (log k) -1/2) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (* (log k) -1/2) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (* (log k) -1/2) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (log (pow k -1/2)) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (log (pow k -1/2)) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (log (pow k -1/2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (log (pow k -1/2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (log (pow k -1/2)) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (log (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (exp (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (* (* (pow k -1/2) (pow k -1/2)) (pow k -1/2)) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (cbrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
  (cbrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (* (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (sqrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (sqrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (pow (sqrt k) -1/2) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (pow (sqrt k) -1/2) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (pow (sqrt k) -1/2) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (pow (sqrt k) -1/2) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (sqrt (pow k -1/2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (sqrt (pow k -1/2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (sqrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (sqrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (pow k (/ -1/2 2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (pow k (/ -1/2 2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (pow k -1/2) (pow (* 2 PI) (/ (- 1 k) 2)))
  (* (pow k -1/2) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
  (* (pow k -1/2) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (pow k -1/2) 1)
  (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (pow (cbrt k) -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (pow (sqrt k) -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (cbrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (sqrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (pow k -1/2) (pow (* (* 2 PI) n) (/ 1 2)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)))))))
10.864 * * [simplify]: iteration 1: (255 enodes)
10.949 * * [simplify]: iteration 2: (709 enodes)
11.850 * * [simplify]: Extracting #0: cost 68 inf + 0
11.851 * * [simplify]: Extracting #1: cost 372 inf + 0
11.856 * * [simplify]: Extracting #2: cost 656 inf + 9393
11.868 * * [simplify]: Extracting #3: cost 643 inf + 54585
11.887 * * [simplify]: Extracting #4: cost 409 inf + 163825
11.923 * * [simplify]: Extracting #5: cost 178 inf + 272234
11.977 * * [simplify]: Extracting #6: cost 73 inf + 309517
12.034 * * [simplify]: Extracting #7: cost 37 inf + 319518
12.080 * * [simplify]: Extracting #8: cost 15 inf + 332525
12.164 * * [simplify]: Extracting #9: cost 3 inf + 340275
12.238 * * [simplify]: Extracting #10: cost 0 inf + 341777
12.310 * * [simplify]: Extracting #11: cost 0 inf + 340887
12.365 * [simplify]: Simplified to:
  (* (/ (- 1 k) 2) (log (* 2 (* PI n))))
  (* (/ (- 1 k) 2) (log (* 2 (* PI n))))
  (* (/ (- 1 k) 2) (log (* 2 (* PI n))))
  (* (/ (- 1 k) 2) (log (* 2 (* PI n))))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ k 2))
  (pow (* 2 (* PI n)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* 2 (* PI n)) (sqrt (/ (- 1 k) 2)))
  (pow (* 2 (* PI n)) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ (cbrt (- 1 k)) (/ (sqrt 2) (cbrt (- 1 k)))))
  (pow (* 2 (* PI n)) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* 2 (* PI n)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* 2 (* PI n)) (sqrt (- 1 k)))
  (pow (* 2 (* PI n)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ 1 (sqrt 2)))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* 2 (* PI n)) (+ (sqrt k) 1))
  (pow (* 2 (* PI n)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* 2 (* PI n)) (+ (sqrt k) 1))
  (pow (* 2 (* PI n)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ 1 (sqrt 2)))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (- 1 k))
  (pow (* PI 2) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* 2 (* PI n))))
  (exp (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))))
  (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (* (* (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (pow (* 2 (* PI n)) (/ (- 1 k) 4))
  (pow (* 2 (* PI n)) (/ (- 1 k) 4))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* n (* n n)) (* (* PI (* PI PI)) 8))
  (* (* 2 (* PI n)) (* (* 2 (* PI n)) (* 2 (* PI n))))
  (* (cbrt (* 2 (* PI n))) (cbrt (* 2 (* PI n))))
  (cbrt (* 2 (* PI n)))
  (* (* 2 (* PI n)) (* (* 2 (* PI n)) (* 2 (* PI n))))
  (sqrt (* 2 (* PI n)))
  (sqrt (* 2 (* PI n)))
  (* (* PI 2) (* (cbrt n) (cbrt n)))
  (* 2 (* PI (sqrt n)))
  (* PI 2)
  (* PI n)
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (+ (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (* -1/2 (log k)))
  (exp (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))
  (* (* (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (pow k -1/2))) (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (* (cbrt (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2)))) (cbrt (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2)))))
  (cbrt (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))
  (* (* (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (pow k -1/2))) (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (sqrt (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))
  (sqrt (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))
  (* (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (pow (sqrt k) -1/2))
  (* (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (pow (sqrt k) -1/2))
  (* (pow (* 2 (* PI n)) (/ (- 1 k) 4)) (pow (sqrt k) -1/2))
  (* (pow (* 2 (* PI n)) (/ (- 1 k) 4)) (pow (sqrt k) -1/2))
  (* (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (fabs (pow k -1/4)))
  (* (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (fabs (pow k -1/4)))
  (* (pow (* 2 (* PI n)) (/ (- 1 k) 4)) (fabs (pow k -1/4)))
  (* (pow (* 2 (* PI n)) (/ (- 1 k) 4)) (fabs (pow k -1/4)))
  (* (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (pow k -1/4))
  (* (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (pow k -1/4))
  (* (pow (* 2 (* PI n)) (/ (- 1 k) 4)) (pow k -1/4))
  (* (pow (* 2 (* PI n)) (/ (- 1 k) 4)) (pow k -1/4))
  (* (pow k -1/2) (pow (* PI 2) (/ (- 1 k) 2)))
  (* (pow k -1/2) (* (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2)))))
  (* (pow k -1/2) (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))))
  (pow k -1/2)
  (* (pow (* 2 (* PI n)) (/ (- 1 k) 4)) (pow k -1/2))
  (* (pow (cbrt k) -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (* (pow (sqrt k) -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (* (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (cbrt (pow k -1/2)))
  (* (fabs (pow k -1/4)) (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (* (pow k -1/2) (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (* (pow k -1/4) (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
  (* (sqrt (* 2 (* PI n))) (pow k -1/2))
  (- (+ (+ (exp (* (log (* 2 (* PI n))) 1/2)) (+ (* (* (exp (* (log (* 2 (* PI n))) 1/2)) (* (* k k) (* (log (* PI 2)) (log (* PI 2))))) 1/8) (* 1/8 (* (* (* (log n) (* k k)) (log n)) (exp (* (log (* 2 (* PI n))) 1/2)))))) (* (* (log (* PI 2)) (exp (* (log (* 2 (* PI n))) 1/2))) (* (* (log n) (* k k)) 1/4))) (* (* k (+ (* (exp (* (log (* 2 (* PI n))) 1/2)) (log n)) (* (log (* PI 2)) (exp (* (log (* 2 (* PI n))) 1/2))))) 1/2))
  (exp (* 1/2 (* (- 1 k) (log (* 2 (* PI n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (+ (* (- (* (* (* PI n) k) (sqrt 2))) +nan.0) (+ (- (* (* +nan.0 (sqrt 2)) (* PI n)) (* (* (log (* PI 2)) (* (* (* PI n) k) (sqrt 2))) +nan.0)) (* (* +nan.0 (sqrt 2)) (- (* (* k (log n)) (* PI n)) (* (* PI n) (* PI n))))))
  (+ (* (/ (exp (* 1/2 (* (- 1 k) (log (* 2 (* PI n)))))) k) (- +nan.0)) (* +nan.0 (- (/ (exp (* 1/2 (* (- 1 k) (log (* 2 (* PI n)))))) (* k k)) (/ (/ (exp (* 1/2 (* (- 1 k) (log (* 2 (* PI n)))))) k) (* k k)))))
  (+ (* (/ (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* k k)) k) (- +nan.0)) (* +nan.0 (- (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* k k)) (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))))
12.372 * * * [progress]: adding candidates to table
13.657 * * [progress]: iteration 4 / 4
13.657 * * * [progress]: picking best candidate
13.692 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))>
13.693 * * * [progress]: localizing error
13.722 * * * [progress]: generating rewritten candidates
13.722 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
13.749 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
13.761 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
13.772 * * * [progress]: generating series expansions
13.772 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
13.773 * [backup-simplify]: Simplify (pow (* (* PI 2) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
13.773 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
13.773 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
13.773 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
13.773 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
13.773 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
13.773 * [taylor]: Taking taylor expansion of 1/2 in k
13.773 * [backup-simplify]: Simplify 1/2 into 1/2
13.773 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.773 * [taylor]: Taking taylor expansion of 1 in k
13.773 * [backup-simplify]: Simplify 1 into 1
13.773 * [taylor]: Taking taylor expansion of k in k
13.773 * [backup-simplify]: Simplify 0 into 0
13.773 * [backup-simplify]: Simplify 1 into 1
13.773 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
13.773 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
13.773 * [taylor]: Taking taylor expansion of 2 in k
13.773 * [backup-simplify]: Simplify 2 into 2
13.773 * [taylor]: Taking taylor expansion of (* n PI) in k
13.773 * [taylor]: Taking taylor expansion of n in k
13.773 * [backup-simplify]: Simplify n into n
13.773 * [taylor]: Taking taylor expansion of PI in k
13.773 * [backup-simplify]: Simplify PI into PI
13.773 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.773 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
13.773 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
13.773 * [backup-simplify]: Simplify (- 0) into 0
13.774 * [backup-simplify]: Simplify (+ 1 0) into 1
13.774 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.774 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
13.774 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
13.774 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
13.774 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
13.774 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
13.774 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
13.774 * [taylor]: Taking taylor expansion of 1/2 in n
13.774 * [backup-simplify]: Simplify 1/2 into 1/2
13.774 * [taylor]: Taking taylor expansion of (- 1 k) in n
13.774 * [taylor]: Taking taylor expansion of 1 in n
13.774 * [backup-simplify]: Simplify 1 into 1
13.774 * [taylor]: Taking taylor expansion of k in n
13.774 * [backup-simplify]: Simplify k into k
13.774 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.774 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.774 * [taylor]: Taking taylor expansion of 2 in n
13.774 * [backup-simplify]: Simplify 2 into 2
13.774 * [taylor]: Taking taylor expansion of (* n PI) in n
13.774 * [taylor]: Taking taylor expansion of n in n
13.774 * [backup-simplify]: Simplify 0 into 0
13.774 * [backup-simplify]: Simplify 1 into 1
13.774 * [taylor]: Taking taylor expansion of PI in n
13.774 * [backup-simplify]: Simplify PI into PI
13.775 * [backup-simplify]: Simplify (* 0 PI) into 0
13.775 * [backup-simplify]: Simplify (* 2 0) into 0
13.776 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.777 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.778 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.778 * [backup-simplify]: Simplify (- k) into (- k)
13.778 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
13.778 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
13.779 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.780 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
13.780 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
13.781 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
13.781 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
13.781 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
13.781 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
13.781 * [taylor]: Taking taylor expansion of 1/2 in n
13.781 * [backup-simplify]: Simplify 1/2 into 1/2
13.781 * [taylor]: Taking taylor expansion of (- 1 k) in n
13.781 * [taylor]: Taking taylor expansion of 1 in n
13.781 * [backup-simplify]: Simplify 1 into 1
13.781 * [taylor]: Taking taylor expansion of k in n
13.781 * [backup-simplify]: Simplify k into k
13.781 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.781 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.781 * [taylor]: Taking taylor expansion of 2 in n
13.781 * [backup-simplify]: Simplify 2 into 2
13.781 * [taylor]: Taking taylor expansion of (* n PI) in n
13.781 * [taylor]: Taking taylor expansion of n in n
13.781 * [backup-simplify]: Simplify 0 into 0
13.781 * [backup-simplify]: Simplify 1 into 1
13.781 * [taylor]: Taking taylor expansion of PI in n
13.781 * [backup-simplify]: Simplify PI into PI
13.782 * [backup-simplify]: Simplify (* 0 PI) into 0
13.782 * [backup-simplify]: Simplify (* 2 0) into 0
13.784 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.785 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.786 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.786 * [backup-simplify]: Simplify (- k) into (- k)
13.787 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
13.787 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
13.788 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.789 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
13.790 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
13.790 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
13.790 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
13.790 * [taylor]: Taking taylor expansion of 1/2 in k
13.790 * [backup-simplify]: Simplify 1/2 into 1/2
13.790 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
13.790 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.790 * [taylor]: Taking taylor expansion of 1 in k
13.790 * [backup-simplify]: Simplify 1 into 1
13.790 * [taylor]: Taking taylor expansion of k in k
13.790 * [backup-simplify]: Simplify 0 into 0
13.790 * [backup-simplify]: Simplify 1 into 1
13.790 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
13.790 * [taylor]: Taking taylor expansion of (log n) in k
13.790 * [taylor]: Taking taylor expansion of n in k
13.790 * [backup-simplify]: Simplify n into n
13.790 * [backup-simplify]: Simplify (log n) into (log n)
13.790 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.790 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.790 * [taylor]: Taking taylor expansion of 2 in k
13.790 * [backup-simplify]: Simplify 2 into 2
13.790 * [taylor]: Taking taylor expansion of PI in k
13.790 * [backup-simplify]: Simplify PI into PI
13.790 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.791 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.791 * [backup-simplify]: Simplify (- 0) into 0
13.791 * [backup-simplify]: Simplify (+ 1 0) into 1
13.792 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.796 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
13.797 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
13.798 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
13.798 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
13.799 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.800 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.801 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.801 * [backup-simplify]: Simplify (- 0) into 0
13.801 * [backup-simplify]: Simplify (+ 0 0) into 0
13.802 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
13.803 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.804 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
13.805 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.805 * [taylor]: Taking taylor expansion of 0 in k
13.805 * [backup-simplify]: Simplify 0 into 0
13.805 * [backup-simplify]: Simplify 0 into 0
13.805 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.806 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.807 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.807 * [backup-simplify]: Simplify (+ 0 0) into 0
13.807 * [backup-simplify]: Simplify (- 1) into -1
13.808 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.809 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
13.810 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
13.812 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
13.814 * [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)))))))
13.815 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.816 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.818 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.818 * [backup-simplify]: Simplify (- 0) into 0
13.818 * [backup-simplify]: Simplify (+ 0 0) into 0
13.819 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
13.820 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.822 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.824 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.824 * [taylor]: Taking taylor expansion of 0 in k
13.824 * [backup-simplify]: Simplify 0 into 0
13.824 * [backup-simplify]: Simplify 0 into 0
13.824 * [backup-simplify]: Simplify 0 into 0
13.826 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.827 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.831 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.831 * [backup-simplify]: Simplify (+ 0 0) into 0
13.832 * [backup-simplify]: Simplify (- 0) into 0
13.832 * [backup-simplify]: Simplify (+ 0 0) into 0
13.835 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.837 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.841 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
13.846 * [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)))))
13.856 * [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)))))
13.857 * [backup-simplify]: Simplify (pow (* (* PI 2) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
13.857 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
13.857 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
13.857 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
13.857 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
13.857 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
13.857 * [taylor]: Taking taylor expansion of 1/2 in k
13.857 * [backup-simplify]: Simplify 1/2 into 1/2
13.857 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.857 * [taylor]: Taking taylor expansion of 1 in k
13.857 * [backup-simplify]: Simplify 1 into 1
13.857 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.857 * [taylor]: Taking taylor expansion of k in k
13.857 * [backup-simplify]: Simplify 0 into 0
13.857 * [backup-simplify]: Simplify 1 into 1
13.857 * [backup-simplify]: Simplify (/ 1 1) into 1
13.857 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
13.858 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
13.858 * [taylor]: Taking taylor expansion of 2 in k
13.858 * [backup-simplify]: Simplify 2 into 2
13.858 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.858 * [taylor]: Taking taylor expansion of PI in k
13.858 * [backup-simplify]: Simplify PI into PI
13.858 * [taylor]: Taking taylor expansion of n in k
13.858 * [backup-simplify]: Simplify n into n
13.858 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.858 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
13.858 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
13.858 * [backup-simplify]: Simplify (- 1) into -1
13.859 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.859 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
13.859 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
13.859 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
13.859 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
13.860 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.860 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.860 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
13.860 * [taylor]: Taking taylor expansion of 1/2 in n
13.860 * [backup-simplify]: Simplify 1/2 into 1/2
13.860 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.860 * [taylor]: Taking taylor expansion of 1 in n
13.860 * [backup-simplify]: Simplify 1 into 1
13.860 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.860 * [taylor]: Taking taylor expansion of k in n
13.860 * [backup-simplify]: Simplify k into k
13.860 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.860 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.860 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.860 * [taylor]: Taking taylor expansion of 2 in n
13.860 * [backup-simplify]: Simplify 2 into 2
13.860 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.860 * [taylor]: Taking taylor expansion of PI in n
13.860 * [backup-simplify]: Simplify PI into PI
13.860 * [taylor]: Taking taylor expansion of n in n
13.860 * [backup-simplify]: Simplify 0 into 0
13.860 * [backup-simplify]: Simplify 1 into 1
13.861 * [backup-simplify]: Simplify (/ PI 1) into PI
13.861 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.862 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.862 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.862 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.862 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
13.864 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.865 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.866 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.866 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
13.866 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.866 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.866 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
13.866 * [taylor]: Taking taylor expansion of 1/2 in n
13.866 * [backup-simplify]: Simplify 1/2 into 1/2
13.866 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.866 * [taylor]: Taking taylor expansion of 1 in n
13.866 * [backup-simplify]: Simplify 1 into 1
13.866 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.866 * [taylor]: Taking taylor expansion of k in n
13.866 * [backup-simplify]: Simplify k into k
13.866 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.866 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.866 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.866 * [taylor]: Taking taylor expansion of 2 in n
13.866 * [backup-simplify]: Simplify 2 into 2
13.866 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.867 * [taylor]: Taking taylor expansion of PI in n
13.867 * [backup-simplify]: Simplify PI into PI
13.867 * [taylor]: Taking taylor expansion of n in n
13.867 * [backup-simplify]: Simplify 0 into 0
13.867 * [backup-simplify]: Simplify 1 into 1
13.867 * [backup-simplify]: Simplify (/ PI 1) into PI
13.868 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.869 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.869 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.869 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.869 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
13.870 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.871 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.872 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.873 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
13.873 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
13.873 * [taylor]: Taking taylor expansion of 1/2 in k
13.873 * [backup-simplify]: Simplify 1/2 into 1/2
13.873 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
13.873 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.873 * [taylor]: Taking taylor expansion of 1 in k
13.873 * [backup-simplify]: Simplify 1 into 1
13.873 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.873 * [taylor]: Taking taylor expansion of k in k
13.873 * [backup-simplify]: Simplify 0 into 0
13.873 * [backup-simplify]: Simplify 1 into 1
13.873 * [backup-simplify]: Simplify (/ 1 1) into 1
13.873 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
13.873 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.873 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.873 * [taylor]: Taking taylor expansion of 2 in k
13.873 * [backup-simplify]: Simplify 2 into 2
13.873 * [taylor]: Taking taylor expansion of PI in k
13.873 * [backup-simplify]: Simplify PI into PI
13.874 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.875 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.875 * [taylor]: Taking taylor expansion of (log n) in k
13.875 * [taylor]: Taking taylor expansion of n in k
13.875 * [backup-simplify]: Simplify n into n
13.875 * [backup-simplify]: Simplify (log n) into (log n)
13.875 * [backup-simplify]: Simplify (- 1) into -1
13.876 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.876 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.877 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
13.878 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
13.879 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
13.880 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.881 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.882 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.883 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.885 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.885 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.886 * [backup-simplify]: Simplify (- 0) into 0
13.886 * [backup-simplify]: Simplify (+ 0 0) into 0
13.886 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
13.888 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.889 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
13.891 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.891 * [taylor]: Taking taylor expansion of 0 in k
13.892 * [backup-simplify]: Simplify 0 into 0
13.892 * [backup-simplify]: Simplify 0 into 0
13.892 * [backup-simplify]: Simplify 0 into 0
13.893 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.894 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.898 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.898 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.898 * [backup-simplify]: Simplify (- 0) into 0
13.899 * [backup-simplify]: Simplify (+ 0 0) into 0
13.900 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
13.902 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.903 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
13.906 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.906 * [taylor]: Taking taylor expansion of 0 in k
13.906 * [backup-simplify]: Simplify 0 into 0
13.906 * [backup-simplify]: Simplify 0 into 0
13.906 * [backup-simplify]: Simplify 0 into 0
13.907 * [backup-simplify]: Simplify 0 into 0
13.908 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.909 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.915 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
13.916 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.916 * [backup-simplify]: Simplify (- 0) into 0
13.916 * [backup-simplify]: Simplify (+ 0 0) into 0
13.918 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
13.919 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.921 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
13.927 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.927 * [taylor]: Taking taylor expansion of 0 in k
13.928 * [backup-simplify]: Simplify 0 into 0
13.928 * [backup-simplify]: Simplify 0 into 0
13.929 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
13.930 * [backup-simplify]: Simplify (pow (* (* PI 2) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
13.930 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
13.930 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
13.930 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
13.930 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
13.930 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
13.930 * [taylor]: Taking taylor expansion of 1/2 in k
13.930 * [backup-simplify]: Simplify 1/2 into 1/2
13.930 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
13.930 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.930 * [taylor]: Taking taylor expansion of k in k
13.930 * [backup-simplify]: Simplify 0 into 0
13.930 * [backup-simplify]: Simplify 1 into 1
13.931 * [backup-simplify]: Simplify (/ 1 1) into 1
13.931 * [taylor]: Taking taylor expansion of 1 in k
13.931 * [backup-simplify]: Simplify 1 into 1
13.931 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.931 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.931 * [taylor]: Taking taylor expansion of -2 in k
13.931 * [backup-simplify]: Simplify -2 into -2
13.931 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.931 * [taylor]: Taking taylor expansion of PI in k
13.931 * [backup-simplify]: Simplify PI into PI
13.931 * [taylor]: Taking taylor expansion of n in k
13.931 * [backup-simplify]: Simplify n into n
13.931 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.931 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.931 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.932 * [backup-simplify]: Simplify (+ 1 0) into 1
13.932 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.932 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
13.932 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
13.932 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
13.932 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
13.932 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
13.932 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
13.933 * [taylor]: Taking taylor expansion of 1/2 in n
13.933 * [backup-simplify]: Simplify 1/2 into 1/2
13.933 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.933 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.933 * [taylor]: Taking taylor expansion of k in n
13.933 * [backup-simplify]: Simplify k into k
13.933 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.933 * [taylor]: Taking taylor expansion of 1 in n
13.933 * [backup-simplify]: Simplify 1 into 1
13.933 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.933 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.933 * [taylor]: Taking taylor expansion of -2 in n
13.933 * [backup-simplify]: Simplify -2 into -2
13.933 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.933 * [taylor]: Taking taylor expansion of PI in n
13.933 * [backup-simplify]: Simplify PI into PI
13.933 * [taylor]: Taking taylor expansion of n in n
13.933 * [backup-simplify]: Simplify 0 into 0
13.933 * [backup-simplify]: Simplify 1 into 1
13.934 * [backup-simplify]: Simplify (/ PI 1) into PI
13.934 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.935 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.935 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.936 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
13.937 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.938 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.940 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.940 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
13.940 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
13.940 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
13.940 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
13.940 * [taylor]: Taking taylor expansion of 1/2 in n
13.940 * [backup-simplify]: Simplify 1/2 into 1/2
13.940 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.940 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.940 * [taylor]: Taking taylor expansion of k in n
13.940 * [backup-simplify]: Simplify k into k
13.940 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.940 * [taylor]: Taking taylor expansion of 1 in n
13.940 * [backup-simplify]: Simplify 1 into 1
13.940 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.940 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.940 * [taylor]: Taking taylor expansion of -2 in n
13.940 * [backup-simplify]: Simplify -2 into -2
13.940 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.940 * [taylor]: Taking taylor expansion of PI in n
13.940 * [backup-simplify]: Simplify PI into PI
13.940 * [taylor]: Taking taylor expansion of n in n
13.940 * [backup-simplify]: Simplify 0 into 0
13.940 * [backup-simplify]: Simplify 1 into 1
13.941 * [backup-simplify]: Simplify (/ PI 1) into PI
13.941 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.943 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.943 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.943 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
13.944 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.946 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.947 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.947 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
13.947 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
13.947 * [taylor]: Taking taylor expansion of 1/2 in k
13.947 * [backup-simplify]: Simplify 1/2 into 1/2
13.947 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
13.947 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
13.947 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.947 * [taylor]: Taking taylor expansion of k in k
13.947 * [backup-simplify]: Simplify 0 into 0
13.947 * [backup-simplify]: Simplify 1 into 1
13.948 * [backup-simplify]: Simplify (/ 1 1) into 1
13.948 * [taylor]: Taking taylor expansion of 1 in k
13.948 * [backup-simplify]: Simplify 1 into 1
13.948 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
13.948 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
13.948 * [taylor]: Taking taylor expansion of (* -2 PI) in k
13.948 * [taylor]: Taking taylor expansion of -2 in k
13.948 * [backup-simplify]: Simplify -2 into -2
13.948 * [taylor]: Taking taylor expansion of PI in k
13.948 * [backup-simplify]: Simplify PI into PI
13.949 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.950 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.950 * [taylor]: Taking taylor expansion of (log n) in k
13.950 * [taylor]: Taking taylor expansion of n in k
13.950 * [backup-simplify]: Simplify n into n
13.950 * [backup-simplify]: Simplify (log n) into (log n)
13.951 * [backup-simplify]: Simplify (+ 1 0) into 1
13.951 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.952 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
13.953 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
13.955 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
13.956 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.957 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.958 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.959 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.961 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
13.961 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.962 * [backup-simplify]: Simplify (+ 0 0) into 0
13.962 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
13.964 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.965 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
13.967 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.967 * [taylor]: Taking taylor expansion of 0 in k
13.967 * [backup-simplify]: Simplify 0 into 0
13.967 * [backup-simplify]: Simplify 0 into 0
13.967 * [backup-simplify]: Simplify 0 into 0
13.968 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.969 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
13.973 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
13.973 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.974 * [backup-simplify]: Simplify (+ 0 0) into 0
13.975 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
13.976 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.978 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
13.981 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.981 * [taylor]: Taking taylor expansion of 0 in k
13.981 * [backup-simplify]: Simplify 0 into 0
13.981 * [backup-simplify]: Simplify 0 into 0
13.981 * [backup-simplify]: Simplify 0 into 0
13.981 * [backup-simplify]: Simplify 0 into 0
13.982 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.983 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.990 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
13.990 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.991 * [backup-simplify]: Simplify (+ 0 0) into 0
13.992 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
13.994 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.996 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
13.999 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.999 * [taylor]: Taking taylor expansion of 0 in k
13.999 * [backup-simplify]: Simplify 0 into 0
13.999 * [backup-simplify]: Simplify 0 into 0
14.001 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
14.001 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
14.001 * [backup-simplify]: Simplify (* (* PI 2) n) into (* 2 (* n PI))
14.001 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
14.001 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
14.001 * [taylor]: Taking taylor expansion of 2 in n
14.001 * [backup-simplify]: Simplify 2 into 2
14.002 * [taylor]: Taking taylor expansion of (* n PI) in n
14.002 * [taylor]: Taking taylor expansion of n in n
14.002 * [backup-simplify]: Simplify 0 into 0
14.002 * [backup-simplify]: Simplify 1 into 1
14.002 * [taylor]: Taking taylor expansion of PI in n
14.002 * [backup-simplify]: Simplify PI into PI
14.002 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
14.002 * [taylor]: Taking taylor expansion of 2 in n
14.002 * [backup-simplify]: Simplify 2 into 2
14.002 * [taylor]: Taking taylor expansion of (* n PI) in n
14.002 * [taylor]: Taking taylor expansion of n in n
14.002 * [backup-simplify]: Simplify 0 into 0
14.002 * [backup-simplify]: Simplify 1 into 1
14.002 * [taylor]: Taking taylor expansion of PI in n
14.002 * [backup-simplify]: Simplify PI into PI
14.002 * [backup-simplify]: Simplify (* 0 PI) into 0
14.003 * [backup-simplify]: Simplify (* 2 0) into 0
14.003 * [backup-simplify]: Simplify 0 into 0
14.005 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
14.006 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
14.007 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
14.008 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
14.009 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
14.009 * [backup-simplify]: Simplify 0 into 0
14.010 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
14.012 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
14.012 * [backup-simplify]: Simplify 0 into 0
14.013 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
14.015 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
14.015 * [backup-simplify]: Simplify 0 into 0
14.017 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
14.018 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
14.018 * [backup-simplify]: Simplify 0 into 0
14.020 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
14.022 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
14.022 * [backup-simplify]: Simplify 0 into 0
14.024 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
14.026 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
14.026 * [backup-simplify]: Simplify 0 into 0
14.027 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
14.028 * [backup-simplify]: Simplify (* (* PI 2) (/ 1 n)) into (* 2 (/ PI n))
14.028 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
14.028 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
14.028 * [taylor]: Taking taylor expansion of 2 in n
14.028 * [backup-simplify]: Simplify 2 into 2
14.028 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.028 * [taylor]: Taking taylor expansion of PI in n
14.028 * [backup-simplify]: Simplify PI into PI
14.028 * [taylor]: Taking taylor expansion of n in n
14.028 * [backup-simplify]: Simplify 0 into 0
14.028 * [backup-simplify]: Simplify 1 into 1
14.028 * [backup-simplify]: Simplify (/ PI 1) into PI
14.029 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
14.029 * [taylor]: Taking taylor expansion of 2 in n
14.029 * [backup-simplify]: Simplify 2 into 2
14.029 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.029 * [taylor]: Taking taylor expansion of PI in n
14.029 * [backup-simplify]: Simplify PI into PI
14.029 * [taylor]: Taking taylor expansion of n in n
14.029 * [backup-simplify]: Simplify 0 into 0
14.029 * [backup-simplify]: Simplify 1 into 1
14.029 * [backup-simplify]: Simplify (/ PI 1) into PI
14.030 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
14.031 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
14.032 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
14.032 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
14.032 * [backup-simplify]: Simplify 0 into 0
14.034 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.035 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
14.035 * [backup-simplify]: Simplify 0 into 0
14.036 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.037 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
14.037 * [backup-simplify]: Simplify 0 into 0
14.039 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.040 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
14.040 * [backup-simplify]: Simplify 0 into 0
14.041 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.043 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
14.043 * [backup-simplify]: Simplify 0 into 0
14.044 * [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
14.046 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
14.046 * [backup-simplify]: Simplify 0 into 0
14.047 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
14.047 * [backup-simplify]: Simplify (* (* PI 2) (/ 1 (- n))) into (* -2 (/ PI n))
14.047 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
14.047 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
14.047 * [taylor]: Taking taylor expansion of -2 in n
14.047 * [backup-simplify]: Simplify -2 into -2
14.047 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.048 * [taylor]: Taking taylor expansion of PI in n
14.048 * [backup-simplify]: Simplify PI into PI
14.048 * [taylor]: Taking taylor expansion of n in n
14.048 * [backup-simplify]: Simplify 0 into 0
14.048 * [backup-simplify]: Simplify 1 into 1
14.048 * [backup-simplify]: Simplify (/ PI 1) into PI
14.048 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
14.048 * [taylor]: Taking taylor expansion of -2 in n
14.048 * [backup-simplify]: Simplify -2 into -2
14.048 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.048 * [taylor]: Taking taylor expansion of PI in n
14.048 * [backup-simplify]: Simplify PI into PI
14.048 * [taylor]: Taking taylor expansion of n in n
14.048 * [backup-simplify]: Simplify 0 into 0
14.048 * [backup-simplify]: Simplify 1 into 1
14.049 * [backup-simplify]: Simplify (/ PI 1) into PI
14.049 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
14.049 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
14.050 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
14.050 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
14.050 * [backup-simplify]: Simplify 0 into 0
14.051 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.051 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
14.052 * [backup-simplify]: Simplify 0 into 0
14.052 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.053 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
14.053 * [backup-simplify]: Simplify 0 into 0
14.054 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.054 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
14.054 * [backup-simplify]: Simplify 0 into 0
14.055 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.056 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
14.056 * [backup-simplify]: Simplify 0 into 0
14.057 * [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
14.058 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
14.058 * [backup-simplify]: Simplify 0 into 0
14.058 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
14.058 * * * * [progress]: [ 3 / 3 ] generating series at (2)
14.059 * [backup-simplify]: Simplify (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
14.059 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (n k) around 0
14.059 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
14.059 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
14.059 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
14.059 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
14.059 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
14.059 * [taylor]: Taking taylor expansion of 1/2 in k
14.059 * [backup-simplify]: Simplify 1/2 into 1/2
14.059 * [taylor]: Taking taylor expansion of (- 1 k) in k
14.059 * [taylor]: Taking taylor expansion of 1 in k
14.059 * [backup-simplify]: Simplify 1 into 1
14.059 * [taylor]: Taking taylor expansion of k in k
14.059 * [backup-simplify]: Simplify 0 into 0
14.059 * [backup-simplify]: Simplify 1 into 1
14.059 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
14.059 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
14.059 * [taylor]: Taking taylor expansion of 2 in k
14.059 * [backup-simplify]: Simplify 2 into 2
14.059 * [taylor]: Taking taylor expansion of (* n PI) in k
14.059 * [taylor]: Taking taylor expansion of n in k
14.059 * [backup-simplify]: Simplify n into n
14.059 * [taylor]: Taking taylor expansion of PI in k
14.059 * [backup-simplify]: Simplify PI into PI
14.059 * [backup-simplify]: Simplify (* n PI) into (* n PI)
14.059 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
14.059 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
14.060 * [backup-simplify]: Simplify (- 0) into 0
14.060 * [backup-simplify]: Simplify (+ 1 0) into 1
14.060 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
14.060 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
14.060 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
14.060 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
14.060 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.060 * [taylor]: Taking taylor expansion of k in k
14.060 * [backup-simplify]: Simplify 0 into 0
14.060 * [backup-simplify]: Simplify 1 into 1
14.061 * [backup-simplify]: Simplify (/ 1 1) into 1
14.061 * [backup-simplify]: Simplify (sqrt 0) into 0
14.062 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
14.062 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
14.062 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
14.062 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
14.062 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
14.062 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
14.062 * [taylor]: Taking taylor expansion of 1/2 in n
14.062 * [backup-simplify]: Simplify 1/2 into 1/2
14.062 * [taylor]: Taking taylor expansion of (- 1 k) in n
14.062 * [taylor]: Taking taylor expansion of 1 in n
14.062 * [backup-simplify]: Simplify 1 into 1
14.062 * [taylor]: Taking taylor expansion of k in n
14.062 * [backup-simplify]: Simplify k into k
14.062 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
14.062 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
14.062 * [taylor]: Taking taylor expansion of 2 in n
14.062 * [backup-simplify]: Simplify 2 into 2
14.062 * [taylor]: Taking taylor expansion of (* n PI) in n
14.062 * [taylor]: Taking taylor expansion of n in n
14.062 * [backup-simplify]: Simplify 0 into 0
14.062 * [backup-simplify]: Simplify 1 into 1
14.062 * [taylor]: Taking taylor expansion of PI in n
14.062 * [backup-simplify]: Simplify PI into PI
14.063 * [backup-simplify]: Simplify (* 0 PI) into 0
14.063 * [backup-simplify]: Simplify (* 2 0) into 0
14.064 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
14.065 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
14.066 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
14.066 * [backup-simplify]: Simplify (- k) into (- k)
14.066 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
14.066 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
14.067 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
14.068 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
14.068 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
14.068 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
14.068 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.068 * [taylor]: Taking taylor expansion of k in n
14.068 * [backup-simplify]: Simplify k into k
14.068 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.069 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
14.069 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
14.069 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
14.069 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
14.069 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
14.069 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
14.069 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
14.069 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
14.069 * [taylor]: Taking taylor expansion of 1/2 in n
14.069 * [backup-simplify]: Simplify 1/2 into 1/2
14.069 * [taylor]: Taking taylor expansion of (- 1 k) in n
14.069 * [taylor]: Taking taylor expansion of 1 in n
14.069 * [backup-simplify]: Simplify 1 into 1
14.069 * [taylor]: Taking taylor expansion of k in n
14.069 * [backup-simplify]: Simplify k into k
14.069 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
14.069 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
14.069 * [taylor]: Taking taylor expansion of 2 in n
14.069 * [backup-simplify]: Simplify 2 into 2
14.069 * [taylor]: Taking taylor expansion of (* n PI) in n
14.069 * [taylor]: Taking taylor expansion of n in n
14.069 * [backup-simplify]: Simplify 0 into 0
14.069 * [backup-simplify]: Simplify 1 into 1
14.069 * [taylor]: Taking taylor expansion of PI in n
14.069 * [backup-simplify]: Simplify PI into PI
14.069 * [backup-simplify]: Simplify (* 0 PI) into 0
14.070 * [backup-simplify]: Simplify (* 2 0) into 0
14.073 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
14.074 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
14.075 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
14.075 * [backup-simplify]: Simplify (- k) into (- k)
14.075 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
14.075 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
14.076 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
14.078 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
14.079 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
14.079 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
14.079 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.079 * [taylor]: Taking taylor expansion of k in n
14.079 * [backup-simplify]: Simplify k into k
14.079 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.079 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
14.079 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
14.079 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
14.080 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k)))
14.080 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
14.080 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
14.080 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
14.080 * [taylor]: Taking taylor expansion of 1/2 in k
14.080 * [backup-simplify]: Simplify 1/2 into 1/2
14.080 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
14.080 * [taylor]: Taking taylor expansion of (- 1 k) in k
14.080 * [taylor]: Taking taylor expansion of 1 in k
14.081 * [backup-simplify]: Simplify 1 into 1
14.081 * [taylor]: Taking taylor expansion of k in k
14.081 * [backup-simplify]: Simplify 0 into 0
14.081 * [backup-simplify]: Simplify 1 into 1
14.081 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
14.081 * [taylor]: Taking taylor expansion of (log n) in k
14.081 * [taylor]: Taking taylor expansion of n in k
14.081 * [backup-simplify]: Simplify n into n
14.081 * [backup-simplify]: Simplify (log n) into (log n)
14.081 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
14.081 * [taylor]: Taking taylor expansion of (* 2 PI) in k
14.081 * [taylor]: Taking taylor expansion of 2 in k
14.081 * [backup-simplify]: Simplify 2 into 2
14.081 * [taylor]: Taking taylor expansion of PI in k
14.081 * [backup-simplify]: Simplify PI into PI
14.081 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
14.082 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
14.083 * [backup-simplify]: Simplify (- 0) into 0
14.083 * [backup-simplify]: Simplify (+ 1 0) into 1
14.084 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
14.085 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
14.086 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
14.087 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
14.087 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
14.087 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.087 * [taylor]: Taking taylor expansion of k in k
14.087 * [backup-simplify]: Simplify 0 into 0
14.087 * [backup-simplify]: Simplify 1 into 1
14.088 * [backup-simplify]: Simplify (/ 1 1) into 1
14.088 * [backup-simplify]: Simplify (sqrt 0) into 0
14.089 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
14.090 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
14.091 * [backup-simplify]: Simplify 0 into 0
14.092 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
14.092 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
14.093 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
14.094 * [backup-simplify]: Simplify (- 0) into 0
14.094 * [backup-simplify]: Simplify (+ 0 0) into 0
14.094 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
14.095 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
14.096 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
14.097 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
14.098 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
14.098 * [taylor]: Taking taylor expansion of 0 in k
14.098 * [backup-simplify]: Simplify 0 into 0
14.098 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
14.099 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
14.100 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
14.100 * [backup-simplify]: Simplify (+ 0 0) into 0
14.100 * [backup-simplify]: Simplify (- 1) into -1
14.101 * [backup-simplify]: Simplify (+ 0 -1) into -1
14.102 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
14.103 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
14.105 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
14.108 * [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)))))))
14.108 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
14.109 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.109 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
14.110 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
14.111 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
14.113 * [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
14.113 * [backup-simplify]: Simplify (- 0) into 0
14.114 * [backup-simplify]: Simplify (+ 0 0) into 0
14.114 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
14.115 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
14.116 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
14.118 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.119 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
14.119 * [taylor]: Taking taylor expansion of 0 in k
14.119 * [backup-simplify]: Simplify 0 into 0
14.119 * [backup-simplify]: Simplify 0 into 0
14.119 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
14.121 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
14.122 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
14.123 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
14.125 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
14.125 * [backup-simplify]: Simplify (+ 0 0) into 0
14.125 * [backup-simplify]: Simplify (- 0) into 0
14.126 * [backup-simplify]: Simplify (+ 0 0) into 0
14.127 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
14.128 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
14.131 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
14.137 * [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))))))))
14.140 * [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))))))))
14.140 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.140 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
14.141 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
14.142 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
14.145 * [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
14.146 * [backup-simplify]: Simplify (- 0) into 0
14.146 * [backup-simplify]: Simplify (+ 0 0) into 0
14.147 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
14.148 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
14.149 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
14.150 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
14.152 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
14.152 * [taylor]: Taking taylor expansion of 0 in k
14.152 * [backup-simplify]: Simplify 0 into 0
14.152 * [backup-simplify]: Simplify 0 into 0
14.152 * [backup-simplify]: Simplify 0 into 0
14.153 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.156 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
14.159 * [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
14.160 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
14.166 * [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
14.167 * [backup-simplify]: Simplify (+ 0 0) into 0
14.167 * [backup-simplify]: Simplify (- 0) into 0
14.168 * [backup-simplify]: Simplify (+ 0 0) into 0
14.170 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
14.178 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
14.183 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 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)))))))
14.193 * [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))))))))))))))
14.200 * [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))))))))))))))
14.215 * [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))))))))))))))))))))))
14.216 * [backup-simplify]: Simplify (/ (pow (* (* PI 2) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
14.216 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (n k) around 0
14.216 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
14.216 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
14.216 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
14.216 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
14.216 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
14.216 * [taylor]: Taking taylor expansion of 1/2 in k
14.216 * [backup-simplify]: Simplify 1/2 into 1/2
14.216 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
14.216 * [taylor]: Taking taylor expansion of 1 in k
14.216 * [backup-simplify]: Simplify 1 into 1
14.216 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.216 * [taylor]: Taking taylor expansion of k in k
14.216 * [backup-simplify]: Simplify 0 into 0
14.216 * [backup-simplify]: Simplify 1 into 1
14.217 * [backup-simplify]: Simplify (/ 1 1) into 1
14.217 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
14.217 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
14.217 * [taylor]: Taking taylor expansion of 2 in k
14.217 * [backup-simplify]: Simplify 2 into 2
14.217 * [taylor]: Taking taylor expansion of (/ PI n) in k
14.217 * [taylor]: Taking taylor expansion of PI in k
14.217 * [backup-simplify]: Simplify PI into PI
14.217 * [taylor]: Taking taylor expansion of n in k
14.217 * [backup-simplify]: Simplify n into n
14.217 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
14.217 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
14.217 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
14.218 * [backup-simplify]: Simplify (- 1) into -1
14.218 * [backup-simplify]: Simplify (+ 0 -1) into -1
14.219 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
14.219 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
14.219 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
14.219 * [taylor]: Taking taylor expansion of (sqrt k) in k
14.219 * [taylor]: Taking taylor expansion of k in k
14.219 * [backup-simplify]: Simplify 0 into 0
14.219 * [backup-simplify]: Simplify 1 into 1
14.219 * [backup-simplify]: Simplify (sqrt 0) into 0
14.221 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
14.221 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
14.221 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
14.221 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
14.221 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
14.221 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
14.221 * [taylor]: Taking taylor expansion of 1/2 in n
14.221 * [backup-simplify]: Simplify 1/2 into 1/2
14.221 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
14.221 * [taylor]: Taking taylor expansion of 1 in n
14.221 * [backup-simplify]: Simplify 1 into 1
14.221 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.221 * [taylor]: Taking taylor expansion of k in n
14.222 * [backup-simplify]: Simplify k into k
14.222 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.222 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
14.222 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
14.222 * [taylor]: Taking taylor expansion of 2 in n
14.222 * [backup-simplify]: Simplify 2 into 2
14.222 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.222 * [taylor]: Taking taylor expansion of PI in n
14.222 * [backup-simplify]: Simplify PI into PI
14.222 * [taylor]: Taking taylor expansion of n in n
14.222 * [backup-simplify]: Simplify 0 into 0
14.222 * [backup-simplify]: Simplify 1 into 1
14.222 * [backup-simplify]: Simplify (/ PI 1) into PI
14.223 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
14.224 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
14.224 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
14.224 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
14.224 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
14.226 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
14.228 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
14.229 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
14.229 * [taylor]: Taking taylor expansion of (sqrt k) in n
14.229 * [taylor]: Taking taylor expansion of k in n
14.229 * [backup-simplify]: Simplify k into k
14.229 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
14.229 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
14.229 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
14.229 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
14.229 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
14.229 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
14.229 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
14.229 * [taylor]: Taking taylor expansion of 1/2 in n
14.229 * [backup-simplify]: Simplify 1/2 into 1/2
14.229 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
14.229 * [taylor]: Taking taylor expansion of 1 in n
14.230 * [backup-simplify]: Simplify 1 into 1
14.230 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.230 * [taylor]: Taking taylor expansion of k in n
14.230 * [backup-simplify]: Simplify k into k
14.230 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.230 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
14.230 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
14.230 * [taylor]: Taking taylor expansion of 2 in n
14.230 * [backup-simplify]: Simplify 2 into 2
14.230 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.230 * [taylor]: Taking taylor expansion of PI in n
14.230 * [backup-simplify]: Simplify PI into PI
14.230 * [taylor]: Taking taylor expansion of n in n
14.230 * [backup-simplify]: Simplify 0 into 0
14.230 * [backup-simplify]: Simplify 1 into 1
14.231 * [backup-simplify]: Simplify (/ PI 1) into PI
14.231 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
14.232 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
14.232 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
14.233 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
14.233 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
14.234 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
14.235 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
14.236 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
14.236 * [taylor]: Taking taylor expansion of (sqrt k) in n
14.236 * [taylor]: Taking taylor expansion of k in n
14.236 * [backup-simplify]: Simplify k into k
14.236 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
14.237 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
14.238 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
14.238 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
14.238 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
14.238 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
14.238 * [taylor]: Taking taylor expansion of 1/2 in k
14.238 * [backup-simplify]: Simplify 1/2 into 1/2
14.238 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
14.238 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
14.238 * [taylor]: Taking taylor expansion of 1 in k
14.238 * [backup-simplify]: Simplify 1 into 1
14.238 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.238 * [taylor]: Taking taylor expansion of k in k
14.238 * [backup-simplify]: Simplify 0 into 0
14.238 * [backup-simplify]: Simplify 1 into 1
14.239 * [backup-simplify]: Simplify (/ 1 1) into 1
14.239 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
14.239 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
14.239 * [taylor]: Taking taylor expansion of (* 2 PI) in k
14.239 * [taylor]: Taking taylor expansion of 2 in k
14.239 * [backup-simplify]: Simplify 2 into 2
14.239 * [taylor]: Taking taylor expansion of PI in k
14.239 * [backup-simplify]: Simplify PI into PI
14.239 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
14.240 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
14.240 * [taylor]: Taking taylor expansion of (log n) in k
14.240 * [taylor]: Taking taylor expansion of n in k
14.240 * [backup-simplify]: Simplify n into n
14.240 * [backup-simplify]: Simplify (log n) into (log n)
14.241 * [backup-simplify]: Simplify (- 1) into -1
14.241 * [backup-simplify]: Simplify (+ 0 -1) into -1
14.241 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
14.242 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
14.243 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
14.244 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
14.245 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
14.245 * [taylor]: Taking taylor expansion of (sqrt k) in k
14.245 * [taylor]: Taking taylor expansion of k in k
14.245 * [backup-simplify]: Simplify 0 into 0
14.245 * [backup-simplify]: Simplify 1 into 1
14.246 * [backup-simplify]: Simplify (sqrt 0) into 0
14.247 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
14.248 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0
14.248 * [backup-simplify]: Simplify 0 into 0
14.249 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
14.250 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
14.252 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
14.252 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
14.253 * [backup-simplify]: Simplify (- 0) into 0
14.253 * [backup-simplify]: Simplify (+ 0 0) into 0
14.254 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
14.255 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
14.256 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
14.258 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
14.259 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
14.259 * [taylor]: Taking taylor expansion of 0 in k
14.259 * [backup-simplify]: Simplify 0 into 0
14.259 * [backup-simplify]: Simplify 0 into 0
14.261 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
14.262 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
14.263 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
14.264 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.265 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
14.268 * [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
14.268 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.269 * [backup-simplify]: Simplify (- 0) into 0
14.269 * [backup-simplify]: Simplify (+ 0 0) into 0
14.270 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
14.272 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
14.274 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
14.276 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.278 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
14.278 * [taylor]: Taking taylor expansion of 0 in k
14.278 * [backup-simplify]: Simplify 0 into 0
14.278 * [backup-simplify]: Simplify 0 into 0
14.278 * [backup-simplify]: Simplify 0 into 0
14.281 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
14.283 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
14.284 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
14.285 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
14.286 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.287 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
14.297 * [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
14.297 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.298 * [backup-simplify]: Simplify (- 0) into 0
14.298 * [backup-simplify]: Simplify (+ 0 0) into 0
14.299 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
14.300 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
14.301 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
14.303 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
14.304 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
14.304 * [taylor]: Taking taylor expansion of 0 in k
14.304 * [backup-simplify]: Simplify 0 into 0
14.305 * [backup-simplify]: Simplify 0 into 0
14.305 * [backup-simplify]: Simplify 0 into 0
14.305 * [backup-simplify]: Simplify 0 into 0
14.307 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
14.308 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
14.309 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
14.312 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
14.312 * [backup-simplify]: Simplify (/ (pow (* (* PI 2) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
14.312 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (n k) around 0
14.312 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
14.312 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
14.312 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
14.312 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
14.312 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
14.312 * [taylor]: Taking taylor expansion of 1/2 in k
14.313 * [backup-simplify]: Simplify 1/2 into 1/2
14.313 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
14.313 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.313 * [taylor]: Taking taylor expansion of k in k
14.313 * [backup-simplify]: Simplify 0 into 0
14.313 * [backup-simplify]: Simplify 1 into 1
14.313 * [backup-simplify]: Simplify (/ 1 1) into 1
14.313 * [taylor]: Taking taylor expansion of 1 in k
14.313 * [backup-simplify]: Simplify 1 into 1
14.313 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
14.313 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
14.313 * [taylor]: Taking taylor expansion of -2 in k
14.313 * [backup-simplify]: Simplify -2 into -2
14.313 * [taylor]: Taking taylor expansion of (/ PI n) in k
14.313 * [taylor]: Taking taylor expansion of PI in k
14.313 * [backup-simplify]: Simplify PI into PI
14.313 * [taylor]: Taking taylor expansion of n in k
14.313 * [backup-simplify]: Simplify n into n
14.313 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
14.313 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
14.313 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
14.313 * [backup-simplify]: Simplify (+ 1 0) into 1
14.314 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
14.314 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
14.314 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
14.314 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
14.314 * [taylor]: Taking taylor expansion of (/ -1 k) in k
14.314 * [taylor]: Taking taylor expansion of -1 in k
14.314 * [backup-simplify]: Simplify -1 into -1
14.314 * [taylor]: Taking taylor expansion of k in k
14.314 * [backup-simplify]: Simplify 0 into 0
14.314 * [backup-simplify]: Simplify 1 into 1
14.314 * [backup-simplify]: Simplify (/ -1 1) into -1
14.315 * [backup-simplify]: Simplify (sqrt 0) into 0
14.315 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
14.315 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
14.316 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
14.316 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
14.316 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
14.316 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
14.316 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
14.316 * [taylor]: Taking taylor expansion of 1/2 in n
14.316 * [backup-simplify]: Simplify 1/2 into 1/2
14.316 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
14.316 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.316 * [taylor]: Taking taylor expansion of k in n
14.316 * [backup-simplify]: Simplify k into k
14.316 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.316 * [taylor]: Taking taylor expansion of 1 in n
14.316 * [backup-simplify]: Simplify 1 into 1
14.316 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
14.316 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
14.316 * [taylor]: Taking taylor expansion of -2 in n
14.316 * [backup-simplify]: Simplify -2 into -2
14.316 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.316 * [taylor]: Taking taylor expansion of PI in n
14.316 * [backup-simplify]: Simplify PI into PI
14.316 * [taylor]: Taking taylor expansion of n in n
14.316 * [backup-simplify]: Simplify 0 into 0
14.316 * [backup-simplify]: Simplify 1 into 1
14.317 * [backup-simplify]: Simplify (/ PI 1) into PI
14.317 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
14.318 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
14.318 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
14.318 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
14.320 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
14.321 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
14.323 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
14.323 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
14.323 * [taylor]: Taking taylor expansion of (/ -1 k) in n
14.323 * [taylor]: Taking taylor expansion of -1 in n
14.323 * [backup-simplify]: Simplify -1 into -1
14.323 * [taylor]: Taking taylor expansion of k in n
14.323 * [backup-simplify]: Simplify k into k
14.323 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
14.323 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
14.323 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
14.323 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
14.325 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
14.325 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
14.325 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
14.325 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
14.325 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
14.325 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
14.325 * [taylor]: Taking taylor expansion of 1/2 in n
14.325 * [backup-simplify]: Simplify 1/2 into 1/2
14.325 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
14.325 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.325 * [taylor]: Taking taylor expansion of k in n
14.325 * [backup-simplify]: Simplify k into k
14.325 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.325 * [taylor]: Taking taylor expansion of 1 in n
14.326 * [backup-simplify]: Simplify 1 into 1
14.326 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
14.326 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
14.326 * [taylor]: Taking taylor expansion of -2 in n
14.326 * [backup-simplify]: Simplify -2 into -2
14.326 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.326 * [taylor]: Taking taylor expansion of PI in n
14.326 * [backup-simplify]: Simplify PI into PI
14.326 * [taylor]: Taking taylor expansion of n in n
14.326 * [backup-simplify]: Simplify 0 into 0
14.326 * [backup-simplify]: Simplify 1 into 1
14.326 * [backup-simplify]: Simplify (/ PI 1) into PI
14.327 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
14.328 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
14.328 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
14.328 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
14.330 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
14.331 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
14.332 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
14.333 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
14.333 * [taylor]: Taking taylor expansion of (/ -1 k) in n
14.333 * [taylor]: Taking taylor expansion of -1 in n
14.333 * [backup-simplify]: Simplify -1 into -1
14.333 * [taylor]: Taking taylor expansion of k in n
14.333 * [backup-simplify]: Simplify k into k
14.333 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
14.333 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
14.333 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
14.333 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
14.335 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
14.335 * [taylor]: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k
14.335 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
14.335 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
14.335 * [taylor]: Taking taylor expansion of 1/2 in k
14.335 * [backup-simplify]: Simplify 1/2 into 1/2
14.335 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
14.335 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
14.335 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.335 * [taylor]: Taking taylor expansion of k in k
14.335 * [backup-simplify]: Simplify 0 into 0
14.335 * [backup-simplify]: Simplify 1 into 1
14.336 * [backup-simplify]: Simplify (/ 1 1) into 1
14.336 * [taylor]: Taking taylor expansion of 1 in k
14.336 * [backup-simplify]: Simplify 1 into 1
14.336 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
14.336 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
14.336 * [taylor]: Taking taylor expansion of (* -2 PI) in k
14.336 * [taylor]: Taking taylor expansion of -2 in k
14.336 * [backup-simplify]: Simplify -2 into -2
14.336 * [taylor]: Taking taylor expansion of PI in k
14.336 * [backup-simplify]: Simplify PI into PI
14.337 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
14.338 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
14.338 * [taylor]: Taking taylor expansion of (log n) in k
14.338 * [taylor]: Taking taylor expansion of n in k
14.338 * [backup-simplify]: Simplify n into n
14.338 * [backup-simplify]: Simplify (log n) into (log n)
14.339 * [backup-simplify]: Simplify (+ 1 0) into 1
14.339 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
14.340 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
14.341 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
14.342 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
14.344 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
14.344 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
14.344 * [taylor]: Taking taylor expansion of (/ -1 k) in k
14.344 * [taylor]: Taking taylor expansion of -1 in k
14.344 * [backup-simplify]: Simplify -1 into -1
14.344 * [taylor]: Taking taylor expansion of k in k
14.344 * [backup-simplify]: Simplify 0 into 0
14.344 * [backup-simplify]: Simplify 1 into 1
14.344 * [backup-simplify]: Simplify (/ -1 1) into -1
14.345 * [backup-simplify]: Simplify (sqrt 0) into 0
14.346 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
14.348 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
14.349 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
14.350 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
14.351 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
14.353 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
14.354 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
14.354 * [backup-simplify]: Simplify (+ 0 0) into 0
14.355 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
14.356 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
14.357 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
14.359 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
14.360 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
14.361 * [taylor]: Taking taylor expansion of 0 in k
14.361 * [backup-simplify]: Simplify 0 into 0
14.361 * [backup-simplify]: Simplify 0 into 0
14.361 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
14.363 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
14.364 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
14.365 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
14.366 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.366 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
14.368 * [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
14.368 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.369 * [backup-simplify]: Simplify (+ 0 0) into 0
14.369 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
14.370 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
14.371 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
14.373 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.373 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.373 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
14.374 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
14.374 * [taylor]: Taking taylor expansion of 0 in k
14.374 * [backup-simplify]: Simplify 0 into 0
14.374 * [backup-simplify]: Simplify 0 into 0
14.374 * [backup-simplify]: Simplify 0 into 0
14.375 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.377 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
14.380 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
14.380 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
14.383 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
14.383 * * * [progress]: simplifying candidates
14.383 * * * * [progress]: [ 1 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (+ (log PI) (log 2)) (log n)) (/ (- 1 k) 2))) (sqrt k)))>
14.383 * * * * [progress]: [ 2 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log (* PI 2)) (log n)) (/ (- 1 k) 2))) (sqrt k)))>
14.383 * * * * [progress]: [ 3 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* PI 2) n)) (/ (- 1 k) 2))) (sqrt k)))>
14.383 * * * * [progress]: [ 4 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* PI 2) n)) (/ (- 1 k) 2))) (sqrt k)))>
14.383 * * * * [progress]: [ 5 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* PI 2) n) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
14.383 * * * * [progress]: [ 6 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* PI 2) n) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
14.383 * * * * [progress]: [ 7 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* PI 2) n) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
14.383 * * * * [progress]: [ 8 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2))) (sqrt k)))>
14.383 * * * * [progress]: [ 9 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k)))>
14.383 * * * * [progress]: [ 10 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 11 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 12 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 13 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2)) (sqrt k)))>
14.384 * * * * [progress]: [ 14 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 15 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 16 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2)) (sqrt k)))>
14.384 * * * * [progress]: [ 17 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 18 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 19 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k)))>
14.384 * * * * [progress]: [ 20 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 21 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 22 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2)) (sqrt k)))>
14.384 * * * * [progress]: [ 23 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 24 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 25 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k)))>
14.384 * * * * [progress]: [ 26 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 27 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k)))>
14.384 * * * * [progress]: [ 28 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k)))>
14.385 * * * * [progress]: [ 29 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) 1) (/ (- 1 k) 2)) (sqrt k)))>
14.385 * * * * [progress]: [ 30 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (- 1 k)) (/ 1 2)) (sqrt k)))>
14.385 * * * * [progress]: [ 31 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* PI 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (sqrt k)))>
14.385 * * * * [progress]: [ 32 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 1) (sqrt k)))>
14.385 * * * * [progress]: [ 33 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt k)))>
14.385 * * * * [progress]: [ 34 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt k)))>
14.385 * * * * [progress]: [ 35 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt k)))>
14.385 * * * * [progress]: [ 36 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt k)))>
14.385 * * * * [progress]: [ 37 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt k)))>
14.385 * * * * [progress]: [ 38 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k)))>
14.385 * * * * [progress]: [ 39 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
14.385 * * * * [progress]: [ 40 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) 1) (/ (- 1 k) 2)) (sqrt k)))>
14.385 * * * * [progress]: [ 41 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) 1) (/ (- 1 k) 2)) (sqrt k)))>
14.385 * * * * [progress]: [ 42 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) 1) (/ (- 1 k) 2)) (sqrt k)))>
14.385 * * * * [progress]: [ 43 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (+ (log PI) (log 2)) (log n))) (/ (- 1 k) 2)) (sqrt k)))>
14.385 * * * * [progress]: [ 44 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log (* PI 2)) (log n))) (/ (- 1 k) 2)) (sqrt k)))>
14.385 * * * * [progress]: [ 45 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* (* PI 2) n))) (/ (- 1 k) 2)) (sqrt k)))>
14.385 * * * * [progress]: [ 46 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* (* PI 2) n))) (/ (- 1 k) 2)) (sqrt k)))>
14.386 * * * * [progress]: [ 47 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* PI PI) PI) (* (* 2 2) 2)) (* (* n n) n))) (/ (- 1 k) 2)) (sqrt k)))>
14.386 * * * * [progress]: [ 48 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* PI 2) (* PI 2)) (* PI 2)) (* (* n n) n))) (/ (- 1 k) 2)) (sqrt k)))>
14.386 * * * * [progress]: [ 49 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n))) (cbrt (* (* PI 2) n))) (/ (- 1 k) 2)) (sqrt k)))>
14.386 * * * * [progress]: [ 50 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))) (/ (- 1 k) 2)) (sqrt k)))>
14.386 * * * * [progress]: [ 51 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n))) (/ (- 1 k) 2)) (sqrt k)))>
14.386 * * * * [progress]: [ 52 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* (* PI 2) n)) (/ (- 1 k) 2)) (sqrt k)))>
14.386 * * * * [progress]: [ 53 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* PI 2) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2)) (sqrt k)))>
14.386 * * * * [progress]: [ 54 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* PI 2) (sqrt n)) (sqrt n)) (/ (- 1 k) 2)) (sqrt k)))>
14.386 * * * * [progress]: [ 55 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* PI 2) 1) n) (/ (- 1 k) 2)) (sqrt k)))>
14.386 * * * * [progress]: [ 56 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI (* 2 n)) (/ (- 1 k) 2)) (sqrt k)))>
14.386 * * * * [progress]: [ 57 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))>
14.386 * * * * [progress]: [ 58 / 124 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) 1))>
14.386 * * * * [progress]: [ 59 / 124 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (+ (log PI) (log 2)) (log n)) (/ (- 1 k) 2)) (log (sqrt k)))))>
14.386 * * * * [progress]: [ 60 / 124 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log (* PI 2)) (log n)) (/ (- 1 k) 2)) (log (sqrt k)))))>
14.386 * * * * [progress]: [ 61 / 124 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* PI 2) n)) (/ (- 1 k) 2)) (log (sqrt k)))))>
14.386 * * * * [progress]: [ 62 / 124 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* PI 2) n)) (/ (- 1 k) 2)) (log (sqrt k)))))>
14.386 * * * * [progress]: [ 63 / 124 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* (* PI 2) n) (/ (- 1 k) 2))) (log (sqrt k)))))>
14.387 * * * * [progress]: [ 64 / 124 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))))>
14.387 * * * * [progress]: [ 65 / 124 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))))>
14.387 * * * * [progress]: [ 66 / 124 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
14.387 * * * * [progress]: [ 67 / 124 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))))>
14.387 * * * * [progress]: [ 68 / 124 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))))>
14.387 * * * * [progress]: [ 69 / 124 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))))>
14.387 * * * * [progress]: [ 70 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* (* PI 2) n) (/ (- 1 k) 2))) (- (sqrt k))))>
14.387 * * * * [progress]: [ 71 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow n (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
14.387 * * * * [progress]: [ 72 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow n (/ (- 1 k) 2)) (sqrt (cbrt k)))))>
14.387 * * * * [progress]: [ 73 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
14.387 * * * * [progress]: [ 74 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt 1)) (/ (pow n (/ (- 1 k) 2)) (sqrt k))))>
14.387 * * * * [progress]: [ 75 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
14.387 * * * * [progress]: [ 76 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI 2) (/ (- 1 k) 2)) 1) (/ (pow n (/ (- 1 k) 2)) (sqrt k))))>
14.387 * * * * [progress]: [ 77 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
14.387 * * * * [progress]: [ 78 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (cbrt k)))))>
14.387 * * * * [progress]: [ 79 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
14.388 * * * * [progress]: [ 80 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt 1)) (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))))>
14.388 * * * * [progress]: [ 81 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
14.388 * * * * [progress]: [ 82 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))))>
14.388 * * * * [progress]: [ 83 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
14.388 * * * * [progress]: [ 84 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (cbrt k)))))>
14.388 * * * * [progress]: [ 85 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
14.388 * * * * [progress]: [ 86 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))))>
14.388 * * * * [progress]: [ 87 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
14.388 * * * * [progress]: [ 88 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))))>
14.388 * * * * [progress]: [ 89 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
14.388 * * * * [progress]: [ 90 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k)))))>
14.388 * * * * [progress]: [ 91 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
14.388 * * * * [progress]: [ 92 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))>
14.388 * * * * [progress]: [ 93 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
14.388 * * * * [progress]: [ 94 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))>
14.388 * * * * [progress]: [ 95 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))))>
14.389 * * * * [progress]: [ 96 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))>
14.389 * * * * [progress]: [ 97 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))>
14.389 * * * * [progress]: [ 98 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt 1)) (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt k))))>
14.389 * * * * [progress]: [ 99 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))>
14.389 * * * * [progress]: [ 100 / 124 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) 1) (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt k))))>
14.389 * * * * [progress]: [ 101 / 124 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))>
14.389 * * * * [progress]: [ 102 / 124 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
14.389 * * * * [progress]: [ 103 / 124 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))))>
14.389 * * * * [progress]: [ 104 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
14.389 * * * * [progress]: [ 105 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
14.389 * * * * [progress]: [ 106 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
14.389 * * * * [progress]: [ 107 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt 1)) (sqrt k)))>
14.389 * * * * [progress]: [ 108 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
14.389 * * * * [progress]: [ 109 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) 1) (sqrt k)))>
14.389 * * * * [progress]: [ 110 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2)))))>
14.389 * * * * [progress]: [ 111 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))))>
14.389 * * * * [progress]: [ 112 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))))>
14.390 * * * * [progress]: [ 113 / 124 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))))>
14.390 * * * * [progress]: [ 114 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (/ (sqrt k) (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)))))>
14.390 * * * * [progress]: [ 115 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* PI 2) n) (/ 1 2)) (* (sqrt k) (pow (* (* PI 2) n) (/ k 2)))))>
14.390 * * * * [progress]: [ 116 / 124 ] 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)))>
14.390 * * * * [progress]: [ 117 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))>
14.390 * * * * [progress]: [ 118 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))>
14.390 * * * * [progress]: [ 119 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
14.390 * * * * [progress]: [ 120 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
14.390 * * * * [progress]: [ 121 / 124 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
14.390 * * * * [progress]: [ 122 / 124 ] 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)))))))))))))))))))))))>
14.390 * * * * [progress]: [ 123 / 124 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
14.390 * * * * [progress]: [ 124 / 124 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
14.393 * [simplify]: Simplifying:
  (* (+ (+ (log PI) (log 2)) (log n)) (/ (- 1 k) 2))
  (* (+ (log (* PI 2)) (log n)) (/ (- 1 k) 2))
  (* (log (* (* PI 2) n)) (/ (- 1 k) 2))
  (* (log (* (* PI 2) n)) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* (* PI 2) n) (/ 1 2))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) 1))
  (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (pow (* (* PI 2) n) (/ 1 1))
  (pow (* (* PI 2) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* (* PI 2) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (+ 1 (sqrt k)) 1))
  (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (pow (* (* PI 2) n) (/ 1 1))
  (pow (* (* PI 2) n) 1)
  (pow (* (* PI 2) n) (- 1 k))
  (pow (* PI 2) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (log (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2))
  (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (+ (+ (log PI) (log 2)) (log n))
  (+ (log (* PI 2)) (log n))
  (log (* (* PI 2) n))
  (exp (* (* PI 2) n))
  (* (* (* (* PI PI) PI) (* (* 2 2) 2)) (* (* n n) n))
  (* (* (* (* PI 2) (* PI 2)) (* PI 2)) (* (* n n) 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))
  (* (* PI 2) (* (cbrt n) (cbrt n)))
  (* (* PI 2) (sqrt n))
  (* (* PI 2) 1)
  (* 2 n)
  (- (* (+ (+ (log PI) (log 2)) (log n)) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (+ (log (* PI 2)) (log n)) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (log (* (* PI 2) n)) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (log (* (* PI 2) n)) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (log (pow (* (* PI 2) n) (/ (- 1 k) 2))) (log (sqrt k)))
  (log (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (exp (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (/ (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (* (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (- (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (- (sqrt k))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow n (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow n (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) 1)
  (/ (pow n (/ (- 1 k) 2)) (sqrt k))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt 1))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) 1)
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt 1))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) 1)
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) 1)
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) 1)
  (/ (sqrt k) (pow n (/ (- 1 k) 2)))
  (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)))
  (* (sqrt k) (pow (* (* PI 2) n) (/ k 2)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (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 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
14.398 * * [simplify]: iteration 1: (289 enodes)
14.542 * * [simplify]: iteration 2: (739 enodes)
15.410 * * [simplify]: Extracting #0: cost 96 inf + 0
15.410 * * [simplify]: Extracting #1: cost 365 inf + 1
15.413 * * [simplify]: Extracting #2: cost 605 inf + 3068
15.419 * * [simplify]: Extracting #3: cost 637 inf + 34641
15.441 * * [simplify]: Extracting #4: cost 386 inf + 134791
15.473 * * [simplify]: Extracting #5: cost 204 inf + 223077
15.515 * * [simplify]: Extracting #6: cost 108 inf + 281807
15.563 * * [simplify]: Extracting #7: cost 58 inf + 309059
15.620 * * [simplify]: Extracting #8: cost 14 inf + 344375
15.728 * * [simplify]: Extracting #9: cost 0 inf + 355173
15.806 * * [simplify]: Extracting #10: cost 0 inf + 353863
15.878 * * [simplify]: Extracting #11: cost 0 inf + 353783
15.954 * [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))))
  (pow (* PI (* 2 n)) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* PI (* 2 n)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* PI (* 2 n)) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* PI (* 2 n)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* PI (* 2 n)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* PI (* 2 n)) (sqrt (- 1 k)))
  (pow (* PI (* 2 n)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* PI (* 2 n)) (/ 1 (sqrt 2)))
  (* PI (* 2 n))
  (pow (* PI (* 2 n)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* PI (* 2 n)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* PI (* 2 n)) (+ (sqrt k) 1))
  (pow (* PI (* 2 n)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* PI (* 2 n)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* PI (* 2 n)) (+ (sqrt k) 1))
  (pow (* PI (* 2 n)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* PI (* 2 n)) (/ 1 (sqrt 2)))
  (* PI (* 2 n))
  (* PI (* 2 n))
  (pow (* PI (* 2 n)) (- 1 k))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (pow n (- 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 (pow (* PI (* 2 n)) (- 1/2 (/ k 2))) 3)
  (sqrt (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))
  (pow (* PI (* 2 n)) (/ (- 1 k) 4))
  (pow (* PI (* 2 n)) (/ (- 1 k) 4))
  (* PI (* 2 n))
  (* PI (* 2 n))
  (log (* PI (* 2 n)))
  (log (* PI (* 2 n)))
  (log (* PI (* 2 n)))
  (exp (* PI (* 2 n)))
  (* (* (* PI PI) PI) (* 8 (* n (* n n))))
  (* (* PI (* 2 n)) (* (* PI (* 2 n)) (* PI (* 2 n))))
  (* (cbrt (* PI (* 2 n))) (cbrt (* PI (* 2 n))))
  (cbrt (* PI (* 2 n)))
  (* (* PI (* 2 n)) (* (* PI (* 2 n)) (* PI (* 2 n))))
  (sqrt (* PI (* 2 n)))
  (sqrt (* PI (* 2 n)))
  (* (* (* PI 2) (cbrt n)) (cbrt n))
  (* (* PI 2) (sqrt n))
  (* PI 2)
  (* 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 (pow (* PI (* 2 n)) (- 1/2 (/ k 2))) 3) (* k (sqrt k)))
  (* (cbrt (/ (pow (* PI (* 2 n)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* PI (* 2 n)) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* PI (* 2 n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (* (/ (pow (* PI (* 2 n)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (* 2 n)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* PI (* 2 n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (* 2 n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (* 2 n)) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow n (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (/ (pow n (- 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 k) 4)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* PI (* 2 n)) (/ (- 1 k) 4)) (cbrt (sqrt k)))
  (/ (pow (* PI (* 2 n)) (/ (- 1 k) 4)) (fabs (cbrt k)))
  (/ (pow (* PI (* 2 n)) (/ (- 1 k) 4)) (sqrt (cbrt k)))
  (/ (pow (* PI (* 2 n)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* PI (* 2 n)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (pow (* PI (* 2 n)) (/ (- 1 k) 4))
  (/ (pow (* PI (* 2 n)) (/ (- 1 k) 4)) (sqrt k))
  (/ (pow (* PI (* 2 n)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* PI (* 2 n)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (pow (* PI (* 2 n)) (/ (- 1 k) 4))
  (/ (pow (* PI (* 2 n)) (/ (- 1 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 n (- 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 k) 4)))
  (* (sqrt k) (pow (* PI (* 2 n)) (/ k 2)))
  (- (+ (+ (+ (exp (* (+ (log (* PI 2)) (log n)) 1/2)) (* (* 1/8 (* (* (log n) (* k k)) (log n))) (exp (* (+ (log (* PI 2)) (log n)) 1/2)))) (* (* (exp (* (+ (log (* PI 2)) (log n)) 1/2)) (* k k)) (* (* (log (* PI 2)) (log (* PI 2))) 1/8))) (* (* (* (log (* PI 2)) 1/4) (* (log n) (* k k))) (exp (* (+ (log (* PI 2)) (log n)) 1/2)))) (* 1/2 (* k (+ (* (log n) (exp (* (+ (log (* PI 2)) (log n)) 1/2))) (* (exp (* (+ (log (* PI 2)) (log n)) 1/2)) (log (* PI 2)))))))
  (exp (* (- 1 k) (* (+ (log (* PI 2)) (log n)) 1/2)))
  (exp (* (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))) (- 1 k)))
  (* PI (* 2 n))
  (* PI (* 2 n))
  (* PI (* 2 n))
  (- (+ (- (* (* (* +nan.0 (log (* PI 2))) (* (log n) (* k k))) (exp (* (+ (log (* PI 2)) (log n)) 1/2))) (* (* +nan.0 (log (* PI 2))) (* (exp (* (+ (log (* PI 2)) (log n)) 1/2)) (* k k)))) (- (* (* +nan.0 (* (* (log n) k) (* (log n) k))) (exp (* (+ (log (* PI 2)) (log n)) 1/2))) (+ (- (* +nan.0 (* (exp (* (+ (log (* PI 2)) (log n)) 1/2)) k)) (* +nan.0 (exp (* (+ (log (* PI 2)) (log n)) 1/2)))) (+ (- (* (* (log (* PI 2)) (log (* PI 2))) (* (exp (* (+ (log (* PI 2)) (log n)) 1/2)) (* (* k k) +nan.0))) (* (* +nan.0 (* (log n) (* k k))) (exp (* (+ (log (* PI 2)) (log n)) 1/2)))) (+ (- (* (exp (* (+ (log (* PI 2)) (log n)) 1/2)) (* (* k k) +nan.0)) (* (* +nan.0 (* (exp (* (+ (log (* PI 2)) (log n)) 1/2)) k)) (log (* PI 2)))) (* (* +nan.0 (exp (* (+ (log (* PI 2)) (log n)) 1/2))) (* k (log n)))))))))
  (+ (* (- +nan.0) (/ (exp (* (- 1 k) (* (+ (log (* PI 2)) (log n)) 1/2))) k)) (- (/ +nan.0 (/ (* k k) (exp (* (- 1 k) (* (+ (log (* PI 2)) (log n)) 1/2))))) (/ (/ +nan.0 (/ (* k k) (exp (* (- 1 k) (* (+ (log (* PI 2)) (log n)) 1/2))))) k)))
  (+ (- (/ (exp (* (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))) (- 1 k))) (/ k +nan.0))) (* +nan.0 (- (/ (/ (exp (* (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))) (- 1 k))) k) k) (exp (* (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))) (- 1 k))))))
15.970 * * * [progress]: adding candidates to table
17.215 * [progress]: [Phase 3 of 3] Extracting.
17.215 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* n 2) PI)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))))> #<alt (λ (k n) (* (pow k (/ -1/2 2)) (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* 2 (* PI n)) (+ (sqrt k) 1)) (/ (- 1 (sqrt k)) 2))))> #<alt (λ (k n) (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))>)
17.216 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2 PI) n) n k)
17.216 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* n 2) PI)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))))> #<alt (λ (k n) (* (pow k (/ -1/2 2)) (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* 2 (* PI n)) (+ (sqrt k) 1)) (/ (- 1 (sqrt k)) 2))))> #<alt (λ (k n) (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))>)
17.265 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (pow k (/ -1/2 2)) (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>)
17.308 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* n 2) PI)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))))> #<alt (λ (k n) (* (pow k (/ -1/2 2)) (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* 2 (* PI n)) (+ (sqrt k) 1)) (/ (- 1 (sqrt k)) 2))))> #<alt (λ (k n) (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))>)
17.361 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* n 2) PI)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))))> #<alt (λ (k n) (* (pow k (/ -1/2 2)) (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (pow k -1/2) (pow (pow (* 2 (* PI n)) (+ (sqrt k) 1)) (/ (- 1 (sqrt k)) 2))))> #<alt (λ (k n) (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))>)
17.405 * * * [regime]: Found split indices: #<option (#s(si 1 255))>
17.405 * [simplify]: Simplifying:
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
17.405 * * [simplify]: iteration 1: (12 enodes)
17.408 * * [simplify]: iteration 2: (14 enodes)
17.410 * * [simplify]: Extracting #0: cost 1 inf + 0
17.410 * * [simplify]: Extracting #1: cost 3 inf + 0
17.410 * * [simplify]: Extracting #2: cost 6 inf + 0
17.410 * * [simplify]: Extracting #3: cost 9 inf + 1
17.410 * * [simplify]: Extracting #4: cost 8 inf + 44
17.410 * * [simplify]: Extracting #5: cost 4 inf + 171
17.410 * * [simplify]: Extracting #6: cost 0 inf + 1126
17.410 * [simplify]: Simplified to:
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
26.427 * [regime-testing]: Baseline error score: 0.35267914722094756
26.429 * [regime-testing]: Oracle error score: 0.04363289786331465
26.434 * [regime-testing]: End program error score: 0.35267914722094756