49.336 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.187 * * * [progress]: [2/2] Setting up program.
0.195 * [progress]: [Phase 2 of 3] Improving.
0.196 * [simplify]: Simplifying:
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.196 * * [simplify]: iteration 0: 13 enodes
0.202 * * [simplify]: iteration 1: 29 enodes
0.209 * * [simplify]: iteration 2: 58 enodes
0.247 * * [simplify]: iteration 3: 114 enodes
0.288 * * [simplify]: iteration 4: 285 enodes
0.392 * * [simplify]: iteration 5: 806 enodes
1.432 * * [simplify]: iteration 6: 2693 enodes
2.413 * * [simplify]: iteration complete: 5001 enodes
2.413 * * [simplify]: Extracting #0: cost 1 inf + 0
2.413 * * [simplify]: Extracting #1: cost 108 inf + 0
2.415 * * [simplify]: Extracting #2: cost 443 inf + 1
2.418 * * [simplify]: Extracting #3: cost 1003 inf + 8
2.424 * * [simplify]: Extracting #4: cost 1325 inf + 10758
2.454 * * [simplify]: Extracting #5: cost 713 inf + 95758
2.558 * * [simplify]: Extracting #6: cost 212 inf + 355864
2.707 * * [simplify]: Extracting #7: cost 1 inf + 567087
2.843 * * [simplify]: Extracting #8: cost 0 inf + 554854
2.989 * [simplify]: Simplified to:
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))
2.990 * * [progress]: iteration 1 / 4
2.990 * * * [progress]: picking best candidate
2.998 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
2.998 * * * [progress]: localizing error
3.047 * * * [progress]: generating rewritten candidates
3.047 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1)
3.057 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
3.076 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
3.107 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2)
3.146 * * * [progress]: generating series expansions
3.146 * * * * [progress]: [ 1 / 4 ] generating series at (2 1)
3.146 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
3.146 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
3.146 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
3.146 * [taylor]: Taking taylor expansion of 1.0 in k
3.146 * [backup-simplify]: Simplify 1.0 into 1.0
3.146 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.146 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.146 * [taylor]: Taking taylor expansion of k in k
3.146 * [backup-simplify]: Simplify 0 into 0
3.146 * [backup-simplify]: Simplify 1 into 1
3.147 * [backup-simplify]: Simplify (/ 1 1) into 1
3.148 * [backup-simplify]: Simplify (sqrt 0) into 0
3.149 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.149 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
3.149 * [taylor]: Taking taylor expansion of 1.0 in k
3.149 * [backup-simplify]: Simplify 1.0 into 1.0
3.149 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.149 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.149 * [taylor]: Taking taylor expansion of k in k
3.149 * [backup-simplify]: Simplify 0 into 0
3.149 * [backup-simplify]: Simplify 1 into 1
3.150 * [backup-simplify]: Simplify (/ 1 1) into 1
3.150 * [backup-simplify]: Simplify (sqrt 0) into 0
3.151 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.152 * [backup-simplify]: Simplify (* 1.0 0) into 0
3.152 * [backup-simplify]: Simplify 0 into 0
3.153 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
3.154 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.155 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
3.158 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.160 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
3.161 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.162 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.166 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.168 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
3.168 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.170 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
3.170 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
3.170 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
3.170 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
3.170 * [taylor]: Taking taylor expansion of 1.0 in k
3.170 * [backup-simplify]: Simplify 1.0 into 1.0
3.170 * [taylor]: Taking taylor expansion of (sqrt k) in k
3.170 * [taylor]: Taking taylor expansion of k in k
3.170 * [backup-simplify]: Simplify 0 into 0
3.170 * [backup-simplify]: Simplify 1 into 1
3.171 * [backup-simplify]: Simplify (sqrt 0) into 0
3.172 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.172 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
3.172 * [taylor]: Taking taylor expansion of 1.0 in k
3.172 * [backup-simplify]: Simplify 1.0 into 1.0
3.172 * [taylor]: Taking taylor expansion of (sqrt k) in k
3.172 * [taylor]: Taking taylor expansion of k in k
3.172 * [backup-simplify]: Simplify 0 into 0
3.172 * [backup-simplify]: Simplify 1 into 1
3.172 * [backup-simplify]: Simplify (sqrt 0) into 0
3.174 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.174 * [backup-simplify]: Simplify (* 1.0 0) into 0
3.174 * [backup-simplify]: Simplify 0 into 0
3.176 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
3.176 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.179 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.181 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
3.181 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.185 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.187 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
3.188 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.189 * [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))))))))
3.189 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
3.189 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
3.189 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
3.189 * [taylor]: Taking taylor expansion of 1.0 in k
3.189 * [backup-simplify]: Simplify 1.0 into 1.0
3.189 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
3.189 * [taylor]: Taking taylor expansion of (/ -1 k) in k
3.189 * [taylor]: Taking taylor expansion of -1 in k
3.189 * [backup-simplify]: Simplify -1 into -1
3.189 * [taylor]: Taking taylor expansion of k in k
3.189 * [backup-simplify]: Simplify 0 into 0
3.189 * [backup-simplify]: Simplify 1 into 1
3.189 * [backup-simplify]: Simplify (/ -1 1) into -1
3.190 * [backup-simplify]: Simplify (sqrt 0) into 0
3.190 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
3.191 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
3.191 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
3.191 * [taylor]: Taking taylor expansion of 1.0 in k
3.191 * [backup-simplify]: Simplify 1.0 into 1.0
3.191 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
3.191 * [taylor]: Taking taylor expansion of (/ -1 k) in k
3.191 * [taylor]: Taking taylor expansion of -1 in k
3.191 * [backup-simplify]: Simplify -1 into -1
3.191 * [taylor]: Taking taylor expansion of k in k
3.191 * [backup-simplify]: Simplify 0 into 0
3.191 * [backup-simplify]: Simplify 1 into 1
3.191 * [backup-simplify]: Simplify (/ -1 1) into -1
3.191 * [backup-simplify]: Simplify (sqrt 0) into 0
3.192 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
3.192 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
3.192 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.193 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
3.195 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.196 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
3.196 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.197 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.199 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.201 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
3.202 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.202 * [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)))))
3.202 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
3.203 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
3.203 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
3.203 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.203 * [taylor]: Taking taylor expansion of 2.0 in n
3.203 * [backup-simplify]: Simplify 2.0 into 2.0
3.203 * [taylor]: Taking taylor expansion of (* n PI) in n
3.203 * [taylor]: Taking taylor expansion of n in n
3.203 * [backup-simplify]: Simplify 0 into 0
3.203 * [backup-simplify]: Simplify 1 into 1
3.203 * [taylor]: Taking taylor expansion of PI in n
3.203 * [backup-simplify]: Simplify PI into PI
3.203 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.203 * [taylor]: Taking taylor expansion of 2.0 in n
3.203 * [backup-simplify]: Simplify 2.0 into 2.0
3.203 * [taylor]: Taking taylor expansion of (* n PI) in n
3.203 * [taylor]: Taking taylor expansion of n in n
3.203 * [backup-simplify]: Simplify 0 into 0
3.203 * [backup-simplify]: Simplify 1 into 1
3.203 * [taylor]: Taking taylor expansion of PI in n
3.203 * [backup-simplify]: Simplify PI into PI
3.203 * [backup-simplify]: Simplify (* 0 PI) into 0
3.204 * [backup-simplify]: Simplify (* 2.0 0) into 0
3.204 * [backup-simplify]: Simplify 0 into 0
3.205 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.206 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
3.206 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.207 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.207 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
3.207 * [backup-simplify]: Simplify 0 into 0
3.208 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.209 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.209 * [backup-simplify]: Simplify 0 into 0
3.209 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.210 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
3.210 * [backup-simplify]: Simplify 0 into 0
3.211 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.212 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
3.212 * [backup-simplify]: Simplify 0 into 0
3.213 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.214 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
3.214 * [backup-simplify]: Simplify 0 into 0
3.215 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
3.216 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
3.216 * [backup-simplify]: Simplify 0 into 0
3.216 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
3.217 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
3.217 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
3.217 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.217 * [taylor]: Taking taylor expansion of 2.0 in n
3.217 * [backup-simplify]: Simplify 2.0 into 2.0
3.217 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.217 * [taylor]: Taking taylor expansion of PI in n
3.217 * [backup-simplify]: Simplify PI into PI
3.217 * [taylor]: Taking taylor expansion of n in n
3.217 * [backup-simplify]: Simplify 0 into 0
3.217 * [backup-simplify]: Simplify 1 into 1
3.218 * [backup-simplify]: Simplify (/ PI 1) into PI
3.218 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.218 * [taylor]: Taking taylor expansion of 2.0 in n
3.218 * [backup-simplify]: Simplify 2.0 into 2.0
3.218 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.218 * [taylor]: Taking taylor expansion of PI in n
3.218 * [backup-simplify]: Simplify PI into PI
3.218 * [taylor]: Taking taylor expansion of n in n
3.218 * [backup-simplify]: Simplify 0 into 0
3.218 * [backup-simplify]: Simplify 1 into 1
3.218 * [backup-simplify]: Simplify (/ PI 1) into PI
3.219 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.219 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.220 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.221 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
3.221 * [backup-simplify]: Simplify 0 into 0
3.222 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.223 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
3.223 * [backup-simplify]: Simplify 0 into 0
3.224 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.225 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.225 * [backup-simplify]: Simplify 0 into 0
3.227 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.228 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.228 * [backup-simplify]: Simplify 0 into 0
3.229 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.231 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.231 * [backup-simplify]: Simplify 0 into 0
3.232 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.234 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.234 * [backup-simplify]: Simplify 0 into 0
3.235 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
3.235 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
3.235 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
3.235 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.235 * [taylor]: Taking taylor expansion of -2.0 in n
3.235 * [backup-simplify]: Simplify -2.0 into -2.0
3.235 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.235 * [taylor]: Taking taylor expansion of PI in n
3.235 * [backup-simplify]: Simplify PI into PI
3.235 * [taylor]: Taking taylor expansion of n in n
3.235 * [backup-simplify]: Simplify 0 into 0
3.235 * [backup-simplify]: Simplify 1 into 1
3.236 * [backup-simplify]: Simplify (/ PI 1) into PI
3.236 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.236 * [taylor]: Taking taylor expansion of -2.0 in n
3.236 * [backup-simplify]: Simplify -2.0 into -2.0
3.236 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.236 * [taylor]: Taking taylor expansion of PI in n
3.236 * [backup-simplify]: Simplify PI into PI
3.236 * [taylor]: Taking taylor expansion of n in n
3.236 * [backup-simplify]: Simplify 0 into 0
3.236 * [backup-simplify]: Simplify 1 into 1
3.237 * [backup-simplify]: Simplify (/ PI 1) into PI
3.237 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.238 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.239 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.239 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
3.240 * [backup-simplify]: Simplify 0 into 0
3.241 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.242 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
3.242 * [backup-simplify]: Simplify 0 into 0
3.243 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.244 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.244 * [backup-simplify]: Simplify 0 into 0
3.245 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.247 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.247 * [backup-simplify]: Simplify 0 into 0
3.255 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.257 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.257 * [backup-simplify]: Simplify 0 into 0
3.259 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.260 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.260 * [backup-simplify]: Simplify 0 into 0
3.261 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
3.261 * * * * [progress]: [ 3 / 4 ] generating series at (2)
3.262 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))))
3.262 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (k n) around 0
3.262 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
3.262 * [taylor]: Taking taylor expansion of 1.0 in n
3.262 * [backup-simplify]: Simplify 1.0 into 1.0
3.262 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
3.262 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
3.262 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
3.262 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
3.262 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
3.262 * [taylor]: Taking taylor expansion of 0.5 in n
3.262 * [backup-simplify]: Simplify 0.5 into 0.5
3.262 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
3.262 * [taylor]: Taking taylor expansion of 1.0 in n
3.262 * [backup-simplify]: Simplify 1.0 into 1.0
3.263 * [taylor]: Taking taylor expansion of k in n
3.263 * [backup-simplify]: Simplify k into k
3.263 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
3.263 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.263 * [taylor]: Taking taylor expansion of 2.0 in n
3.263 * [backup-simplify]: Simplify 2.0 into 2.0
3.263 * [taylor]: Taking taylor expansion of (* n PI) in n
3.263 * [taylor]: Taking taylor expansion of n in n
3.263 * [backup-simplify]: Simplify 0 into 0
3.263 * [backup-simplify]: Simplify 1 into 1
3.263 * [taylor]: Taking taylor expansion of PI in n
3.263 * [backup-simplify]: Simplify PI into PI
3.263 * [backup-simplify]: Simplify (* 0 PI) into 0
3.264 * [backup-simplify]: Simplify (* 2.0 0) into 0
3.265 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.267 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
3.269 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.269 * [backup-simplify]: Simplify (- k) into (- k)
3.269 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
3.269 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
3.270 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.272 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
3.273 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
3.273 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
3.273 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.273 * [taylor]: Taking taylor expansion of k in n
3.273 * [backup-simplify]: Simplify k into k
3.273 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.273 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
3.273 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.273 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
3.273 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
3.274 * [taylor]: Taking taylor expansion of 1.0 in k
3.274 * [backup-simplify]: Simplify 1.0 into 1.0
3.274 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
3.274 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
3.274 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
3.274 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
3.274 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
3.274 * [taylor]: Taking taylor expansion of 0.5 in k
3.274 * [backup-simplify]: Simplify 0.5 into 0.5
3.274 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
3.274 * [taylor]: Taking taylor expansion of 1.0 in k
3.274 * [backup-simplify]: Simplify 1.0 into 1.0
3.274 * [taylor]: Taking taylor expansion of k in k
3.274 * [backup-simplify]: Simplify 0 into 0
3.274 * [backup-simplify]: Simplify 1 into 1
3.274 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
3.274 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
3.274 * [taylor]: Taking taylor expansion of 2.0 in k
3.274 * [backup-simplify]: Simplify 2.0 into 2.0
3.274 * [taylor]: Taking taylor expansion of (* n PI) in k
3.274 * [taylor]: Taking taylor expansion of n in k
3.274 * [backup-simplify]: Simplify n into n
3.274 * [taylor]: Taking taylor expansion of PI in k
3.274 * [backup-simplify]: Simplify PI into PI
3.274 * [backup-simplify]: Simplify (* n PI) into (* n PI)
3.274 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
3.274 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
3.275 * [backup-simplify]: Simplify (- 0) into 0
3.275 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
3.276 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
3.276 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
3.276 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
3.276 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.276 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.276 * [taylor]: Taking taylor expansion of k in k
3.276 * [backup-simplify]: Simplify 0 into 0
3.276 * [backup-simplify]: Simplify 1 into 1
3.277 * [backup-simplify]: Simplify (/ 1 1) into 1
3.277 * [backup-simplify]: Simplify (sqrt 0) into 0
3.279 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.279 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
3.279 * [taylor]: Taking taylor expansion of 1.0 in k
3.279 * [backup-simplify]: Simplify 1.0 into 1.0
3.279 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
3.279 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
3.279 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
3.279 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
3.279 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
3.279 * [taylor]: Taking taylor expansion of 0.5 in k
3.279 * [backup-simplify]: Simplify 0.5 into 0.5
3.279 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
3.279 * [taylor]: Taking taylor expansion of 1.0 in k
3.279 * [backup-simplify]: Simplify 1.0 into 1.0
3.279 * [taylor]: Taking taylor expansion of k in k
3.279 * [backup-simplify]: Simplify 0 into 0
3.279 * [backup-simplify]: Simplify 1 into 1
3.279 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
3.279 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
3.279 * [taylor]: Taking taylor expansion of 2.0 in k
3.279 * [backup-simplify]: Simplify 2.0 into 2.0
3.279 * [taylor]: Taking taylor expansion of (* n PI) in k
3.279 * [taylor]: Taking taylor expansion of n in k
3.279 * [backup-simplify]: Simplify n into n
3.279 * [taylor]: Taking taylor expansion of PI in k
3.279 * [backup-simplify]: Simplify PI into PI
3.279 * [backup-simplify]: Simplify (* n PI) into (* n PI)
3.279 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
3.280 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
3.280 * [backup-simplify]: Simplify (- 0) into 0
3.280 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
3.281 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
3.281 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
3.281 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
3.281 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.281 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.281 * [taylor]: Taking taylor expansion of k in k
3.281 * [backup-simplify]: Simplify 0 into 0
3.281 * [backup-simplify]: Simplify 1 into 1
3.282 * [backup-simplify]: Simplify (/ 1 1) into 1
3.282 * [backup-simplify]: Simplify (sqrt 0) into 0
3.283 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.284 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0
3.284 * [backup-simplify]: Simplify (* 1.0 0) into 0
3.284 * [taylor]: Taking taylor expansion of 0 in n
3.284 * [backup-simplify]: Simplify 0 into 0
3.284 * [backup-simplify]: Simplify 0 into 0
3.285 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
3.285 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
3.286 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
3.287 * [backup-simplify]: Simplify (- 1) into -1
3.287 * [backup-simplify]: Simplify (+ 0 -1) into -1
3.289 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
3.290 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
3.290 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))))
3.292 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 0)) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))
3.294 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
3.294 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n
3.294 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n
3.294 * [taylor]: Taking taylor expansion of +nan.0 in n
3.294 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.294 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
3.294 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
3.294 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
3.294 * [taylor]: Taking taylor expansion of 0.5 in n
3.295 * [backup-simplify]: Simplify 0.5 into 0.5
3.295 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
3.295 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
3.295 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
3.295 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
3.295 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
3.295 * [taylor]: Taking taylor expansion of 1.0 in n
3.295 * [backup-simplify]: Simplify 1.0 into 1.0
3.295 * [taylor]: Taking taylor expansion of (log PI) in n
3.295 * [taylor]: Taking taylor expansion of PI in n
3.295 * [backup-simplify]: Simplify PI into PI
3.295 * [backup-simplify]: Simplify (log PI) into (log PI)
3.296 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
3.298 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
3.298 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
3.298 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
3.298 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
3.298 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
3.298 * [taylor]: Taking taylor expansion of 1.0 in n
3.298 * [backup-simplify]: Simplify 1.0 into 1.0
3.298 * [taylor]: Taking taylor expansion of (log n) in n
3.298 * [taylor]: Taking taylor expansion of n in n
3.298 * [backup-simplify]: Simplify 0 into 0
3.298 * [backup-simplify]: Simplify 1 into 1
3.299 * [backup-simplify]: Simplify (log 1) into 0
3.299 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.299 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
3.299 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
3.299 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
3.299 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
3.299 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
3.299 * [taylor]: Taking taylor expansion of 1.0 in n
3.300 * [backup-simplify]: Simplify 1.0 into 1.0
3.300 * [taylor]: Taking taylor expansion of (log 2.0) in n
3.300 * [taylor]: Taking taylor expansion of 2.0 in n
3.300 * [backup-simplify]: Simplify 2.0 into 2.0
3.300 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
3.301 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
3.302 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
3.303 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
3.304 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
3.306 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
3.307 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
3.309 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
3.310 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))
3.312 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))
3.313 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
3.313 * [backup-simplify]: Simplify 0 into 0
3.314 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
3.317 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.318 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
3.319 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
3.321 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0
3.321 * [backup-simplify]: Simplify (- 0) into 0
3.321 * [backup-simplify]: Simplify (+ 0 0) into 0
3.322 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
3.323 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
3.325 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))
3.327 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))
3.330 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))
3.330 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) in n
3.330 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) in n
3.330 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n
3.330 * [taylor]: Taking taylor expansion of +nan.0 in n
3.330 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.330 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n
3.330 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
3.330 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
3.330 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
3.330 * [taylor]: Taking taylor expansion of 0.5 in n
3.330 * [backup-simplify]: Simplify 0.5 into 0.5
3.330 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
3.330 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
3.330 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
3.330 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
3.330 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
3.330 * [taylor]: Taking taylor expansion of 1.0 in n
3.330 * [backup-simplify]: Simplify 1.0 into 1.0
3.330 * [taylor]: Taking taylor expansion of (log PI) in n
3.330 * [taylor]: Taking taylor expansion of PI in n
3.330 * [backup-simplify]: Simplify PI into PI
3.330 * [backup-simplify]: Simplify (log PI) into (log PI)
3.331 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
3.332 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
3.332 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
3.332 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
3.332 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
3.332 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
3.332 * [taylor]: Taking taylor expansion of 1.0 in n
3.332 * [backup-simplify]: Simplify 1.0 into 1.0
3.332 * [taylor]: Taking taylor expansion of (log n) in n
3.332 * [taylor]: Taking taylor expansion of n in n
3.332 * [backup-simplify]: Simplify 0 into 0
3.332 * [backup-simplify]: Simplify 1 into 1
3.332 * [backup-simplify]: Simplify (log 1) into 0
3.333 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.333 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
3.333 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
3.333 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
3.333 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
3.333 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
3.333 * [taylor]: Taking taylor expansion of 1.0 in n
3.333 * [backup-simplify]: Simplify 1.0 into 1.0
3.333 * [taylor]: Taking taylor expansion of (log 2.0) in n
3.333 * [taylor]: Taking taylor expansion of 2.0 in n
3.333 * [backup-simplify]: Simplify 2.0 into 2.0
3.333 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
3.334 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
3.335 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
3.335 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
3.336 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
3.337 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
3.337 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
3.338 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
3.338 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
3.338 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.338 * [taylor]: Taking taylor expansion of 2.0 in n
3.338 * [backup-simplify]: Simplify 2.0 into 2.0
3.338 * [taylor]: Taking taylor expansion of (* n PI) in n
3.338 * [taylor]: Taking taylor expansion of n in n
3.338 * [backup-simplify]: Simplify 0 into 0
3.338 * [backup-simplify]: Simplify 1 into 1
3.338 * [taylor]: Taking taylor expansion of PI in n
3.338 * [backup-simplify]: Simplify PI into PI
3.339 * [backup-simplify]: Simplify (* 0 PI) into 0
3.339 * [backup-simplify]: Simplify (* 2.0 0) into 0
3.341 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.342 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
3.343 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.343 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n
3.343 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n
3.343 * [taylor]: Taking taylor expansion of +nan.0 in n
3.343 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.343 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
3.343 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
3.343 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
3.343 * [taylor]: Taking taylor expansion of 0.5 in n
3.344 * [backup-simplify]: Simplify 0.5 into 0.5
3.344 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
3.344 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
3.344 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
3.344 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
3.344 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
3.344 * [taylor]: Taking taylor expansion of 1.0 in n
3.344 * [backup-simplify]: Simplify 1.0 into 1.0
3.344 * [taylor]: Taking taylor expansion of (log PI) in n
3.344 * [taylor]: Taking taylor expansion of PI in n
3.344 * [backup-simplify]: Simplify PI into PI
3.344 * [backup-simplify]: Simplify (log PI) into (log PI)
3.345 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
3.347 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
3.347 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
3.347 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
3.347 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
3.347 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
3.347 * [taylor]: Taking taylor expansion of 1.0 in n
3.347 * [backup-simplify]: Simplify 1.0 into 1.0
3.347 * [taylor]: Taking taylor expansion of (log n) in n
3.347 * [taylor]: Taking taylor expansion of n in n
3.347 * [backup-simplify]: Simplify 0 into 0
3.347 * [backup-simplify]: Simplify 1 into 1
3.348 * [backup-simplify]: Simplify (log 1) into 0
3.348 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.348 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
3.349 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
3.349 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
3.349 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
3.349 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
3.349 * [taylor]: Taking taylor expansion of 1.0 in n
3.349 * [backup-simplify]: Simplify 1.0 into 1.0
3.349 * [taylor]: Taking taylor expansion of (log 2.0) in n
3.349 * [taylor]: Taking taylor expansion of 2.0 in n
3.349 * [backup-simplify]: Simplify 2.0 into 2.0
3.349 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
3.350 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
3.352 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
3.352 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
3.354 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
3.355 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
3.356 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
3.358 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
3.359 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.362 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))
3.365 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))))
3.366 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))
3.368 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))
3.372 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))
3.378 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))))))))
3.384 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))
3.386 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
3.387 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
3.388 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
3.390 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
3.390 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.391 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
3.392 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
3.392 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
3.394 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
3.395 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
3.396 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
3.398 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
3.406 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0
3.408 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0
3.410 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.412 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0
3.413 * [backup-simplify]: Simplify (- 0) into 0
3.413 * [backup-simplify]: Simplify 0 into 0
3.413 * [backup-simplify]: Simplify 0 into 0
3.414 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.418 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.419 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.420 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
3.423 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0
3.423 * [backup-simplify]: Simplify (- 0) into 0
3.424 * [backup-simplify]: Simplify (+ 0 0) into 0
3.425 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
3.427 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
3.429 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3)))
3.434 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (+ (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) +nan.0) (* (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))
3.445 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))
3.445 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n
3.445 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n
3.445 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n
3.445 * [taylor]: Taking taylor expansion of +nan.0 in n
3.445 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.445 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n
3.445 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
3.445 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
3.445 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
3.445 * [taylor]: Taking taylor expansion of 0.5 in n
3.445 * [backup-simplify]: Simplify 0.5 into 0.5
3.445 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
3.445 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
3.446 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
3.446 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
3.446 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
3.446 * [taylor]: Taking taylor expansion of 1.0 in n
3.446 * [backup-simplify]: Simplify 1.0 into 1.0
3.446 * [taylor]: Taking taylor expansion of (log PI) in n
3.446 * [taylor]: Taking taylor expansion of PI in n
3.446 * [backup-simplify]: Simplify PI into PI
3.446 * [backup-simplify]: Simplify (log PI) into (log PI)
3.447 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
3.449 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
3.449 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
3.449 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
3.449 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
3.449 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
3.449 * [taylor]: Taking taylor expansion of 1.0 in n
3.449 * [backup-simplify]: Simplify 1.0 into 1.0
3.449 * [taylor]: Taking taylor expansion of (log n) in n
3.449 * [taylor]: Taking taylor expansion of n in n
3.449 * [backup-simplify]: Simplify 0 into 0
3.449 * [backup-simplify]: Simplify 1 into 1
3.449 * [backup-simplify]: Simplify (log 1) into 0
3.450 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.450 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
3.450 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
3.450 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
3.450 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
3.450 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
3.450 * [taylor]: Taking taylor expansion of 1.0 in n
3.450 * [backup-simplify]: Simplify 1.0 into 1.0
3.450 * [taylor]: Taking taylor expansion of (log 2.0) in n
3.450 * [taylor]: Taking taylor expansion of 2.0 in n
3.450 * [backup-simplify]: Simplify 2.0 into 2.0
3.451 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
3.452 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
3.453 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
3.454 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
3.455 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
3.456 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
3.458 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
3.459 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
3.459 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
3.459 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.459 * [taylor]: Taking taylor expansion of 2.0 in n
3.459 * [backup-simplify]: Simplify 2.0 into 2.0
3.459 * [taylor]: Taking taylor expansion of (* n PI) in n
3.459 * [taylor]: Taking taylor expansion of n in n
3.459 * [backup-simplify]: Simplify 0 into 0
3.459 * [backup-simplify]: Simplify 1 into 1
3.459 * [taylor]: Taking taylor expansion of PI in n
3.459 * [backup-simplify]: Simplify PI into PI
3.460 * [backup-simplify]: Simplify (* 0 PI) into 0
3.460 * [backup-simplify]: Simplify (* 2.0 0) into 0
3.462 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.463 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
3.464 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.464 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n
3.464 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n
3.465 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n
3.465 * [taylor]: Taking taylor expansion of +nan.0 in n
3.465 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.465 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n
3.465 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
3.465 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
3.465 * [taylor]: Taking taylor expansion of 0.5 in n
3.465 * [backup-simplify]: Simplify 0.5 into 0.5
3.465 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
3.465 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
3.465 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
3.465 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
3.465 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
3.465 * [taylor]: Taking taylor expansion of 1.0 in n
3.465 * [backup-simplify]: Simplify 1.0 into 1.0
3.465 * [taylor]: Taking taylor expansion of (log 2.0) in n
3.465 * [taylor]: Taking taylor expansion of 2.0 in n
3.465 * [backup-simplify]: Simplify 2.0 into 2.0
3.465 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
3.467 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
3.468 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
3.468 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
3.468 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
3.468 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
3.468 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
3.468 * [taylor]: Taking taylor expansion of 1.0 in n
3.468 * [backup-simplify]: Simplify 1.0 into 1.0
3.468 * [taylor]: Taking taylor expansion of (log n) in n
3.468 * [taylor]: Taking taylor expansion of n in n
3.468 * [backup-simplify]: Simplify 0 into 0
3.468 * [backup-simplify]: Simplify 1 into 1
3.469 * [backup-simplify]: Simplify (log 1) into 0
3.469 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.469 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
3.469 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
3.469 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
3.469 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
3.469 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
3.469 * [taylor]: Taking taylor expansion of 1.0 in n
3.469 * [backup-simplify]: Simplify 1.0 into 1.0
3.469 * [taylor]: Taking taylor expansion of (log PI) in n
3.469 * [taylor]: Taking taylor expansion of PI in n
3.470 * [backup-simplify]: Simplify PI into PI
3.470 * [backup-simplify]: Simplify (log PI) into (log PI)
3.471 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
3.472 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
3.473 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
3.474 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
3.476 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))
3.477 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))
3.478 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
3.478 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n
3.478 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n
3.479 * [taylor]: Taking taylor expansion of +nan.0 in n
3.479 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.479 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n
3.479 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
3.479 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
3.479 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
3.479 * [taylor]: Taking taylor expansion of 0.5 in n
3.479 * [backup-simplify]: Simplify 0.5 into 0.5
3.479 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
3.479 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
3.479 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
3.479 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
3.479 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
3.479 * [taylor]: Taking taylor expansion of 1.0 in n
3.479 * [backup-simplify]: Simplify 1.0 into 1.0
3.479 * [taylor]: Taking taylor expansion of (log PI) in n
3.479 * [taylor]: Taking taylor expansion of PI in n
3.479 * [backup-simplify]: Simplify PI into PI
3.479 * [backup-simplify]: Simplify (log PI) into (log PI)
3.480 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
3.482 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
3.482 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
3.482 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
3.482 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
3.482 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
3.482 * [taylor]: Taking taylor expansion of 1.0 in n
3.482 * [backup-simplify]: Simplify 1.0 into 1.0
3.482 * [taylor]: Taking taylor expansion of (log n) in n
3.482 * [taylor]: Taking taylor expansion of n in n
3.482 * [backup-simplify]: Simplify 0 into 0
3.482 * [backup-simplify]: Simplify 1 into 1
3.483 * [backup-simplify]: Simplify (log 1) into 0
3.483 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.483 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
3.483 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
3.483 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
3.483 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
3.483 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
3.483 * [taylor]: Taking taylor expansion of 1.0 in n
3.483 * [backup-simplify]: Simplify 1.0 into 1.0
3.483 * [taylor]: Taking taylor expansion of (log 2.0) in n
3.483 * [taylor]: Taking taylor expansion of 2.0 in n
3.483 * [backup-simplify]: Simplify 2.0 into 2.0
3.484 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
3.485 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
3.486 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
3.487 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
3.488 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
3.489 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
3.491 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
3.492 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
3.492 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
3.492 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
3.492 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.492 * [taylor]: Taking taylor expansion of 2.0 in n
3.492 * [backup-simplify]: Simplify 2.0 into 2.0
3.492 * [taylor]: Taking taylor expansion of (* n PI) in n
3.492 * [taylor]: Taking taylor expansion of n in n
3.492 * [backup-simplify]: Simplify 0 into 0
3.492 * [backup-simplify]: Simplify 1 into 1
3.492 * [taylor]: Taking taylor expansion of PI in n
3.492 * [backup-simplify]: Simplify PI into PI
3.493 * [backup-simplify]: Simplify (* 0 PI) into 0
3.493 * [backup-simplify]: Simplify (* 2.0 0) into 0
3.495 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.496 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
3.497 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.499 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.500 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.503 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))
3.505 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))))
3.507 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
3.508 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.509 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.512 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
3.514 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))
3.517 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)))
3.520 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))
3.531 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))
3.542 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))))
3.562 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))
3.580 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))
3.596 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))))))))))))))
3.623 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2)))))))))))))))))))))))
3.624 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)))
3.624 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (k n) around 0
3.624 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
3.624 * [taylor]: Taking taylor expansion of 1.0 in n
3.624 * [backup-simplify]: Simplify 1.0 into 1.0
3.624 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
3.624 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
3.624 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
3.624 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
3.624 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
3.624 * [taylor]: Taking taylor expansion of 0.5 in n
3.624 * [backup-simplify]: Simplify 0.5 into 0.5
3.624 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
3.624 * [taylor]: Taking taylor expansion of 1.0 in n
3.624 * [backup-simplify]: Simplify 1.0 into 1.0
3.624 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.624 * [taylor]: Taking taylor expansion of k in n
3.624 * [backup-simplify]: Simplify k into k
3.625 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.625 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
3.625 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.625 * [taylor]: Taking taylor expansion of 2.0 in n
3.625 * [backup-simplify]: Simplify 2.0 into 2.0
3.625 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.625 * [taylor]: Taking taylor expansion of PI in n
3.625 * [backup-simplify]: Simplify PI into PI
3.625 * [taylor]: Taking taylor expansion of n in n
3.625 * [backup-simplify]: Simplify 0 into 0
3.625 * [backup-simplify]: Simplify 1 into 1
3.625 * [backup-simplify]: Simplify (/ PI 1) into PI
3.626 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.627 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.627 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
3.627 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
3.627 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
3.629 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.630 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
3.631 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
3.631 * [taylor]: Taking taylor expansion of (sqrt k) in n
3.631 * [taylor]: Taking taylor expansion of k in n
3.631 * [backup-simplify]: Simplify k into k
3.631 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
3.631 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
3.631 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
3.631 * [taylor]: Taking taylor expansion of 1.0 in k
3.631 * [backup-simplify]: Simplify 1.0 into 1.0
3.631 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
3.631 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
3.631 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
3.631 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
3.631 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
3.631 * [taylor]: Taking taylor expansion of 0.5 in k
3.631 * [backup-simplify]: Simplify 0.5 into 0.5
3.631 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
3.632 * [taylor]: Taking taylor expansion of 1.0 in k
3.632 * [backup-simplify]: Simplify 1.0 into 1.0
3.632 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.632 * [taylor]: Taking taylor expansion of k in k
3.632 * [backup-simplify]: Simplify 0 into 0
3.632 * [backup-simplify]: Simplify 1 into 1
3.632 * [backup-simplify]: Simplify (/ 1 1) into 1
3.632 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
3.632 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
3.632 * [taylor]: Taking taylor expansion of 2.0 in k
3.632 * [backup-simplify]: Simplify 2.0 into 2.0
3.632 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.632 * [taylor]: Taking taylor expansion of PI in k
3.632 * [backup-simplify]: Simplify PI into PI
3.632 * [taylor]: Taking taylor expansion of n in k
3.632 * [backup-simplify]: Simplify n into n
3.632 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.632 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
3.632 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
3.633 * [backup-simplify]: Simplify (- 1) into -1
3.633 * [backup-simplify]: Simplify (+ 0 -1) into -1
3.634 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
3.634 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
3.634 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
3.634 * [taylor]: Taking taylor expansion of (sqrt k) in k
3.634 * [taylor]: Taking taylor expansion of k in k
3.634 * [backup-simplify]: Simplify 0 into 0
3.634 * [backup-simplify]: Simplify 1 into 1
3.635 * [backup-simplify]: Simplify (sqrt 0) into 0
3.636 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.636 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
3.636 * [taylor]: Taking taylor expansion of 1.0 in k
3.636 * [backup-simplify]: Simplify 1.0 into 1.0
3.636 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
3.636 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
3.636 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
3.636 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
3.636 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
3.637 * [taylor]: Taking taylor expansion of 0.5 in k
3.637 * [backup-simplify]: Simplify 0.5 into 0.5
3.637 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
3.637 * [taylor]: Taking taylor expansion of 1.0 in k
3.637 * [backup-simplify]: Simplify 1.0 into 1.0
3.637 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.637 * [taylor]: Taking taylor expansion of k in k
3.637 * [backup-simplify]: Simplify 0 into 0
3.637 * [backup-simplify]: Simplify 1 into 1
3.637 * [backup-simplify]: Simplify (/ 1 1) into 1
3.637 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
3.637 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
3.637 * [taylor]: Taking taylor expansion of 2.0 in k
3.637 * [backup-simplify]: Simplify 2.0 into 2.0
3.637 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.637 * [taylor]: Taking taylor expansion of PI in k
3.637 * [backup-simplify]: Simplify PI into PI
3.637 * [taylor]: Taking taylor expansion of n in k
3.637 * [backup-simplify]: Simplify n into n
3.638 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.638 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
3.638 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
3.638 * [backup-simplify]: Simplify (- 1) into -1
3.639 * [backup-simplify]: Simplify (+ 0 -1) into -1
3.639 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
3.639 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
3.640 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
3.640 * [taylor]: Taking taylor expansion of (sqrt k) in k
3.640 * [taylor]: Taking taylor expansion of k in k
3.640 * [backup-simplify]: Simplify 0 into 0
3.640 * [backup-simplify]: Simplify 1 into 1
3.640 * [backup-simplify]: Simplify (sqrt 0) into 0
3.641 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.642 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0
3.642 * [backup-simplify]: Simplify (* 1.0 0) into 0
3.642 * [taylor]: Taking taylor expansion of 0 in n
3.642 * [backup-simplify]: Simplify 0 into 0
3.642 * [backup-simplify]: Simplify 0 into 0
3.643 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
3.644 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
3.644 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n
3.644 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n
3.644 * [taylor]: Taking taylor expansion of +nan.0 in n
3.644 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.644 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n
3.644 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n
3.644 * [taylor]: Taking taylor expansion of 0.5 in n
3.644 * [backup-simplify]: Simplify 0.5 into 0.5
3.644 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n
3.644 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
3.644 * [taylor]: Taking taylor expansion of 1.0 in n
3.644 * [backup-simplify]: Simplify 1.0 into 1.0
3.644 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.644 * [taylor]: Taking taylor expansion of k in n
3.644 * [backup-simplify]: Simplify k into k
3.644 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.644 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
3.644 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.644 * [taylor]: Taking taylor expansion of 2.0 in n
3.645 * [backup-simplify]: Simplify 2.0 into 2.0
3.645 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.645 * [taylor]: Taking taylor expansion of PI in n
3.645 * [backup-simplify]: Simplify PI into PI
3.645 * [taylor]: Taking taylor expansion of n in n
3.645 * [backup-simplify]: Simplify 0 into 0
3.645 * [backup-simplify]: Simplify 1 into 1
3.645 * [backup-simplify]: Simplify (/ PI 1) into PI
3.646 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.647 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.647 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
3.647 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
3.648 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.650 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))
3.651 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
3.652 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
3.653 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
3.655 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
3.656 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
3.656 * [backup-simplify]: Simplify 0 into 0
3.659 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.660 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
3.661 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
3.661 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n
3.661 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n
3.661 * [taylor]: Taking taylor expansion of +nan.0 in n
3.661 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.661 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n
3.661 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n
3.662 * [taylor]: Taking taylor expansion of 0.5 in n
3.662 * [backup-simplify]: Simplify 0.5 into 0.5
3.662 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n
3.662 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
3.662 * [taylor]: Taking taylor expansion of 1.0 in n
3.662 * [backup-simplify]: Simplify 1.0 into 1.0
3.662 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.662 * [taylor]: Taking taylor expansion of k in n
3.662 * [backup-simplify]: Simplify k into k
3.662 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.662 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
3.662 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.662 * [taylor]: Taking taylor expansion of 2.0 in n
3.662 * [backup-simplify]: Simplify 2.0 into 2.0
3.662 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.662 * [taylor]: Taking taylor expansion of PI in n
3.662 * [backup-simplify]: Simplify PI into PI
3.662 * [taylor]: Taking taylor expansion of n in n
3.662 * [backup-simplify]: Simplify 0 into 0
3.662 * [backup-simplify]: Simplify 1 into 1
3.663 * [backup-simplify]: Simplify (/ PI 1) into PI
3.663 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.664 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.664 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
3.664 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
3.666 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.667 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))
3.669 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
3.670 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
3.671 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
3.672 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
3.674 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
3.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.675 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
3.677 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
3.678 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.678 * [backup-simplify]: Simplify (- 0) into 0
3.678 * [backup-simplify]: Simplify (+ 0 0) into 0
3.680 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.681 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
3.683 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0
3.684 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
3.686 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0
3.687 * [backup-simplify]: Simplify (- 0) into 0
3.687 * [backup-simplify]: Simplify 0 into 0
3.687 * [backup-simplify]: Simplify 0 into 0
3.691 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.692 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
3.693 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
3.693 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n
3.693 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n
3.693 * [taylor]: Taking taylor expansion of +nan.0 in n
3.693 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.693 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n
3.693 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n
3.693 * [taylor]: Taking taylor expansion of 0.5 in n
3.693 * [backup-simplify]: Simplify 0.5 into 0.5
3.693 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n
3.694 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
3.694 * [taylor]: Taking taylor expansion of 1.0 in n
3.694 * [backup-simplify]: Simplify 1.0 into 1.0
3.694 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.694 * [taylor]: Taking taylor expansion of k in n
3.694 * [backup-simplify]: Simplify k into k
3.694 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.694 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
3.694 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.694 * [taylor]: Taking taylor expansion of 2.0 in n
3.694 * [backup-simplify]: Simplify 2.0 into 2.0
3.694 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.694 * [taylor]: Taking taylor expansion of PI in n
3.694 * [backup-simplify]: Simplify PI into PI
3.694 * [taylor]: Taking taylor expansion of n in n
3.694 * [backup-simplify]: Simplify 0 into 0
3.694 * [backup-simplify]: Simplify 1 into 1
3.694 * [backup-simplify]: Simplify (/ PI 1) into PI
3.695 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.696 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.696 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
3.696 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
3.697 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.699 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))
3.700 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
3.701 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
3.702 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
3.709 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
3.711 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
3.716 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
3.717 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))))
3.717 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0
3.717 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
3.717 * [taylor]: Taking taylor expansion of 1.0 in n
3.717 * [backup-simplify]: Simplify 1.0 into 1.0
3.717 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
3.717 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
3.717 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
3.717 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
3.717 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
3.718 * [taylor]: Taking taylor expansion of 0.5 in n
3.718 * [backup-simplify]: Simplify 0.5 into 0.5
3.718 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
3.718 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.718 * [taylor]: Taking taylor expansion of k in n
3.718 * [backup-simplify]: Simplify k into k
3.718 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.718 * [taylor]: Taking taylor expansion of 1.0 in n
3.718 * [backup-simplify]: Simplify 1.0 into 1.0
3.718 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
3.718 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.718 * [taylor]: Taking taylor expansion of -2.0 in n
3.718 * [backup-simplify]: Simplify -2.0 into -2.0
3.718 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.718 * [taylor]: Taking taylor expansion of PI in n
3.718 * [backup-simplify]: Simplify PI into PI
3.718 * [taylor]: Taking taylor expansion of n in n
3.718 * [backup-simplify]: Simplify 0 into 0
3.718 * [backup-simplify]: Simplify 1 into 1
3.719 * [backup-simplify]: Simplify (/ PI 1) into PI
3.719 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.720 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
3.720 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
3.721 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
3.721 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.722 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
3.723 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
3.723 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
3.723 * [taylor]: Taking taylor expansion of (/ -1 k) in n
3.723 * [taylor]: Taking taylor expansion of -1 in n
3.723 * [backup-simplify]: Simplify -1 into -1
3.723 * [taylor]: Taking taylor expansion of k in n
3.723 * [backup-simplify]: Simplify k into k
3.723 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
3.723 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
3.723 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
3.723 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
3.724 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
3.724 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
3.724 * [taylor]: Taking taylor expansion of 1.0 in k
3.724 * [backup-simplify]: Simplify 1.0 into 1.0
3.724 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
3.724 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
3.724 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
3.724 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
3.724 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
3.724 * [taylor]: Taking taylor expansion of 0.5 in k
3.724 * [backup-simplify]: Simplify 0.5 into 0.5
3.724 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
3.724 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.724 * [taylor]: Taking taylor expansion of k in k
3.724 * [backup-simplify]: Simplify 0 into 0
3.724 * [backup-simplify]: Simplify 1 into 1
3.725 * [backup-simplify]: Simplify (/ 1 1) into 1
3.725 * [taylor]: Taking taylor expansion of 1.0 in k
3.725 * [backup-simplify]: Simplify 1.0 into 1.0
3.725 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
3.725 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
3.725 * [taylor]: Taking taylor expansion of -2.0 in k
3.725 * [backup-simplify]: Simplify -2.0 into -2.0
3.725 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.725 * [taylor]: Taking taylor expansion of PI in k
3.725 * [backup-simplify]: Simplify PI into PI
3.725 * [taylor]: Taking taylor expansion of n in k
3.725 * [backup-simplify]: Simplify n into n
3.725 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.725 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
3.725 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
3.725 * [backup-simplify]: Simplify (+ 1 0) into 1
3.725 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
3.725 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
3.726 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
3.726 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
3.726 * [taylor]: Taking taylor expansion of (/ -1 k) in k
3.726 * [taylor]: Taking taylor expansion of -1 in k
3.726 * [backup-simplify]: Simplify -1 into -1
3.726 * [taylor]: Taking taylor expansion of k in k
3.726 * [backup-simplify]: Simplify 0 into 0
3.726 * [backup-simplify]: Simplify 1 into 1
3.726 * [backup-simplify]: Simplify (/ -1 1) into -1
3.726 * [backup-simplify]: Simplify (sqrt 0) into 0
3.727 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
3.727 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
3.727 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
3.727 * [taylor]: Taking taylor expansion of 1.0 in k
3.727 * [backup-simplify]: Simplify 1.0 into 1.0
3.727 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
3.727 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
3.727 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
3.727 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
3.727 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
3.727 * [taylor]: Taking taylor expansion of 0.5 in k
3.727 * [backup-simplify]: Simplify 0.5 into 0.5
3.727 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
3.727 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.727 * [taylor]: Taking taylor expansion of k in k
3.728 * [backup-simplify]: Simplify 0 into 0
3.728 * [backup-simplify]: Simplify 1 into 1
3.728 * [backup-simplify]: Simplify (/ 1 1) into 1
3.728 * [taylor]: Taking taylor expansion of 1.0 in k
3.728 * [backup-simplify]: Simplify 1.0 into 1.0
3.728 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
3.728 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
3.728 * [taylor]: Taking taylor expansion of -2.0 in k
3.728 * [backup-simplify]: Simplify -2.0 into -2.0
3.728 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.728 * [taylor]: Taking taylor expansion of PI in k
3.728 * [backup-simplify]: Simplify PI into PI
3.728 * [taylor]: Taking taylor expansion of n in k
3.728 * [backup-simplify]: Simplify n into n
3.728 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.728 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
3.728 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
3.728 * [backup-simplify]: Simplify (+ 1 0) into 1
3.729 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
3.729 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
3.729 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
3.729 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
3.729 * [taylor]: Taking taylor expansion of (/ -1 k) in k
3.729 * [taylor]: Taking taylor expansion of -1 in k
3.729 * [backup-simplify]: Simplify -1 into -1
3.729 * [taylor]: Taking taylor expansion of k in k
3.729 * [backup-simplify]: Simplify 0 into 0
3.729 * [backup-simplify]: Simplify 1 into 1
3.729 * [backup-simplify]: Simplify (/ -1 1) into -1
3.729 * [backup-simplify]: Simplify (sqrt 0) into 0
3.730 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
3.730 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
3.731 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
3.731 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n
3.731 * [taylor]: Taking taylor expansion of +nan.0 in n
3.731 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.731 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n
3.731 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n
3.731 * [taylor]: Taking taylor expansion of 0.5 in n
3.731 * [backup-simplify]: Simplify 0.5 into 0.5
3.731 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n
3.731 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
3.731 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.731 * [taylor]: Taking taylor expansion of -2.0 in n
3.731 * [backup-simplify]: Simplify -2.0 into -2.0
3.731 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.731 * [taylor]: Taking taylor expansion of PI in n
3.731 * [backup-simplify]: Simplify PI into PI
3.731 * [taylor]: Taking taylor expansion of n in n
3.731 * [backup-simplify]: Simplify 0 into 0
3.731 * [backup-simplify]: Simplify 1 into 1
3.731 * [backup-simplify]: Simplify (/ PI 1) into PI
3.731 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.732 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
3.732 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
3.732 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.732 * [taylor]: Taking taylor expansion of k in n
3.732 * [backup-simplify]: Simplify k into k
3.732 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.732 * [taylor]: Taking taylor expansion of 1.0 in n
3.732 * [backup-simplify]: Simplify 1.0 into 1.0
3.733 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.733 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
3.734 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))
3.735 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
3.735 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
3.736 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
3.737 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
3.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
3.739 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.740 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
3.740 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
3.740 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n
3.740 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n
3.740 * [taylor]: Taking taylor expansion of +nan.0 in n
3.740 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.740 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n
3.740 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n
3.740 * [taylor]: Taking taylor expansion of 0.5 in n
3.740 * [backup-simplify]: Simplify 0.5 into 0.5
3.740 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n
3.740 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
3.741 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.741 * [taylor]: Taking taylor expansion of -2.0 in n
3.741 * [backup-simplify]: Simplify -2.0 into -2.0
3.741 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.741 * [taylor]: Taking taylor expansion of PI in n
3.741 * [backup-simplify]: Simplify PI into PI
3.741 * [taylor]: Taking taylor expansion of n in n
3.741 * [backup-simplify]: Simplify 0 into 0
3.741 * [backup-simplify]: Simplify 1 into 1
3.741 * [backup-simplify]: Simplify (/ PI 1) into PI
3.741 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.742 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
3.742 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
3.742 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.742 * [taylor]: Taking taylor expansion of k in n
3.742 * [backup-simplify]: Simplify k into k
3.742 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.742 * [taylor]: Taking taylor expansion of 1.0 in n
3.742 * [backup-simplify]: Simplify 1.0 into 1.0
3.743 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.743 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
3.744 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))
3.744 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
3.745 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
3.746 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
3.747 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
3.747 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
3.748 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.748 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.749 * [backup-simplify]: Simplify (+ 0 0) into 0
3.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.750 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
3.751 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
3.751 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0
3.752 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0
3.754 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.756 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0
3.756 * [backup-simplify]: Simplify 0 into 0
3.757 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.760 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.762 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
3.763 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
3.764 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n
3.764 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n
3.764 * [taylor]: Taking taylor expansion of +nan.0 in n
3.764 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.764 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n
3.764 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n
3.764 * [taylor]: Taking taylor expansion of 0.5 in n
3.764 * [backup-simplify]: Simplify 0.5 into 0.5
3.764 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n
3.764 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
3.764 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.764 * [taylor]: Taking taylor expansion of -2.0 in n
3.764 * [backup-simplify]: Simplify -2.0 into -2.0
3.764 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.764 * [taylor]: Taking taylor expansion of PI in n
3.764 * [backup-simplify]: Simplify PI into PI
3.764 * [taylor]: Taking taylor expansion of n in n
3.764 * [backup-simplify]: Simplify 0 into 0
3.764 * [backup-simplify]: Simplify 1 into 1
3.765 * [backup-simplify]: Simplify (/ PI 1) into PI
3.765 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.766 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
3.766 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
3.766 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.766 * [taylor]: Taking taylor expansion of k in n
3.766 * [backup-simplify]: Simplify k into k
3.766 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.766 * [taylor]: Taking taylor expansion of 1.0 in n
3.766 * [backup-simplify]: Simplify 1.0 into 1.0
3.768 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.768 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
3.769 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))
3.771 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
3.772 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
3.773 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
3.774 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
3.776 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
3.780 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
3.781 * * * * [progress]: [ 4 / 4 ] generating series at (2 2)
3.781 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
3.781 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
3.781 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
3.781 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
3.782 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
3.782 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
3.782 * [taylor]: Taking taylor expansion of 0.5 in k
3.782 * [backup-simplify]: Simplify 0.5 into 0.5
3.782 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
3.782 * [taylor]: Taking taylor expansion of 1.0 in k
3.782 * [backup-simplify]: Simplify 1.0 into 1.0
3.782 * [taylor]: Taking taylor expansion of k in k
3.782 * [backup-simplify]: Simplify 0 into 0
3.782 * [backup-simplify]: Simplify 1 into 1
3.782 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
3.782 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
3.782 * [taylor]: Taking taylor expansion of 2.0 in k
3.782 * [backup-simplify]: Simplify 2.0 into 2.0
3.782 * [taylor]: Taking taylor expansion of (* n PI) in k
3.782 * [taylor]: Taking taylor expansion of n in k
3.782 * [backup-simplify]: Simplify n into n
3.782 * [taylor]: Taking taylor expansion of PI in k
3.782 * [backup-simplify]: Simplify PI into PI
3.782 * [backup-simplify]: Simplify (* n PI) into (* n PI)
3.782 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
3.782 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
3.783 * [backup-simplify]: Simplify (- 0) into 0
3.783 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
3.784 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
3.784 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
3.784 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
3.784 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
3.784 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
3.784 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
3.784 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
3.784 * [taylor]: Taking taylor expansion of 0.5 in n
3.784 * [backup-simplify]: Simplify 0.5 into 0.5
3.784 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
3.784 * [taylor]: Taking taylor expansion of 1.0 in n
3.784 * [backup-simplify]: Simplify 1.0 into 1.0
3.784 * [taylor]: Taking taylor expansion of k in n
3.784 * [backup-simplify]: Simplify k into k
3.784 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
3.784 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.784 * [taylor]: Taking taylor expansion of 2.0 in n
3.784 * [backup-simplify]: Simplify 2.0 into 2.0
3.784 * [taylor]: Taking taylor expansion of (* n PI) in n
3.784 * [taylor]: Taking taylor expansion of n in n
3.784 * [backup-simplify]: Simplify 0 into 0
3.784 * [backup-simplify]: Simplify 1 into 1
3.784 * [taylor]: Taking taylor expansion of PI in n
3.784 * [backup-simplify]: Simplify PI into PI
3.785 * [backup-simplify]: Simplify (* 0 PI) into 0
3.785 * [backup-simplify]: Simplify (* 2.0 0) into 0
3.787 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.788 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
3.789 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.789 * [backup-simplify]: Simplify (- k) into (- k)
3.789 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
3.789 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
3.790 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.791 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
3.792 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
3.792 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
3.792 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
3.792 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
3.792 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
3.792 * [taylor]: Taking taylor expansion of 0.5 in n
3.792 * [backup-simplify]: Simplify 0.5 into 0.5
3.792 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
3.792 * [taylor]: Taking taylor expansion of 1.0 in n
3.792 * [backup-simplify]: Simplify 1.0 into 1.0
3.792 * [taylor]: Taking taylor expansion of k in n
3.792 * [backup-simplify]: Simplify k into k
3.792 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
3.792 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.792 * [taylor]: Taking taylor expansion of 2.0 in n
3.792 * [backup-simplify]: Simplify 2.0 into 2.0
3.792 * [taylor]: Taking taylor expansion of (* n PI) in n
3.792 * [taylor]: Taking taylor expansion of n in n
3.792 * [backup-simplify]: Simplify 0 into 0
3.792 * [backup-simplify]: Simplify 1 into 1
3.792 * [taylor]: Taking taylor expansion of PI in n
3.792 * [backup-simplify]: Simplify PI into PI
3.792 * [backup-simplify]: Simplify (* 0 PI) into 0
3.792 * [backup-simplify]: Simplify (* 2.0 0) into 0
3.793 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.794 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
3.795 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.795 * [backup-simplify]: Simplify (- k) into (- k)
3.795 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
3.795 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
3.796 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.797 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
3.797 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
3.797 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
3.797 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
3.797 * [taylor]: Taking taylor expansion of 0.5 in k
3.798 * [backup-simplify]: Simplify 0.5 into 0.5
3.798 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
3.798 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
3.798 * [taylor]: Taking taylor expansion of 1.0 in k
3.798 * [backup-simplify]: Simplify 1.0 into 1.0
3.798 * [taylor]: Taking taylor expansion of k in k
3.798 * [backup-simplify]: Simplify 0 into 0
3.798 * [backup-simplify]: Simplify 1 into 1
3.798 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
3.798 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
3.798 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
3.798 * [taylor]: Taking taylor expansion of 2.0 in k
3.798 * [backup-simplify]: Simplify 2.0 into 2.0
3.798 * [taylor]: Taking taylor expansion of PI in k
3.798 * [backup-simplify]: Simplify PI into PI
3.798 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.799 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.799 * [taylor]: Taking taylor expansion of (log n) in k
3.799 * [taylor]: Taking taylor expansion of n in k
3.799 * [backup-simplify]: Simplify n into n
3.799 * [backup-simplify]: Simplify (log n) into (log n)
3.799 * [backup-simplify]: Simplify (- 0) into 0
3.799 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
3.800 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
3.801 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
3.801 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
3.802 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
3.803 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
3.803 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.804 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
3.805 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
3.805 * [backup-simplify]: Simplify (- 0) into 0
3.805 * [backup-simplify]: Simplify (+ 0 0) into 0
3.806 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
3.806 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.807 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
3.808 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
3.808 * [taylor]: Taking taylor expansion of 0 in k
3.808 * [backup-simplify]: Simplify 0 into 0
3.808 * [backup-simplify]: Simplify 0 into 0
3.809 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
3.810 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
3.810 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
3.810 * [backup-simplify]: Simplify (+ 0 0) into 0
3.811 * [backup-simplify]: Simplify (- 1) into -1
3.811 * [backup-simplify]: Simplify (+ 0 -1) into -1
3.812 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
3.813 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
3.815 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
3.823 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
3.825 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.826 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.830 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
3.830 * [backup-simplify]: Simplify (- 0) into 0
3.830 * [backup-simplify]: Simplify (+ 0 0) into 0
3.831 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
3.833 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.834 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
3.837 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.837 * [taylor]: Taking taylor expansion of 0 in k
3.837 * [backup-simplify]: Simplify 0 into 0
3.837 * [backup-simplify]: Simplify 0 into 0
3.837 * [backup-simplify]: Simplify 0 into 0
3.838 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
3.841 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
3.843 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
3.844 * [backup-simplify]: Simplify (+ 0 0) into 0
3.844 * [backup-simplify]: Simplify (- 0) into 0
3.844 * [backup-simplify]: Simplify (+ 0 0) into 0
3.846 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
3.849 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
3.853 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
3.858 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
3.869 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))
3.870 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))
3.870 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
3.870 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
3.870 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
3.870 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
3.870 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
3.871 * [taylor]: Taking taylor expansion of 0.5 in k
3.871 * [backup-simplify]: Simplify 0.5 into 0.5
3.871 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
3.871 * [taylor]: Taking taylor expansion of 1.0 in k
3.871 * [backup-simplify]: Simplify 1.0 into 1.0
3.871 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.871 * [taylor]: Taking taylor expansion of k in k
3.871 * [backup-simplify]: Simplify 0 into 0
3.871 * [backup-simplify]: Simplify 1 into 1
3.871 * [backup-simplify]: Simplify (/ 1 1) into 1
3.871 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
3.871 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
3.871 * [taylor]: Taking taylor expansion of 2.0 in k
3.871 * [backup-simplify]: Simplify 2.0 into 2.0
3.871 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.871 * [taylor]: Taking taylor expansion of PI in k
3.871 * [backup-simplify]: Simplify PI into PI
3.871 * [taylor]: Taking taylor expansion of n in k
3.871 * [backup-simplify]: Simplify n into n
3.872 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.872 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
3.872 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
3.872 * [backup-simplify]: Simplify (- 1) into -1
3.873 * [backup-simplify]: Simplify (+ 0 -1) into -1
3.873 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
3.873 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
3.873 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
3.873 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
3.873 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
3.873 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
3.873 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
3.873 * [taylor]: Taking taylor expansion of 0.5 in n
3.873 * [backup-simplify]: Simplify 0.5 into 0.5
3.874 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
3.874 * [taylor]: Taking taylor expansion of 1.0 in n
3.874 * [backup-simplify]: Simplify 1.0 into 1.0
3.874 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.874 * [taylor]: Taking taylor expansion of k in n
3.874 * [backup-simplify]: Simplify k into k
3.874 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.874 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
3.874 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.874 * [taylor]: Taking taylor expansion of 2.0 in n
3.874 * [backup-simplify]: Simplify 2.0 into 2.0
3.874 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.874 * [taylor]: Taking taylor expansion of PI in n
3.874 * [backup-simplify]: Simplify PI into PI
3.874 * [taylor]: Taking taylor expansion of n in n
3.874 * [backup-simplify]: Simplify 0 into 0
3.874 * [backup-simplify]: Simplify 1 into 1
3.874 * [backup-simplify]: Simplify (/ PI 1) into PI
3.875 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.876 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.876 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
3.876 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
3.876 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
3.878 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.879 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
3.880 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
3.880 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
3.880 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
3.880 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
3.881 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
3.881 * [taylor]: Taking taylor expansion of 0.5 in n
3.881 * [backup-simplify]: Simplify 0.5 into 0.5
3.881 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
3.882 * [taylor]: Taking taylor expansion of 1.0 in n
3.882 * [backup-simplify]: Simplify 1.0 into 1.0
3.882 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.882 * [taylor]: Taking taylor expansion of k in n
3.882 * [backup-simplify]: Simplify k into k
3.882 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.882 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
3.882 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.882 * [taylor]: Taking taylor expansion of 2.0 in n
3.882 * [backup-simplify]: Simplify 2.0 into 2.0
3.882 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.882 * [taylor]: Taking taylor expansion of PI in n
3.882 * [backup-simplify]: Simplify PI into PI
3.882 * [taylor]: Taking taylor expansion of n in n
3.882 * [backup-simplify]: Simplify 0 into 0
3.882 * [backup-simplify]: Simplify 1 into 1
3.883 * [backup-simplify]: Simplify (/ PI 1) into PI
3.883 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.884 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.884 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
3.884 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
3.885 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
3.886 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.887 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
3.889 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
3.889 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
3.889 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
3.889 * [taylor]: Taking taylor expansion of 0.5 in k
3.889 * [backup-simplify]: Simplify 0.5 into 0.5
3.889 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
3.889 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
3.889 * [taylor]: Taking taylor expansion of 1.0 in k
3.889 * [backup-simplify]: Simplify 1.0 into 1.0
3.889 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.889 * [taylor]: Taking taylor expansion of k in k
3.889 * [backup-simplify]: Simplify 0 into 0
3.889 * [backup-simplify]: Simplify 1 into 1
3.889 * [backup-simplify]: Simplify (/ 1 1) into 1
3.890 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
3.890 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
3.890 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
3.890 * [taylor]: Taking taylor expansion of 2.0 in k
3.890 * [backup-simplify]: Simplify 2.0 into 2.0
3.890 * [taylor]: Taking taylor expansion of PI in k
3.890 * [backup-simplify]: Simplify PI into PI
3.890 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.891 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.891 * [taylor]: Taking taylor expansion of (log n) in k
3.891 * [taylor]: Taking taylor expansion of n in k
3.891 * [backup-simplify]: Simplify n into n
3.891 * [backup-simplify]: Simplify (log n) into (log n)
3.892 * [backup-simplify]: Simplify (- 1) into -1
3.892 * [backup-simplify]: Simplify (+ 0 -1) into -1
3.892 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.893 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
3.894 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
3.894 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
3.895 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
3.896 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
3.896 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.897 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
3.898 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
3.898 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.898 * [backup-simplify]: Simplify (- 0) into 0
3.899 * [backup-simplify]: Simplify (+ 0 0) into 0
3.899 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
3.900 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.900 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
3.902 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
3.902 * [taylor]: Taking taylor expansion of 0 in k
3.902 * [backup-simplify]: Simplify 0 into 0
3.902 * [backup-simplify]: Simplify 0 into 0
3.902 * [backup-simplify]: Simplify 0 into 0
3.902 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.903 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
3.905 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
3.905 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.905 * [backup-simplify]: Simplify (- 0) into 0
3.905 * [backup-simplify]: Simplify (+ 0 0) into 0
3.906 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
3.907 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.908 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
3.909 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.909 * [taylor]: Taking taylor expansion of 0 in k
3.909 * [backup-simplify]: Simplify 0 into 0
3.909 * [backup-simplify]: Simplify 0 into 0
3.909 * [backup-simplify]: Simplify 0 into 0
3.909 * [backup-simplify]: Simplify 0 into 0
3.910 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.911 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.914 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
3.914 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.914 * [backup-simplify]: Simplify (- 0) into 0
3.914 * [backup-simplify]: Simplify (+ 0 0) into 0
3.915 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
3.916 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.917 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
3.919 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
3.919 * [taylor]: Taking taylor expansion of 0 in k
3.919 * [backup-simplify]: Simplify 0 into 0
3.919 * [backup-simplify]: Simplify 0 into 0
3.919 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n))))))
3.920 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))
3.920 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
3.920 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
3.920 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
3.920 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
3.920 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
3.920 * [taylor]: Taking taylor expansion of 0.5 in k
3.920 * [backup-simplify]: Simplify 0.5 into 0.5
3.920 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
3.920 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.920 * [taylor]: Taking taylor expansion of k in k
3.920 * [backup-simplify]: Simplify 0 into 0
3.920 * [backup-simplify]: Simplify 1 into 1
3.920 * [backup-simplify]: Simplify (/ 1 1) into 1
3.920 * [taylor]: Taking taylor expansion of 1.0 in k
3.920 * [backup-simplify]: Simplify 1.0 into 1.0
3.920 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
3.920 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
3.920 * [taylor]: Taking taylor expansion of -2.0 in k
3.921 * [backup-simplify]: Simplify -2.0 into -2.0
3.921 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.921 * [taylor]: Taking taylor expansion of PI in k
3.921 * [backup-simplify]: Simplify PI into PI
3.921 * [taylor]: Taking taylor expansion of n in k
3.921 * [backup-simplify]: Simplify n into n
3.921 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.921 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
3.921 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
3.921 * [backup-simplify]: Simplify (+ 1 0) into 1
3.921 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
3.921 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
3.921 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
3.922 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
3.922 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
3.922 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
3.922 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
3.922 * [taylor]: Taking taylor expansion of 0.5 in n
3.922 * [backup-simplify]: Simplify 0.5 into 0.5
3.922 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
3.922 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.922 * [taylor]: Taking taylor expansion of k in n
3.922 * [backup-simplify]: Simplify k into k
3.922 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.922 * [taylor]: Taking taylor expansion of 1.0 in n
3.922 * [backup-simplify]: Simplify 1.0 into 1.0
3.922 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
3.922 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.922 * [taylor]: Taking taylor expansion of -2.0 in n
3.922 * [backup-simplify]: Simplify -2.0 into -2.0
3.922 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.922 * [taylor]: Taking taylor expansion of PI in n
3.922 * [backup-simplify]: Simplify PI into PI
3.922 * [taylor]: Taking taylor expansion of n in n
3.922 * [backup-simplify]: Simplify 0 into 0
3.922 * [backup-simplify]: Simplify 1 into 1
3.922 * [backup-simplify]: Simplify (/ PI 1) into PI
3.922 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.923 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
3.923 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
3.923 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
3.924 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.925 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
3.926 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
3.926 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
3.926 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
3.926 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
3.926 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
3.926 * [taylor]: Taking taylor expansion of 0.5 in n
3.926 * [backup-simplify]: Simplify 0.5 into 0.5
3.926 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
3.926 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.926 * [taylor]: Taking taylor expansion of k in n
3.926 * [backup-simplify]: Simplify k into k
3.926 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.926 * [taylor]: Taking taylor expansion of 1.0 in n
3.926 * [backup-simplify]: Simplify 1.0 into 1.0
3.926 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
3.926 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.926 * [taylor]: Taking taylor expansion of -2.0 in n
3.926 * [backup-simplify]: Simplify -2.0 into -2.0
3.926 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.926 * [taylor]: Taking taylor expansion of PI in n
3.926 * [backup-simplify]: Simplify PI into PI
3.926 * [taylor]: Taking taylor expansion of n in n
3.926 * [backup-simplify]: Simplify 0 into 0
3.926 * [backup-simplify]: Simplify 1 into 1
3.926 * [backup-simplify]: Simplify (/ PI 1) into PI
3.927 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.927 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
3.927 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
3.927 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
3.928 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.929 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
3.931 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
3.931 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
3.931 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
3.931 * [taylor]: Taking taylor expansion of 0.5 in k
3.931 * [backup-simplify]: Simplify 0.5 into 0.5
3.931 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
3.931 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
3.931 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
3.931 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
3.931 * [taylor]: Taking taylor expansion of -2.0 in k
3.931 * [backup-simplify]: Simplify -2.0 into -2.0
3.931 * [taylor]: Taking taylor expansion of PI in k
3.931 * [backup-simplify]: Simplify PI into PI
3.931 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.932 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
3.933 * [taylor]: Taking taylor expansion of (log n) in k
3.933 * [taylor]: Taking taylor expansion of n in k
3.933 * [backup-simplify]: Simplify n into n
3.933 * [backup-simplify]: Simplify (log n) into (log n)
3.933 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
3.933 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.933 * [taylor]: Taking taylor expansion of k in k
3.933 * [backup-simplify]: Simplify 0 into 0
3.933 * [backup-simplify]: Simplify 1 into 1
3.933 * [backup-simplify]: Simplify (/ 1 1) into 1
3.933 * [taylor]: Taking taylor expansion of 1.0 in k
3.933 * [backup-simplify]: Simplify 1.0 into 1.0
3.933 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.934 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
3.935 * [backup-simplify]: Simplify (+ 1 0) into 1
3.936 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
3.937 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
3.938 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
3.939 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
3.940 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.941 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
3.949 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
3.949 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.949 * [backup-simplify]: Simplify (+ 0 0) into 0
3.950 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
3.951 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.952 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
3.954 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.954 * [taylor]: Taking taylor expansion of 0 in k
3.954 * [backup-simplify]: Simplify 0 into 0
3.954 * [backup-simplify]: Simplify 0 into 0
3.955 * [backup-simplify]: Simplify 0 into 0
3.956 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.957 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
3.960 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
3.960 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.961 * [backup-simplify]: Simplify (+ 0 0) into 0
3.962 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
3.963 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.965 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
3.967 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.967 * [taylor]: Taking taylor expansion of 0 in k
3.967 * [backup-simplify]: Simplify 0 into 0
3.967 * [backup-simplify]: Simplify 0 into 0
3.967 * [backup-simplify]: Simplify 0 into 0
3.967 * [backup-simplify]: Simplify 0 into 0
3.968 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.970 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.974 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
3.974 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.975 * [backup-simplify]: Simplify (+ 0 0) into 0
3.976 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
3.976 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.978 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
3.979 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
3.979 * [taylor]: Taking taylor expansion of 0 in k
3.979 * [backup-simplify]: Simplify 0 into 0
3.979 * [backup-simplify]: Simplify 0 into 0
3.980 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
3.980 * * * [progress]: simplifying candidates
3.983 * [simplify]: Simplifying:
  (- (log 1.0) (log (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) 1)
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt 1))
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt k)) 1)
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (- (+ (* +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)))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2)))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
  (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n))))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
3.986 * * [simplify]: iteration 0: 353 enodes
4.146 * * [simplify]: iteration 1: 977 enodes
4.614 * * [simplify]: iteration 2: 3274 enodes
5.544 * * [simplify]: iteration complete: 5001 enodes
5.544 * * [simplify]: Extracting #0: cost 117 inf + 0
5.545 * * [simplify]: Extracting #1: cost 636 inf + 2
5.548 * * [simplify]: Extracting #2: cost 1071 inf + 2671
5.570 * * [simplify]: Extracting #3: cost 1276 inf + 26530
5.599 * * [simplify]: Extracting #4: cost 879 inf + 165682
5.656 * * [simplify]: Extracting #5: cost 488 inf + 371056
5.740 * * [simplify]: Extracting #6: cost 434 inf + 450048
5.855 * * [simplify]: Extracting #7: cost 221 inf + 615557
6.011 * * [simplify]: Extracting #8: cost 54 inf + 785021
6.179 * * [simplify]: Extracting #9: cost 11 inf + 839258
6.338 * * [simplify]: Extracting #10: cost 0 inf + 857114
6.513 * [simplify]: Simplified to:
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (* (/ (* 1.0 1.0) k) 1.0) (sqrt k))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (/ (* (/ (* 1.0 1.0) k) 1.0) (sqrt k))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k)))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (fabs (cbrt k)))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (fabs (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1.0
  (/ 1.0 (sqrt (sqrt k)))
  1.0
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* 2.0 (* (* PI (cbrt n)) (cbrt n)))
  (* 2.0 (* PI (sqrt n)))
  (* 2.0 PI)
  (* n PI)
  (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k))))
  (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0)
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k))))
  (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))
  (* (* (/ 1.0 (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (sqrt k))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0))) (sqrt k))
  (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k))))
  (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (cbrt k))))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (cbrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (cbrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (cbrt (sqrt k))))
  (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (cbrt k))))
  (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k))))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k))))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (/ 1.0 (sqrt k)))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))
  (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))
  (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))
  (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k)))))
  (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (* (* 2.0 PI) n)
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2) 2.0))
  (+ (* (- (* k k)) +nan.0) (- +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)))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (- (* (* (- +nan.0) (pow (* (pow n 1.0) (* (pow 2.0 1.0) (pow PI 1.0))) 0.5)) k) (+ (* (- +nan.0) (* (* k k) (pow (* (pow n 1.0) (* (pow 2.0 1.0) (pow PI 1.0))) 0.5))) (+ (- (* (pow (* (pow n 1.0) (* (pow 2.0 1.0) (pow PI 1.0))) 0.5) (* +nan.0 (* (* k k) (log n)))) (* +nan.0 (pow (* (pow n 1.0) (* (pow 2.0 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow n 1.0) (* (pow 2.0 1.0) (pow PI 1.0))) 0.5) (* (* (log (* 2.0 PI)) k) (* (log (* 2.0 PI)) k)))) (+ (- (* (* +nan.0 (pow (* (pow n 1.0) (* (pow 2.0 1.0) (pow PI 1.0))) 0.5)) (* (* (* k k) (log (* 2.0 PI))) (log n))) (* +nan.0 (* (pow (* (pow n 1.0) (* (pow 2.0 1.0) (pow PI 1.0))) 0.5) (* k (log (* 2.0 PI)))))) (- (* (pow (* (pow n 1.0) (* (pow 2.0 1.0) (pow PI 1.0))) 0.5) (* +nan.0 (* (log n) k))) (- (* +nan.0 (* (pow (* (pow n 1.0) (* (pow 2.0 1.0) (pow PI 1.0))) 0.5) (* (* k k) (log (* 2.0 PI))))) (* +nan.0 (* (pow (* (pow n 1.0) (* (pow 2.0 1.0) (pow PI 1.0))) 0.5) (* (* k (log n)) (* k (log n))))))))))))
  (- (* (- +nan.0) (/ (exp (* (* (log (* (* 2.0 PI) n)) (- 1.0 k)) 0.5)) (* k k))) (* (- +nan.0) (+ (/ (- (exp (* (* (log (* (* 2.0 PI) n)) (- 1.0 k)) 0.5))) (* (* k k) k)) (/ (exp (* (* (log (* (* 2.0 PI) n)) (- 1.0 k)) 0.5)) k))))
  (+ (* (- +nan.0) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ -1 n))) (- 1.0 k))))) (* +nan.0 (+ (- (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ -1 n))) (- 1.0 k)))) (* k k))) (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ -1 n))) (- 1.0 k)))) k))))
  (- (+ (+ (+ (* (* (* (log (* 2.0 PI)) 0.25) (* (* k k) (log n))) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (* (* 0.125 (* (* k k) (* (log n) (log n)))) (exp (* (log (* (* 2.0 PI) n)) 0.5)))) (* (* 0.125 (* (log (* 2.0 PI)) (log (* 2.0 PI)))) (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (* k k)))) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (* (* k (+ (* (log n) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (* (log (* 2.0 PI)) (exp (* (log (* (* 2.0 PI) n)) 0.5))))) 0.5))
  (exp (* (* (log (* (* 2.0 PI) n)) (- 1.0 k)) 0.5))
  (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ -1 n))) (- 1.0 k))))
6.525 * * * [progress]: adding candidates to table
7.389 * * [progress]: iteration 2 / 4
7.389 * * * [progress]: picking best candidate
7.450 * * * * [pick]: Picked  #<alt (λ (k n) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))>
7.450 * * * [progress]: localizing error
7.479 * * * [progress]: generating rewritten candidates
7.479 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1 2 1)
7.494 * * * * [progress]: [ 2 / 3 ] rewriting at (2)
7.514 * * * * [progress]: [ 3 / 3 ] rewriting at (2 1 2)
7.549 * * * [progress]: generating series expansions
7.549 * * * * [progress]: [ 1 / 3 ] generating series at (2 1 2 1)
7.550 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
7.550 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
7.550 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.550 * [taylor]: Taking taylor expansion of 2.0 in n
7.550 * [backup-simplify]: Simplify 2.0 into 2.0
7.550 * [taylor]: Taking taylor expansion of (* n PI) in n
7.550 * [taylor]: Taking taylor expansion of n in n
7.550 * [backup-simplify]: Simplify 0 into 0
7.550 * [backup-simplify]: Simplify 1 into 1
7.550 * [taylor]: Taking taylor expansion of PI in n
7.550 * [backup-simplify]: Simplify PI into PI
7.550 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.550 * [taylor]: Taking taylor expansion of 2.0 in n
7.550 * [backup-simplify]: Simplify 2.0 into 2.0
7.550 * [taylor]: Taking taylor expansion of (* n PI) in n
7.550 * [taylor]: Taking taylor expansion of n in n
7.550 * [backup-simplify]: Simplify 0 into 0
7.550 * [backup-simplify]: Simplify 1 into 1
7.550 * [taylor]: Taking taylor expansion of PI in n
7.550 * [backup-simplify]: Simplify PI into PI
7.550 * [backup-simplify]: Simplify (* 0 PI) into 0
7.551 * [backup-simplify]: Simplify (* 2.0 0) into 0
7.551 * [backup-simplify]: Simplify 0 into 0
7.552 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.552 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
7.553 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.553 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.554 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
7.554 * [backup-simplify]: Simplify 0 into 0
7.555 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.555 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.555 * [backup-simplify]: Simplify 0 into 0
7.556 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.557 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
7.557 * [backup-simplify]: Simplify 0 into 0
7.558 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
7.559 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
7.559 * [backup-simplify]: Simplify 0 into 0
7.560 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
7.560 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
7.560 * [backup-simplify]: Simplify 0 into 0
7.562 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
7.563 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
7.563 * [backup-simplify]: Simplify 0 into 0
7.563 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
7.563 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
7.563 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
7.564 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.564 * [taylor]: Taking taylor expansion of 2.0 in n
7.564 * [backup-simplify]: Simplify 2.0 into 2.0
7.564 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.564 * [taylor]: Taking taylor expansion of PI in n
7.564 * [backup-simplify]: Simplify PI into PI
7.564 * [taylor]: Taking taylor expansion of n in n
7.564 * [backup-simplify]: Simplify 0 into 0
7.564 * [backup-simplify]: Simplify 1 into 1
7.564 * [backup-simplify]: Simplify (/ PI 1) into PI
7.564 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.564 * [taylor]: Taking taylor expansion of 2.0 in n
7.564 * [backup-simplify]: Simplify 2.0 into 2.0
7.564 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.564 * [taylor]: Taking taylor expansion of PI in n
7.564 * [backup-simplify]: Simplify PI into PI
7.564 * [taylor]: Taking taylor expansion of n in n
7.564 * [backup-simplify]: Simplify 0 into 0
7.564 * [backup-simplify]: Simplify 1 into 1
7.564 * [backup-simplify]: Simplify (/ PI 1) into PI
7.565 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.565 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.566 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.566 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
7.566 * [backup-simplify]: Simplify 0 into 0
7.567 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.567 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.567 * [backup-simplify]: Simplify 0 into 0
7.568 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.569 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.569 * [backup-simplify]: Simplify 0 into 0
7.569 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.570 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.570 * [backup-simplify]: Simplify 0 into 0
7.571 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.572 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
7.572 * [backup-simplify]: Simplify 0 into 0
7.572 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.573 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
7.573 * [backup-simplify]: Simplify 0 into 0
7.574 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
7.574 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
7.574 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
7.574 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.574 * [taylor]: Taking taylor expansion of -2.0 in n
7.574 * [backup-simplify]: Simplify -2.0 into -2.0
7.574 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.574 * [taylor]: Taking taylor expansion of PI in n
7.574 * [backup-simplify]: Simplify PI into PI
7.574 * [taylor]: Taking taylor expansion of n in n
7.574 * [backup-simplify]: Simplify 0 into 0
7.574 * [backup-simplify]: Simplify 1 into 1
7.574 * [backup-simplify]: Simplify (/ PI 1) into PI
7.574 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.574 * [taylor]: Taking taylor expansion of -2.0 in n
7.574 * [backup-simplify]: Simplify -2.0 into -2.0
7.574 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.574 * [taylor]: Taking taylor expansion of PI in n
7.574 * [backup-simplify]: Simplify PI into PI
7.575 * [taylor]: Taking taylor expansion of n in n
7.575 * [backup-simplify]: Simplify 0 into 0
7.575 * [backup-simplify]: Simplify 1 into 1
7.575 * [backup-simplify]: Simplify (/ PI 1) into PI
7.575 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.575 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.576 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.576 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
7.576 * [backup-simplify]: Simplify 0 into 0
7.577 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.578 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.578 * [backup-simplify]: Simplify 0 into 0
7.579 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.581 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.581 * [backup-simplify]: Simplify 0 into 0
7.582 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.583 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.583 * [backup-simplify]: Simplify 0 into 0
7.584 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.586 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
7.586 * [backup-simplify]: Simplify 0 into 0
7.587 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.589 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
7.589 * [backup-simplify]: Simplify 0 into 0
7.589 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
7.589 * * * * [progress]: [ 2 / 3 ] generating series at (2)
7.590 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))))
7.590 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (n k) around 0
7.590 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
7.590 * [taylor]: Taking taylor expansion of 1.0 in k
7.590 * [backup-simplify]: Simplify 1.0 into 1.0
7.590 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
7.590 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
7.591 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
7.591 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
7.591 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
7.591 * [taylor]: Taking taylor expansion of 0.5 in k
7.591 * [backup-simplify]: Simplify 0.5 into 0.5
7.591 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
7.591 * [taylor]: Taking taylor expansion of 1.0 in k
7.591 * [backup-simplify]: Simplify 1.0 into 1.0
7.591 * [taylor]: Taking taylor expansion of k in k
7.591 * [backup-simplify]: Simplify 0 into 0
7.591 * [backup-simplify]: Simplify 1 into 1
7.591 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
7.591 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
7.591 * [taylor]: Taking taylor expansion of 2.0 in k
7.591 * [backup-simplify]: Simplify 2.0 into 2.0
7.591 * [taylor]: Taking taylor expansion of (* n PI) in k
7.591 * [taylor]: Taking taylor expansion of n in k
7.591 * [backup-simplify]: Simplify n into n
7.591 * [taylor]: Taking taylor expansion of PI in k
7.591 * [backup-simplify]: Simplify PI into PI
7.591 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.591 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
7.591 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
7.592 * [backup-simplify]: Simplify (- 0) into 0
7.592 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
7.593 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
7.593 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
7.593 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
7.593 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.593 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.593 * [taylor]: Taking taylor expansion of k in k
7.593 * [backup-simplify]: Simplify 0 into 0
7.593 * [backup-simplify]: Simplify 1 into 1
7.593 * [backup-simplify]: Simplify (/ 1 1) into 1
7.594 * [backup-simplify]: Simplify (sqrt 0) into 0
7.595 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.595 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
7.595 * [taylor]: Taking taylor expansion of 1.0 in n
7.595 * [backup-simplify]: Simplify 1.0 into 1.0
7.595 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
7.595 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
7.595 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
7.595 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
7.595 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
7.595 * [taylor]: Taking taylor expansion of 0.5 in n
7.595 * [backup-simplify]: Simplify 0.5 into 0.5
7.596 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
7.596 * [taylor]: Taking taylor expansion of 1.0 in n
7.596 * [backup-simplify]: Simplify 1.0 into 1.0
7.596 * [taylor]: Taking taylor expansion of k in n
7.596 * [backup-simplify]: Simplify k into k
7.596 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
7.596 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.596 * [taylor]: Taking taylor expansion of 2.0 in n
7.596 * [backup-simplify]: Simplify 2.0 into 2.0
7.596 * [taylor]: Taking taylor expansion of (* n PI) in n
7.596 * [taylor]: Taking taylor expansion of n in n
7.596 * [backup-simplify]: Simplify 0 into 0
7.596 * [backup-simplify]: Simplify 1 into 1
7.596 * [taylor]: Taking taylor expansion of PI in n
7.596 * [backup-simplify]: Simplify PI into PI
7.602 * [backup-simplify]: Simplify (* 0 PI) into 0
7.603 * [backup-simplify]: Simplify (* 2.0 0) into 0
7.604 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.606 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
7.607 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.607 * [backup-simplify]: Simplify (- k) into (- k)
7.607 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
7.607 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
7.608 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.609 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
7.610 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
7.611 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
7.611 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.611 * [taylor]: Taking taylor expansion of k in n
7.611 * [backup-simplify]: Simplify k into k
7.611 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.611 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
7.611 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.611 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
7.611 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
7.611 * [taylor]: Taking taylor expansion of 1.0 in n
7.611 * [backup-simplify]: Simplify 1.0 into 1.0
7.611 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
7.611 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
7.611 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
7.611 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
7.611 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
7.611 * [taylor]: Taking taylor expansion of 0.5 in n
7.611 * [backup-simplify]: Simplify 0.5 into 0.5
7.611 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
7.611 * [taylor]: Taking taylor expansion of 1.0 in n
7.611 * [backup-simplify]: Simplify 1.0 into 1.0
7.611 * [taylor]: Taking taylor expansion of k in n
7.611 * [backup-simplify]: Simplify k into k
7.611 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
7.611 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.611 * [taylor]: Taking taylor expansion of 2.0 in n
7.611 * [backup-simplify]: Simplify 2.0 into 2.0
7.611 * [taylor]: Taking taylor expansion of (* n PI) in n
7.612 * [taylor]: Taking taylor expansion of n in n
7.612 * [backup-simplify]: Simplify 0 into 0
7.612 * [backup-simplify]: Simplify 1 into 1
7.612 * [taylor]: Taking taylor expansion of PI in n
7.612 * [backup-simplify]: Simplify PI into PI
7.612 * [backup-simplify]: Simplify (* 0 PI) into 0
7.613 * [backup-simplify]: Simplify (* 2.0 0) into 0
7.614 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.616 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
7.617 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.617 * [backup-simplify]: Simplify (- k) into (- k)
7.617 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
7.617 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
7.618 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.620 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
7.621 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
7.621 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
7.621 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.621 * [taylor]: Taking taylor expansion of k in n
7.621 * [backup-simplify]: Simplify k into k
7.621 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.621 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
7.621 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.621 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
7.623 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))
7.624 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))
7.624 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k
7.624 * [taylor]: Taking taylor expansion of 1.0 in k
7.624 * [backup-simplify]: Simplify 1.0 into 1.0
7.624 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k
7.624 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
7.624 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
7.624 * [taylor]: Taking taylor expansion of 0.5 in k
7.624 * [backup-simplify]: Simplify 0.5 into 0.5
7.624 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
7.624 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
7.624 * [taylor]: Taking taylor expansion of 1.0 in k
7.624 * [backup-simplify]: Simplify 1.0 into 1.0
7.624 * [taylor]: Taking taylor expansion of k in k
7.624 * [backup-simplify]: Simplify 0 into 0
7.624 * [backup-simplify]: Simplify 1 into 1
7.624 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
7.624 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
7.624 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
7.624 * [taylor]: Taking taylor expansion of 2.0 in k
7.624 * [backup-simplify]: Simplify 2.0 into 2.0
7.624 * [taylor]: Taking taylor expansion of PI in k
7.624 * [backup-simplify]: Simplify PI into PI
7.625 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.626 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.626 * [taylor]: Taking taylor expansion of (log n) in k
7.626 * [taylor]: Taking taylor expansion of n in k
7.626 * [backup-simplify]: Simplify n into n
7.626 * [backup-simplify]: Simplify (log n) into (log n)
7.627 * [backup-simplify]: Simplify (- 0) into 0
7.627 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
7.628 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
7.629 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
7.630 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
7.631 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
7.631 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.631 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.632 * [taylor]: Taking taylor expansion of k in k
7.632 * [backup-simplify]: Simplify 0 into 0
7.632 * [backup-simplify]: Simplify 1 into 1
7.632 * [backup-simplify]: Simplify (/ 1 1) into 1
7.632 * [backup-simplify]: Simplify (sqrt 0) into 0
7.634 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.635 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0
7.635 * [backup-simplify]: Simplify (* 1.0 0) into 0
7.635 * [backup-simplify]: Simplify 0 into 0
7.636 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.637 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
7.638 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.638 * [backup-simplify]: Simplify (- 0) into 0
7.639 * [backup-simplify]: Simplify (+ 0 0) into 0
7.639 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
7.640 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.641 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
7.642 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.642 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
7.644 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0
7.644 * [taylor]: Taking taylor expansion of 0 in k
7.644 * [backup-simplify]: Simplify 0 into 0
7.644 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
7.645 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.646 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
7.646 * [backup-simplify]: Simplify (+ 0 0) into 0
7.646 * [backup-simplify]: Simplify (- 1) into -1
7.646 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.647 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
7.648 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
7.650 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
7.653 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
7.654 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
7.655 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
7.655 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.655 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
7.656 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.657 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.659 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
7.659 * [backup-simplify]: Simplify (- 0) into 0
7.659 * [backup-simplify]: Simplify (+ 0 0) into 0
7.660 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
7.661 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.662 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
7.664 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.665 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
7.667 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))))) into 0
7.667 * [taylor]: Taking taylor expansion of 0 in k
7.667 * [backup-simplify]: Simplify 0 into 0
7.667 * [backup-simplify]: Simplify 0 into 0
7.668 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
7.671 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.672 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.675 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
7.677 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
7.678 * [backup-simplify]: Simplify (+ 0 0) into 0
7.678 * [backup-simplify]: Simplify (- 0) into 0
7.678 * [backup-simplify]: Simplify (+ 0 0) into 0
7.680 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
7.683 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
7.687 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
7.698 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
7.705 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
7.710 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
7.710 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.711 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
7.713 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.715 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
7.721 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
7.721 * [backup-simplify]: Simplify (- 0) into 0
7.722 * [backup-simplify]: Simplify (+ 0 0) into 0
7.723 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
7.724 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.732 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
7.735 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
7.737 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
7.740 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))))) into 0
7.740 * [taylor]: Taking taylor expansion of 0 in k
7.740 * [backup-simplify]: Simplify 0 into 0
7.740 * [backup-simplify]: Simplify 0 into 0
7.740 * [backup-simplify]: Simplify 0 into 0
7.741 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.745 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.746 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.749 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
7.750 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
7.751 * [backup-simplify]: Simplify (+ 0 0) into 0
7.751 * [backup-simplify]: Simplify (- 0) into 0
7.751 * [backup-simplify]: Simplify (+ 0 0) into 0
7.752 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
7.754 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0
7.758 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
7.769 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
7.788 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
7.796 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
7.808 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))))))))))))))))))
7.809 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)))
7.809 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (n k) around 0
7.809 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
7.809 * [taylor]: Taking taylor expansion of 1.0 in k
7.809 * [backup-simplify]: Simplify 1.0 into 1.0
7.809 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
7.809 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
7.809 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
7.809 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
7.809 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
7.809 * [taylor]: Taking taylor expansion of 0.5 in k
7.809 * [backup-simplify]: Simplify 0.5 into 0.5
7.809 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
7.809 * [taylor]: Taking taylor expansion of 1.0 in k
7.809 * [backup-simplify]: Simplify 1.0 into 1.0
7.809 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.809 * [taylor]: Taking taylor expansion of k in k
7.809 * [backup-simplify]: Simplify 0 into 0
7.809 * [backup-simplify]: Simplify 1 into 1
7.809 * [backup-simplify]: Simplify (/ 1 1) into 1
7.809 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
7.809 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
7.809 * [taylor]: Taking taylor expansion of 2.0 in k
7.809 * [backup-simplify]: Simplify 2.0 into 2.0
7.809 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.809 * [taylor]: Taking taylor expansion of PI in k
7.809 * [backup-simplify]: Simplify PI into PI
7.809 * [taylor]: Taking taylor expansion of n in k
7.809 * [backup-simplify]: Simplify n into n
7.810 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.810 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
7.810 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
7.810 * [backup-simplify]: Simplify (- 1) into -1
7.810 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.810 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
7.810 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
7.811 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
7.811 * [taylor]: Taking taylor expansion of (sqrt k) in k
7.811 * [taylor]: Taking taylor expansion of k in k
7.811 * [backup-simplify]: Simplify 0 into 0
7.811 * [backup-simplify]: Simplify 1 into 1
7.811 * [backup-simplify]: Simplify (sqrt 0) into 0
7.812 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.812 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
7.812 * [taylor]: Taking taylor expansion of 1.0 in n
7.812 * [backup-simplify]: Simplify 1.0 into 1.0
7.812 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
7.812 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
7.812 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
7.812 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
7.812 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
7.812 * [taylor]: Taking taylor expansion of 0.5 in n
7.812 * [backup-simplify]: Simplify 0.5 into 0.5
7.812 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
7.812 * [taylor]: Taking taylor expansion of 1.0 in n
7.812 * [backup-simplify]: Simplify 1.0 into 1.0
7.812 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.812 * [taylor]: Taking taylor expansion of k in n
7.812 * [backup-simplify]: Simplify k into k
7.812 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.812 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
7.812 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.812 * [taylor]: Taking taylor expansion of 2.0 in n
7.812 * [backup-simplify]: Simplify 2.0 into 2.0
7.812 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.812 * [taylor]: Taking taylor expansion of PI in n
7.812 * [backup-simplify]: Simplify PI into PI
7.812 * [taylor]: Taking taylor expansion of n in n
7.812 * [backup-simplify]: Simplify 0 into 0
7.812 * [backup-simplify]: Simplify 1 into 1
7.813 * [backup-simplify]: Simplify (/ PI 1) into PI
7.813 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.813 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.814 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.814 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
7.814 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
7.814 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.815 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
7.816 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
7.816 * [taylor]: Taking taylor expansion of (sqrt k) in n
7.816 * [taylor]: Taking taylor expansion of k in n
7.816 * [backup-simplify]: Simplify k into k
7.816 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
7.816 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
7.816 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
7.816 * [taylor]: Taking taylor expansion of 1.0 in n
7.816 * [backup-simplify]: Simplify 1.0 into 1.0
7.816 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
7.816 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
7.816 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
7.816 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
7.816 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
7.816 * [taylor]: Taking taylor expansion of 0.5 in n
7.816 * [backup-simplify]: Simplify 0.5 into 0.5
7.816 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
7.816 * [taylor]: Taking taylor expansion of 1.0 in n
7.816 * [backup-simplify]: Simplify 1.0 into 1.0
7.816 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.816 * [taylor]: Taking taylor expansion of k in n
7.816 * [backup-simplify]: Simplify k into k
7.816 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.816 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
7.816 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.816 * [taylor]: Taking taylor expansion of 2.0 in n
7.816 * [backup-simplify]: Simplify 2.0 into 2.0
7.816 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.816 * [taylor]: Taking taylor expansion of PI in n
7.817 * [backup-simplify]: Simplify PI into PI
7.817 * [taylor]: Taking taylor expansion of n in n
7.817 * [backup-simplify]: Simplify 0 into 0
7.817 * [backup-simplify]: Simplify 1 into 1
7.817 * [backup-simplify]: Simplify (/ PI 1) into PI
7.817 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.819 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.819 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.819 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
7.819 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
7.820 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.822 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
7.823 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
7.823 * [taylor]: Taking taylor expansion of (sqrt k) in n
7.823 * [taylor]: Taking taylor expansion of k in n
7.823 * [backup-simplify]: Simplify k into k
7.823 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
7.823 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
7.825 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))
7.826 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))
7.826 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k
7.826 * [taylor]: Taking taylor expansion of 1.0 in k
7.826 * [backup-simplify]: Simplify 1.0 into 1.0
7.826 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k
7.826 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
7.826 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
7.826 * [taylor]: Taking taylor expansion of 0.5 in k
7.826 * [backup-simplify]: Simplify 0.5 into 0.5
7.826 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
7.826 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
7.826 * [taylor]: Taking taylor expansion of 1.0 in k
7.826 * [backup-simplify]: Simplify 1.0 into 1.0
7.826 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.826 * [taylor]: Taking taylor expansion of k in k
7.826 * [backup-simplify]: Simplify 0 into 0
7.826 * [backup-simplify]: Simplify 1 into 1
7.827 * [backup-simplify]: Simplify (/ 1 1) into 1
7.827 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
7.827 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
7.827 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
7.827 * [taylor]: Taking taylor expansion of 2.0 in k
7.827 * [backup-simplify]: Simplify 2.0 into 2.0
7.827 * [taylor]: Taking taylor expansion of PI in k
7.827 * [backup-simplify]: Simplify PI into PI
7.827 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.828 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.828 * [taylor]: Taking taylor expansion of (log n) in k
7.829 * [taylor]: Taking taylor expansion of n in k
7.829 * [backup-simplify]: Simplify n into n
7.829 * [backup-simplify]: Simplify (log n) into (log n)
7.829 * [backup-simplify]: Simplify (- 1) into -1
7.829 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.830 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.831 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
7.832 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
7.839 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
7.840 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
7.840 * [taylor]: Taking taylor expansion of (sqrt k) in k
7.840 * [taylor]: Taking taylor expansion of k in k
7.840 * [backup-simplify]: Simplify 0 into 0
7.840 * [backup-simplify]: Simplify 1 into 1
7.841 * [backup-simplify]: Simplify (sqrt 0) into 0
7.841 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.842 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0
7.842 * [backup-simplify]: Simplify (* 1.0 0) into 0
7.843 * [backup-simplify]: Simplify 0 into 0
7.843 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.844 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
7.845 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.845 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.845 * [backup-simplify]: Simplify (- 0) into 0
7.845 * [backup-simplify]: Simplify (+ 0 0) into 0
7.846 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
7.847 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.847 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
7.848 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.849 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
7.850 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0
7.850 * [taylor]: Taking taylor expansion of 0 in k
7.850 * [backup-simplify]: Simplify 0 into 0
7.850 * [backup-simplify]: Simplify 0 into 0
7.851 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.853 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.853 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.854 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
7.854 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.855 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.857 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
7.857 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.857 * [backup-simplify]: Simplify (- 0) into 0
7.858 * [backup-simplify]: Simplify (+ 0 0) into 0
7.858 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
7.859 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.860 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
7.861 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.862 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
7.864 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))))) into 0
7.864 * [taylor]: Taking taylor expansion of 0 in k
7.864 * [backup-simplify]: Simplify 0 into 0
7.864 * [backup-simplify]: Simplify 0 into 0
7.864 * [backup-simplify]: Simplify 0 into 0
7.866 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.867 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.869 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.870 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.871 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
7.871 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.872 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.876 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
7.876 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.876 * [backup-simplify]: Simplify (- 0) into 0
7.876 * [backup-simplify]: Simplify (+ 0 0) into 0
7.877 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
7.878 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.879 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
7.881 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
7.882 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
7.883 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))))) into 0
7.883 * [taylor]: Taking taylor expansion of 0 in k
7.883 * [backup-simplify]: Simplify 0 into 0
7.883 * [backup-simplify]: Simplify 0 into 0
7.884 * [backup-simplify]: Simplify 0 into 0
7.884 * [backup-simplify]: Simplify 0 into 0
7.886 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.887 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.890 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.892 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.896 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
7.897 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k)))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))))
7.897 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (n k) around 0
7.897 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
7.898 * [taylor]: Taking taylor expansion of 1.0 in k
7.898 * [backup-simplify]: Simplify 1.0 into 1.0
7.898 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
7.898 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
7.898 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
7.898 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
7.898 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
7.898 * [taylor]: Taking taylor expansion of 0.5 in k
7.898 * [backup-simplify]: Simplify 0.5 into 0.5
7.898 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
7.898 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.898 * [taylor]: Taking taylor expansion of k in k
7.898 * [backup-simplify]: Simplify 0 into 0
7.898 * [backup-simplify]: Simplify 1 into 1
7.898 * [backup-simplify]: Simplify (/ 1 1) into 1
7.898 * [taylor]: Taking taylor expansion of 1.0 in k
7.898 * [backup-simplify]: Simplify 1.0 into 1.0
7.898 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
7.898 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
7.898 * [taylor]: Taking taylor expansion of -2.0 in k
7.899 * [backup-simplify]: Simplify -2.0 into -2.0
7.899 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.899 * [taylor]: Taking taylor expansion of PI in k
7.899 * [backup-simplify]: Simplify PI into PI
7.899 * [taylor]: Taking taylor expansion of n in k
7.899 * [backup-simplify]: Simplify n into n
7.899 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.899 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
7.899 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
7.899 * [backup-simplify]: Simplify (+ 1 0) into 1
7.900 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
7.900 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
7.900 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
7.900 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
7.900 * [taylor]: Taking taylor expansion of (/ -1 k) in k
7.900 * [taylor]: Taking taylor expansion of -1 in k
7.900 * [backup-simplify]: Simplify -1 into -1
7.900 * [taylor]: Taking taylor expansion of k in k
7.900 * [backup-simplify]: Simplify 0 into 0
7.900 * [backup-simplify]: Simplify 1 into 1
7.901 * [backup-simplify]: Simplify (/ -1 1) into -1
7.901 * [backup-simplify]: Simplify (sqrt 0) into 0
7.903 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
7.903 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
7.903 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
7.903 * [taylor]: Taking taylor expansion of 1.0 in n
7.903 * [backup-simplify]: Simplify 1.0 into 1.0
7.903 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
7.903 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
7.903 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
7.903 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
7.903 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
7.903 * [taylor]: Taking taylor expansion of 0.5 in n
7.903 * [backup-simplify]: Simplify 0.5 into 0.5
7.903 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
7.903 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.903 * [taylor]: Taking taylor expansion of k in n
7.903 * [backup-simplify]: Simplify k into k
7.903 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.903 * [taylor]: Taking taylor expansion of 1.0 in n
7.903 * [backup-simplify]: Simplify 1.0 into 1.0
7.903 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
7.904 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.904 * [taylor]: Taking taylor expansion of -2.0 in n
7.904 * [backup-simplify]: Simplify -2.0 into -2.0
7.904 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.904 * [taylor]: Taking taylor expansion of PI in n
7.904 * [backup-simplify]: Simplify PI into PI
7.904 * [taylor]: Taking taylor expansion of n in n
7.904 * [backup-simplify]: Simplify 0 into 0
7.904 * [backup-simplify]: Simplify 1 into 1
7.904 * [backup-simplify]: Simplify (/ PI 1) into PI
7.905 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.906 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.906 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
7.906 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
7.907 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.909 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
7.910 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
7.910 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
7.910 * [taylor]: Taking taylor expansion of (/ -1 k) in n
7.910 * [taylor]: Taking taylor expansion of -1 in n
7.910 * [backup-simplify]: Simplify -1 into -1
7.910 * [taylor]: Taking taylor expansion of k in n
7.910 * [backup-simplify]: Simplify k into k
7.910 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
7.911 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
7.911 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
7.911 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
7.913 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
7.913 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
7.913 * [taylor]: Taking taylor expansion of 1.0 in n
7.913 * [backup-simplify]: Simplify 1.0 into 1.0
7.913 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
7.913 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
7.913 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
7.913 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
7.913 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
7.913 * [taylor]: Taking taylor expansion of 0.5 in n
7.913 * [backup-simplify]: Simplify 0.5 into 0.5
7.913 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
7.913 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.913 * [taylor]: Taking taylor expansion of k in n
7.913 * [backup-simplify]: Simplify k into k
7.913 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.913 * [taylor]: Taking taylor expansion of 1.0 in n
7.913 * [backup-simplify]: Simplify 1.0 into 1.0
7.913 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
7.913 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.913 * [taylor]: Taking taylor expansion of -2.0 in n
7.913 * [backup-simplify]: Simplify -2.0 into -2.0
7.913 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.913 * [taylor]: Taking taylor expansion of PI in n
7.913 * [backup-simplify]: Simplify PI into PI
7.914 * [taylor]: Taking taylor expansion of n in n
7.914 * [backup-simplify]: Simplify 0 into 0
7.914 * [backup-simplify]: Simplify 1 into 1
7.914 * [backup-simplify]: Simplify (/ PI 1) into PI
7.915 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.916 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.916 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
7.916 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
7.917 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.918 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
7.920 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
7.920 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
7.920 * [taylor]: Taking taylor expansion of (/ -1 k) in n
7.920 * [taylor]: Taking taylor expansion of -1 in n
7.920 * [backup-simplify]: Simplify -1 into -1
7.920 * [taylor]: Taking taylor expansion of k in n
7.920 * [backup-simplify]: Simplify k into k
7.920 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
7.920 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
7.920 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
7.920 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
7.922 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
7.923 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))
7.923 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) in k
7.923 * [taylor]: Taking taylor expansion of 1.0 in k
7.923 * [backup-simplify]: Simplify 1.0 into 1.0
7.923 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
7.923 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
7.923 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
7.923 * [taylor]: Taking taylor expansion of 0.5 in k
7.923 * [backup-simplify]: Simplify 0.5 into 0.5
7.923 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
7.923 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
7.923 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
7.924 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
7.924 * [taylor]: Taking taylor expansion of -2.0 in k
7.924 * [backup-simplify]: Simplify -2.0 into -2.0
7.924 * [taylor]: Taking taylor expansion of PI in k
7.924 * [backup-simplify]: Simplify PI into PI
7.924 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.925 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.925 * [taylor]: Taking taylor expansion of (log n) in k
7.925 * [taylor]: Taking taylor expansion of n in k
7.925 * [backup-simplify]: Simplify n into n
7.925 * [backup-simplify]: Simplify (log n) into (log n)
7.925 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
7.925 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.925 * [taylor]: Taking taylor expansion of k in k
7.925 * [backup-simplify]: Simplify 0 into 0
7.926 * [backup-simplify]: Simplify 1 into 1
7.926 * [backup-simplify]: Simplify (/ 1 1) into 1
7.926 * [taylor]: Taking taylor expansion of 1.0 in k
7.926 * [backup-simplify]: Simplify 1.0 into 1.0
7.926 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.927 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
7.928 * [backup-simplify]: Simplify (+ 1 0) into 1
7.929 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
7.930 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
7.931 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
7.931 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
7.931 * [taylor]: Taking taylor expansion of (/ -1 k) in k
7.931 * [taylor]: Taking taylor expansion of -1 in k
7.931 * [backup-simplify]: Simplify -1 into -1
7.931 * [taylor]: Taking taylor expansion of k in k
7.931 * [backup-simplify]: Simplify 0 into 0
7.931 * [backup-simplify]: Simplify 1 into 1
7.932 * [backup-simplify]: Simplify (/ -1 1) into -1
7.932 * [backup-simplify]: Simplify (sqrt 0) into 0
7.933 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
7.935 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
7.936 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
7.937 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
7.938 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.939 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
7.941 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
7.941 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.942 * [backup-simplify]: Simplify (+ 0 0) into 0
7.942 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
7.943 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.945 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
7.947 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
7.948 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
7.950 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))) into 0
7.950 * [taylor]: Taking taylor expansion of 0 in k
7.950 * [backup-simplify]: Simplify 0 into 0
7.950 * [backup-simplify]: Simplify 0 into 0
7.951 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
7.961 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.963 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
7.966 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
7.967 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
7.968 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.969 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.973 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
7.973 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.973 * [backup-simplify]: Simplify (+ 0 0) into 0
7.974 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
7.976 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.977 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
7.980 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.980 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.981 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
7.982 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
7.983 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))))) into 0
7.983 * [taylor]: Taking taylor expansion of 0 in k
7.983 * [backup-simplify]: Simplify 0 into 0
7.983 * [backup-simplify]: Simplify 0 into 0
7.983 * [backup-simplify]: Simplify 0 into 0
7.984 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.986 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.988 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
7.991 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
7.991 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
7.994 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
7.994 * * * * [progress]: [ 3 / 3 ] generating series at (2 1 2)
7.995 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
7.995 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
7.995 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
7.995 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
7.995 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
7.995 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
7.995 * [taylor]: Taking taylor expansion of 0.5 in k
7.995 * [backup-simplify]: Simplify 0.5 into 0.5
7.995 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
7.995 * [taylor]: Taking taylor expansion of 1.0 in k
7.995 * [backup-simplify]: Simplify 1.0 into 1.0
7.995 * [taylor]: Taking taylor expansion of k in k
7.995 * [backup-simplify]: Simplify 0 into 0
7.995 * [backup-simplify]: Simplify 1 into 1
7.995 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
7.995 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
7.995 * [taylor]: Taking taylor expansion of 2.0 in k
7.995 * [backup-simplify]: Simplify 2.0 into 2.0
7.995 * [taylor]: Taking taylor expansion of (* n PI) in k
7.995 * [taylor]: Taking taylor expansion of n in k
7.995 * [backup-simplify]: Simplify n into n
7.995 * [taylor]: Taking taylor expansion of PI in k
7.995 * [backup-simplify]: Simplify PI into PI
7.995 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.995 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
7.995 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
7.995 * [backup-simplify]: Simplify (- 0) into 0
7.996 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
7.996 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
7.996 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
7.996 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
7.996 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
7.996 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
7.996 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
7.996 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
7.996 * [taylor]: Taking taylor expansion of 0.5 in n
7.996 * [backup-simplify]: Simplify 0.5 into 0.5
7.996 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
7.996 * [taylor]: Taking taylor expansion of 1.0 in n
7.996 * [backup-simplify]: Simplify 1.0 into 1.0
7.996 * [taylor]: Taking taylor expansion of k in n
7.996 * [backup-simplify]: Simplify k into k
7.996 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
7.996 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.996 * [taylor]: Taking taylor expansion of 2.0 in n
7.996 * [backup-simplify]: Simplify 2.0 into 2.0
7.996 * [taylor]: Taking taylor expansion of (* n PI) in n
7.996 * [taylor]: Taking taylor expansion of n in n
7.996 * [backup-simplify]: Simplify 0 into 0
7.996 * [backup-simplify]: Simplify 1 into 1
7.996 * [taylor]: Taking taylor expansion of PI in n
7.996 * [backup-simplify]: Simplify PI into PI
7.997 * [backup-simplify]: Simplify (* 0 PI) into 0
7.997 * [backup-simplify]: Simplify (* 2.0 0) into 0
7.998 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.999 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
7.999 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.999 * [backup-simplify]: Simplify (- k) into (- k)
8.000 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
8.000 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
8.000 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.001 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
8.002 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
8.002 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
8.002 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
8.002 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
8.002 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
8.002 * [taylor]: Taking taylor expansion of 0.5 in n
8.002 * [backup-simplify]: Simplify 0.5 into 0.5
8.002 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
8.002 * [taylor]: Taking taylor expansion of 1.0 in n
8.002 * [backup-simplify]: Simplify 1.0 into 1.0
8.002 * [taylor]: Taking taylor expansion of k in n
8.002 * [backup-simplify]: Simplify k into k
8.002 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
8.002 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.002 * [taylor]: Taking taylor expansion of 2.0 in n
8.002 * [backup-simplify]: Simplify 2.0 into 2.0
8.002 * [taylor]: Taking taylor expansion of (* n PI) in n
8.002 * [taylor]: Taking taylor expansion of n in n
8.002 * [backup-simplify]: Simplify 0 into 0
8.002 * [backup-simplify]: Simplify 1 into 1
8.002 * [taylor]: Taking taylor expansion of PI in n
8.002 * [backup-simplify]: Simplify PI into PI
8.003 * [backup-simplify]: Simplify (* 0 PI) into 0
8.003 * [backup-simplify]: Simplify (* 2.0 0) into 0
8.004 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.005 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
8.005 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.005 * [backup-simplify]: Simplify (- k) into (- k)
8.005 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
8.005 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
8.006 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.007 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
8.008 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
8.008 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
8.008 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
8.008 * [taylor]: Taking taylor expansion of 0.5 in k
8.008 * [backup-simplify]: Simplify 0.5 into 0.5
8.008 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
8.008 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
8.008 * [taylor]: Taking taylor expansion of 1.0 in k
8.008 * [backup-simplify]: Simplify 1.0 into 1.0
8.008 * [taylor]: Taking taylor expansion of k in k
8.008 * [backup-simplify]: Simplify 0 into 0
8.008 * [backup-simplify]: Simplify 1 into 1
8.008 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
8.008 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
8.008 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
8.008 * [taylor]: Taking taylor expansion of 2.0 in k
8.008 * [backup-simplify]: Simplify 2.0 into 2.0
8.008 * [taylor]: Taking taylor expansion of PI in k
8.008 * [backup-simplify]: Simplify PI into PI
8.008 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.009 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.009 * [taylor]: Taking taylor expansion of (log n) in k
8.009 * [taylor]: Taking taylor expansion of n in k
8.009 * [backup-simplify]: Simplify n into n
8.009 * [backup-simplify]: Simplify (log n) into (log n)
8.010 * [backup-simplify]: Simplify (- 0) into 0
8.010 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
8.011 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
8.012 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
8.013 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
8.015 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
8.016 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
8.017 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.018 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
8.019 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
8.020 * [backup-simplify]: Simplify (- 0) into 0
8.020 * [backup-simplify]: Simplify (+ 0 0) into 0
8.021 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
8.022 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.023 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
8.025 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.025 * [taylor]: Taking taylor expansion of 0 in k
8.025 * [backup-simplify]: Simplify 0 into 0
8.025 * [backup-simplify]: Simplify 0 into 0
8.026 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
8.028 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
8.029 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
8.029 * [backup-simplify]: Simplify (+ 0 0) into 0
8.030 * [backup-simplify]: Simplify (- 1) into -1
8.030 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.032 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
8.034 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
8.038 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
8.041 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
8.042 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
8.042 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
8.044 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
8.045 * [backup-simplify]: Simplify (- 0) into 0
8.045 * [backup-simplify]: Simplify (+ 0 0) into 0
8.045 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
8.046 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.047 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
8.049 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.049 * [taylor]: Taking taylor expansion of 0 in k
8.049 * [backup-simplify]: Simplify 0 into 0
8.049 * [backup-simplify]: Simplify 0 into 0
8.049 * [backup-simplify]: Simplify 0 into 0
8.049 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.051 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
8.052 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
8.053 * [backup-simplify]: Simplify (+ 0 0) into 0
8.053 * [backup-simplify]: Simplify (- 0) into 0
8.053 * [backup-simplify]: Simplify (+ 0 0) into 0
8.054 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
8.056 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
8.058 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
8.062 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
8.075 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))
8.076 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))
8.076 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
8.076 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
8.076 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
8.076 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
8.076 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
8.076 * [taylor]: Taking taylor expansion of 0.5 in k
8.076 * [backup-simplify]: Simplify 0.5 into 0.5
8.076 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
8.076 * [taylor]: Taking taylor expansion of 1.0 in k
8.076 * [backup-simplify]: Simplify 1.0 into 1.0
8.076 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.076 * [taylor]: Taking taylor expansion of k in k
8.076 * [backup-simplify]: Simplify 0 into 0
8.076 * [backup-simplify]: Simplify 1 into 1
8.076 * [backup-simplify]: Simplify (/ 1 1) into 1
8.077 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
8.077 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
8.077 * [taylor]: Taking taylor expansion of 2.0 in k
8.077 * [backup-simplify]: Simplify 2.0 into 2.0
8.077 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.077 * [taylor]: Taking taylor expansion of PI in k
8.077 * [backup-simplify]: Simplify PI into PI
8.077 * [taylor]: Taking taylor expansion of n in k
8.077 * [backup-simplify]: Simplify n into n
8.077 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.077 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
8.077 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
8.077 * [backup-simplify]: Simplify (- 1) into -1
8.077 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.078 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
8.078 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
8.078 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
8.078 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
8.078 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
8.078 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
8.078 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
8.078 * [taylor]: Taking taylor expansion of 0.5 in n
8.078 * [backup-simplify]: Simplify 0.5 into 0.5
8.078 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
8.078 * [taylor]: Taking taylor expansion of 1.0 in n
8.078 * [backup-simplify]: Simplify 1.0 into 1.0
8.078 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.078 * [taylor]: Taking taylor expansion of k in n
8.078 * [backup-simplify]: Simplify k into k
8.078 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.078 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
8.078 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.078 * [taylor]: Taking taylor expansion of 2.0 in n
8.078 * [backup-simplify]: Simplify 2.0 into 2.0
8.078 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.078 * [taylor]: Taking taylor expansion of PI in n
8.078 * [backup-simplify]: Simplify PI into PI
8.078 * [taylor]: Taking taylor expansion of n in n
8.078 * [backup-simplify]: Simplify 0 into 0
8.078 * [backup-simplify]: Simplify 1 into 1
8.078 * [backup-simplify]: Simplify (/ PI 1) into PI
8.079 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.079 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.079 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.080 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
8.080 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
8.080 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.081 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
8.082 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
8.082 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
8.082 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
8.082 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
8.082 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
8.082 * [taylor]: Taking taylor expansion of 0.5 in n
8.082 * [backup-simplify]: Simplify 0.5 into 0.5
8.082 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
8.082 * [taylor]: Taking taylor expansion of 1.0 in n
8.082 * [backup-simplify]: Simplify 1.0 into 1.0
8.082 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.082 * [taylor]: Taking taylor expansion of k in n
8.082 * [backup-simplify]: Simplify k into k
8.082 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.082 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
8.082 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.082 * [taylor]: Taking taylor expansion of 2.0 in n
8.082 * [backup-simplify]: Simplify 2.0 into 2.0
8.082 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.082 * [taylor]: Taking taylor expansion of PI in n
8.082 * [backup-simplify]: Simplify PI into PI
8.082 * [taylor]: Taking taylor expansion of n in n
8.082 * [backup-simplify]: Simplify 0 into 0
8.082 * [backup-simplify]: Simplify 1 into 1
8.083 * [backup-simplify]: Simplify (/ PI 1) into PI
8.083 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.084 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.084 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.084 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
8.084 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
8.085 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.086 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
8.087 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
8.088 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
8.088 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
8.088 * [taylor]: Taking taylor expansion of 0.5 in k
8.088 * [backup-simplify]: Simplify 0.5 into 0.5
8.088 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
8.088 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
8.088 * [taylor]: Taking taylor expansion of 1.0 in k
8.088 * [backup-simplify]: Simplify 1.0 into 1.0
8.088 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.088 * [taylor]: Taking taylor expansion of k in k
8.088 * [backup-simplify]: Simplify 0 into 0
8.088 * [backup-simplify]: Simplify 1 into 1
8.088 * [backup-simplify]: Simplify (/ 1 1) into 1
8.088 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
8.088 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
8.088 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
8.088 * [taylor]: Taking taylor expansion of 2.0 in k
8.088 * [backup-simplify]: Simplify 2.0 into 2.0
8.088 * [taylor]: Taking taylor expansion of PI in k
8.088 * [backup-simplify]: Simplify PI into PI
8.089 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.090 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.090 * [taylor]: Taking taylor expansion of (log n) in k
8.090 * [taylor]: Taking taylor expansion of n in k
8.090 * [backup-simplify]: Simplify n into n
8.090 * [backup-simplify]: Simplify (log n) into (log n)
8.090 * [backup-simplify]: Simplify (- 1) into -1
8.091 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.091 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
8.092 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
8.093 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
8.095 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
8.096 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
8.097 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
8.098 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.099 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
8.101 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
8.101 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.101 * [backup-simplify]: Simplify (- 0) into 0
8.102 * [backup-simplify]: Simplify (+ 0 0) into 0
8.102 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
8.103 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.105 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
8.107 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.107 * [taylor]: Taking taylor expansion of 0 in k
8.107 * [backup-simplify]: Simplify 0 into 0
8.107 * [backup-simplify]: Simplify 0 into 0
8.107 * [backup-simplify]: Simplify 0 into 0
8.108 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.109 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.112 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
8.113 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.113 * [backup-simplify]: Simplify (- 0) into 0
8.113 * [backup-simplify]: Simplify (+ 0 0) into 0
8.114 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
8.116 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.117 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
8.120 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.120 * [taylor]: Taking taylor expansion of 0 in k
8.120 * [backup-simplify]: Simplify 0 into 0
8.120 * [backup-simplify]: Simplify 0 into 0
8.120 * [backup-simplify]: Simplify 0 into 0
8.120 * [backup-simplify]: Simplify 0 into 0
8.121 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.122 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.128 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
8.129 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.129 * [backup-simplify]: Simplify (- 0) into 0
8.130 * [backup-simplify]: Simplify (+ 0 0) into 0
8.131 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
8.132 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.134 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
8.137 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
8.137 * [taylor]: Taking taylor expansion of 0 in k
8.137 * [backup-simplify]: Simplify 0 into 0
8.137 * [backup-simplify]: Simplify 0 into 0
8.139 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n))))))
8.140 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))
8.140 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
8.140 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
8.140 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
8.140 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
8.140 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
8.140 * [taylor]: Taking taylor expansion of 0.5 in k
8.140 * [backup-simplify]: Simplify 0.5 into 0.5
8.140 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
8.140 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.140 * [taylor]: Taking taylor expansion of k in k
8.140 * [backup-simplify]: Simplify 0 into 0
8.140 * [backup-simplify]: Simplify 1 into 1
8.140 * [backup-simplify]: Simplify (/ 1 1) into 1
8.140 * [taylor]: Taking taylor expansion of 1.0 in k
8.140 * [backup-simplify]: Simplify 1.0 into 1.0
8.141 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
8.141 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
8.141 * [taylor]: Taking taylor expansion of -2.0 in k
8.141 * [backup-simplify]: Simplify -2.0 into -2.0
8.141 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.141 * [taylor]: Taking taylor expansion of PI in k
8.141 * [backup-simplify]: Simplify PI into PI
8.141 * [taylor]: Taking taylor expansion of n in k
8.141 * [backup-simplify]: Simplify n into n
8.141 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.141 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
8.141 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
8.142 * [backup-simplify]: Simplify (+ 1 0) into 1
8.142 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
8.142 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
8.142 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
8.142 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
8.142 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
8.143 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
8.143 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
8.143 * [taylor]: Taking taylor expansion of 0.5 in n
8.143 * [backup-simplify]: Simplify 0.5 into 0.5
8.143 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
8.143 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.143 * [taylor]: Taking taylor expansion of k in n
8.143 * [backup-simplify]: Simplify k into k
8.143 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.143 * [taylor]: Taking taylor expansion of 1.0 in n
8.143 * [backup-simplify]: Simplify 1.0 into 1.0
8.143 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
8.143 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
8.143 * [taylor]: Taking taylor expansion of -2.0 in n
8.143 * [backup-simplify]: Simplify -2.0 into -2.0
8.143 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.143 * [taylor]: Taking taylor expansion of PI in n
8.143 * [backup-simplify]: Simplify PI into PI
8.143 * [taylor]: Taking taylor expansion of n in n
8.143 * [backup-simplify]: Simplify 0 into 0
8.143 * [backup-simplify]: Simplify 1 into 1
8.144 * [backup-simplify]: Simplify (/ PI 1) into PI
8.144 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.146 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
8.146 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
8.146 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
8.147 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.149 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
8.150 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
8.150 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
8.150 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
8.150 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
8.150 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
8.150 * [taylor]: Taking taylor expansion of 0.5 in n
8.150 * [backup-simplify]: Simplify 0.5 into 0.5
8.150 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
8.150 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.150 * [taylor]: Taking taylor expansion of k in n
8.150 * [backup-simplify]: Simplify k into k
8.150 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.150 * [taylor]: Taking taylor expansion of 1.0 in n
8.150 * [backup-simplify]: Simplify 1.0 into 1.0
8.150 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
8.150 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
8.151 * [taylor]: Taking taylor expansion of -2.0 in n
8.151 * [backup-simplify]: Simplify -2.0 into -2.0
8.151 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.151 * [taylor]: Taking taylor expansion of PI in n
8.151 * [backup-simplify]: Simplify PI into PI
8.151 * [taylor]: Taking taylor expansion of n in n
8.151 * [backup-simplify]: Simplify 0 into 0
8.151 * [backup-simplify]: Simplify 1 into 1
8.151 * [backup-simplify]: Simplify (/ PI 1) into PI
8.152 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.153 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
8.153 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
8.153 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
8.155 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.156 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
8.157 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
8.157 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
8.157 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
8.157 * [taylor]: Taking taylor expansion of 0.5 in k
8.157 * [backup-simplify]: Simplify 0.5 into 0.5
8.157 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
8.157 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
8.157 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
8.157 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
8.158 * [taylor]: Taking taylor expansion of -2.0 in k
8.158 * [backup-simplify]: Simplify -2.0 into -2.0
8.158 * [taylor]: Taking taylor expansion of PI in k
8.158 * [backup-simplify]: Simplify PI into PI
8.158 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.159 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
8.159 * [taylor]: Taking taylor expansion of (log n) in k
8.159 * [taylor]: Taking taylor expansion of n in k
8.159 * [backup-simplify]: Simplify n into n
8.159 * [backup-simplify]: Simplify (log n) into (log n)
8.159 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
8.159 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.159 * [taylor]: Taking taylor expansion of k in k
8.160 * [backup-simplify]: Simplify 0 into 0
8.160 * [backup-simplify]: Simplify 1 into 1
8.160 * [backup-simplify]: Simplify (/ 1 1) into 1
8.160 * [taylor]: Taking taylor expansion of 1.0 in k
8.160 * [backup-simplify]: Simplify 1.0 into 1.0
8.160 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
8.161 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
8.162 * [backup-simplify]: Simplify (+ 1 0) into 1
8.163 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
8.164 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
8.165 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
8.167 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
8.168 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.169 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
8.170 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
8.171 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.171 * [backup-simplify]: Simplify (+ 0 0) into 0
8.172 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
8.173 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.174 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
8.176 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
8.176 * [taylor]: Taking taylor expansion of 0 in k
8.177 * [backup-simplify]: Simplify 0 into 0
8.177 * [backup-simplify]: Simplify 0 into 0
8.177 * [backup-simplify]: Simplify 0 into 0
8.178 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.179 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.183 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
8.183 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.183 * [backup-simplify]: Simplify (+ 0 0) into 0
8.184 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
8.186 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.187 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
8.190 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.190 * [taylor]: Taking taylor expansion of 0 in k
8.190 * [backup-simplify]: Simplify 0 into 0
8.190 * [backup-simplify]: Simplify 0 into 0
8.190 * [backup-simplify]: Simplify 0 into 0
8.190 * [backup-simplify]: Simplify 0 into 0
8.191 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.193 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.200 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
8.200 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.201 * [backup-simplify]: Simplify (+ 0 0) into 0
8.202 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
8.203 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.205 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
8.208 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
8.209 * [taylor]: Taking taylor expansion of 0 in k
8.209 * [backup-simplify]: Simplify 0 into 0
8.209 * [backup-simplify]: Simplify 0 into 0
8.210 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
8.210 * * * [progress]: simplifying candidates
8.219 * [simplify]: Simplifying:
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (- (+ (log 1.0) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (- (log (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (exp (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (/ (* (* (* 1.0 1.0) 1.0) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (/ (* (* (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1)
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
  (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n))))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
8.221 * * [simplify]: iteration 0: 262 enodes
8.295 * * [simplify]: iteration 1: 736 enodes
8.595 * * [simplify]: iteration 2: 2440 enodes
9.430 * * [simplify]: iteration complete: 5005 enodes
9.430 * * [simplify]: Extracting #0: cost 67 inf + 0
9.431 * * [simplify]: Extracting #1: cost 648 inf + 1
9.434 * * [simplify]: Extracting #2: cost 1335 inf + 1949
9.445 * * [simplify]: Extracting #3: cost 1439 inf + 53222
9.498 * * [simplify]: Extracting #4: cost 917 inf + 271972
9.615 * * [simplify]: Extracting #5: cost 368 inf + 555462
9.816 * * [simplify]: Extracting #6: cost 180 inf + 645216
9.963 * * [simplify]: Extracting #7: cost 53 inf + 718698
10.133 * * [simplify]: Extracting #8: cost 4 inf + 750414
10.313 * * [simplify]: Extracting #9: cost 0 inf + 749265
10.493 * * [simplify]: Extracting #10: cost 0 inf + 746755
10.715 * * [simplify]: Extracting #11: cost 0 inf + 746185
10.906 * * [simplify]: Extracting #12: cost 0 inf + 746145
11.135 * [simplify]: Simplified to:
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (exp (* 2.0 (* n PI)))
  (* (* (* 2.0 (* n PI)) (sqrt (* 2.0 (* n PI)))) (* (* 2.0 (* n PI)) (sqrt (* 2.0 (* n PI)))))
  (* (* (* 2.0 (* n PI)) (sqrt (* 2.0 (* n PI)))) (* (* 2.0 (* n PI)) (sqrt (* 2.0 (* n PI)))))
  (* (cbrt (* 2.0 (* n PI))) (cbrt (* 2.0 (* n PI))))
  (cbrt (* 2.0 (* n PI)))
  (* (* (* 2.0 (* n PI)) (sqrt (* 2.0 (* n PI)))) (* (* 2.0 (* n PI)) (sqrt (* 2.0 (* n PI)))))
  (sqrt (* 2.0 (* n PI)))
  (sqrt (* 2.0 (* n PI)))
  (* (* (cbrt n) (cbrt n)) (* PI 2.0))
  (* (* (sqrt n) 2.0) PI)
  (* PI 2.0)
  (* n PI)
  (+ (log (/ 1.0 (sqrt k))) (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k))))
  (+ (log (/ 1.0 (sqrt k))) (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k))))
  (+ (log (/ 1.0 (sqrt k))) (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k))))
  (+ (log (/ 1.0 (sqrt k))) (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k))))
  (+ (log (/ 1.0 (sqrt k))) (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k))))
  (+ (log (/ 1.0 (sqrt k))) (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k))))
  (+ (log (/ 1.0 (sqrt k))) (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k))))
  (exp (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (* (/ (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt k)) (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) k))
  (* (/ (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt k)) (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) k))
  (* (cbrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (cbrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))))
  (cbrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (* (/ (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt k)) (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) k))
  (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (- (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (/ (sqrt k) 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (fabs (cbrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* 2.0 (* n PI)) (/ k 2.0)))
  (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k)))
  (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k)))
  (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k)))
  (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k)))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* 2.0 (* n PI)) (/ 1.0 2.0))
  (pow (* 2.0 (* n PI)) (/ k 2.0))
  (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* 2.0 (* n PI)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* 2.0 (* n PI)) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k)))))
  (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* 2.0 (* n PI)) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k)))
  (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0)))
  (* 2.0 (* n PI))
  (pow (* 2.0 (* n PI)) (/ (/ (+ (sqrt k) (sqrt 1.0)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0)))
  (pow (* 2.0 (* n PI)) (+ (sqrt k) (sqrt 1.0)))
  (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (pow (* 2.0 (* n PI)) (- 1.0 k))
  (pow (* PI 2.0) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k)))
  (exp (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (pow (* 2.0 (* n PI)) (/ (- 1.0 k) (* 2.0 2)))
  (pow (* 2.0 (* n PI)) (/ (- 1.0 k) (* 2.0 2)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (+ (- (- (* (* (* +nan.0 (log (* PI 2.0))) (* (log n) (* k k))) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) +nan.0))) (- (* (* (* +nan.0 (log (* PI 2.0))) (log (* PI 2.0))) (* (- (* k k)) (exp (* (log (* 2.0 (* n PI))) 0.5)))) (+ (- (* (* (* (log n) k) (* (log n) k)) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) +nan.0)) (- (- (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (* (log n) (* k k)) +nan.0)) (+ (* (- (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) +nan.0) (log n))) k) (* (* k (exp (* (log (* 2.0 (* n PI))) 0.5))) (- (* +nan.0 (log (* PI 2.0))) +nan.0)))) (* (* (* +nan.0 (log (* PI 2.0))) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* k k)))) (* (* (- (* k k)) (exp (* (log (* 2.0 (* n PI))) 0.5))) +nan.0))))
  (+ (* (- (/ +nan.0 k)) (/ (exp (* 0.5 (* (log (* 2.0 (* n PI))) (- 1.0 k)))) k)) (* +nan.0 (- (/ (exp (* 0.5 (* (log (* 2.0 (* n PI))) (- 1.0 k)))) k) (/ (exp (* 0.5 (* (log (* 2.0 (* n PI))) (- 1.0 k)))) (* (* k k) k)))))
  (- (* (- +nan.0) (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k)))) (+ (/ (* (- +nan.0) (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k)))) k) (* (/ (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k))) (* k k)) +nan.0)))
  (+ (+ (pow (* 2.0 (* n PI)) 0.5) (+ (* 0.125 (* (* k k) (* (log (* PI 2.0)) (* (log (* PI 2.0)) (pow (* 2.0 (* n PI)) 0.5))))) (* (* (* (pow (* 2.0 (* n PI)) 0.5) 0.125) (* k k)) (* (log n) (log n))))) (- (* (log (* PI 2.0)) (* (* (* (log n) (pow (* 2.0 (* n PI)) 0.5)) (* k k)) 0.25)) (* 0.5 (* k (+ (* (log n) (pow (* 2.0 (* n PI)) 0.5)) (* (log (* PI 2.0)) (pow (* 2.0 (* n PI)) 0.5)))))))
  (exp (* 0.5 (* (log (* 2.0 (* n PI))) (- 1.0 k))))
  (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k)))
11.149 * * * [progress]: adding candidates to table
11.697 * * [progress]: iteration 3 / 4
11.697 * * * [progress]: picking best candidate
11.778 * * * * [pick]: Picked  #<alt (λ (k n) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))>
11.778 * * * [progress]: localizing error
11.812 * * * [progress]: generating rewritten candidates
11.812 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1 2 1)
11.831 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 2 1)
11.863 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
11.908 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1)
11.949 * * * [progress]: generating series expansions
11.949 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1 2 1)
11.950 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
11.950 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
11.950 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.950 * [taylor]: Taking taylor expansion of 2.0 in n
11.950 * [backup-simplify]: Simplify 2.0 into 2.0
11.950 * [taylor]: Taking taylor expansion of (* n PI) in n
11.950 * [taylor]: Taking taylor expansion of n in n
11.950 * [backup-simplify]: Simplify 0 into 0
11.950 * [backup-simplify]: Simplify 1 into 1
11.950 * [taylor]: Taking taylor expansion of PI in n
11.951 * [backup-simplify]: Simplify PI into PI
11.951 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.951 * [taylor]: Taking taylor expansion of 2.0 in n
11.951 * [backup-simplify]: Simplify 2.0 into 2.0
11.951 * [taylor]: Taking taylor expansion of (* n PI) in n
11.951 * [taylor]: Taking taylor expansion of n in n
11.951 * [backup-simplify]: Simplify 0 into 0
11.951 * [backup-simplify]: Simplify 1 into 1
11.951 * [taylor]: Taking taylor expansion of PI in n
11.951 * [backup-simplify]: Simplify PI into PI
11.951 * [backup-simplify]: Simplify (* 0 PI) into 0
11.952 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.952 * [backup-simplify]: Simplify 0 into 0
11.953 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.955 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.956 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.957 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.958 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
11.958 * [backup-simplify]: Simplify 0 into 0
11.959 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.961 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.961 * [backup-simplify]: Simplify 0 into 0
12.309 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.310 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.310 * [backup-simplify]: Simplify 0 into 0
12.311 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.312 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
12.312 * [backup-simplify]: Simplify 0 into 0
12.313 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.314 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
12.314 * [backup-simplify]: Simplify 0 into 0
12.315 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
12.316 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
12.316 * [backup-simplify]: Simplify 0 into 0
12.316 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
12.317 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
12.317 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
12.317 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.317 * [taylor]: Taking taylor expansion of 2.0 in n
12.317 * [backup-simplify]: Simplify 2.0 into 2.0
12.317 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.317 * [taylor]: Taking taylor expansion of PI in n
12.317 * [backup-simplify]: Simplify PI into PI
12.317 * [taylor]: Taking taylor expansion of n in n
12.317 * [backup-simplify]: Simplify 0 into 0
12.317 * [backup-simplify]: Simplify 1 into 1
12.317 * [backup-simplify]: Simplify (/ PI 1) into PI
12.317 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.317 * [taylor]: Taking taylor expansion of 2.0 in n
12.317 * [backup-simplify]: Simplify 2.0 into 2.0
12.317 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.317 * [taylor]: Taking taylor expansion of PI in n
12.317 * [backup-simplify]: Simplify PI into PI
12.317 * [taylor]: Taking taylor expansion of n in n
12.317 * [backup-simplify]: Simplify 0 into 0
12.317 * [backup-simplify]: Simplify 1 into 1
12.318 * [backup-simplify]: Simplify (/ PI 1) into PI
12.318 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.318 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.319 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.321 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.321 * [backup-simplify]: Simplify 0 into 0
12.322 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.322 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.322 * [backup-simplify]: Simplify 0 into 0
12.323 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.324 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.324 * [backup-simplify]: Simplify 0 into 0
12.324 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.325 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.325 * [backup-simplify]: Simplify 0 into 0
12.326 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.327 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.327 * [backup-simplify]: Simplify 0 into 0
12.327 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.328 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.328 * [backup-simplify]: Simplify 0 into 0
12.329 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
12.329 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
12.329 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
12.329 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.329 * [taylor]: Taking taylor expansion of -2.0 in n
12.329 * [backup-simplify]: Simplify -2.0 into -2.0
12.329 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.329 * [taylor]: Taking taylor expansion of PI in n
12.329 * [backup-simplify]: Simplify PI into PI
12.329 * [taylor]: Taking taylor expansion of n in n
12.329 * [backup-simplify]: Simplify 0 into 0
12.329 * [backup-simplify]: Simplify 1 into 1
12.330 * [backup-simplify]: Simplify (/ PI 1) into PI
12.330 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.330 * [taylor]: Taking taylor expansion of -2.0 in n
12.330 * [backup-simplify]: Simplify -2.0 into -2.0
12.330 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.330 * [taylor]: Taking taylor expansion of PI in n
12.330 * [backup-simplify]: Simplify PI into PI
12.330 * [taylor]: Taking taylor expansion of n in n
12.330 * [backup-simplify]: Simplify 0 into 0
12.330 * [backup-simplify]: Simplify 1 into 1
12.330 * [backup-simplify]: Simplify (/ PI 1) into PI
12.330 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.331 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.331 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.332 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
12.332 * [backup-simplify]: Simplify 0 into 0
12.332 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.333 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.333 * [backup-simplify]: Simplify 0 into 0
12.334 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.334 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.334 * [backup-simplify]: Simplify 0 into 0
12.335 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.336 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.336 * [backup-simplify]: Simplify 0 into 0
12.336 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.338 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.338 * [backup-simplify]: Simplify 0 into 0
12.339 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.341 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.341 * [backup-simplify]: Simplify 0 into 0
12.341 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
12.341 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 2 1)
12.342 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
12.342 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
12.342 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
12.342 * [taylor]: Taking taylor expansion of 2.0 in n
12.342 * [backup-simplify]: Simplify 2.0 into 2.0
12.342 * [taylor]: Taking taylor expansion of (* n PI) in n
12.342 * [taylor]: Taking taylor expansion of n in n
12.342 * [backup-simplify]: Simplify 0 into 0
12.342 * [backup-simplify]: Simplify 1 into 1
12.342 * [taylor]: Taking taylor expansion of PI in n
12.342 * [backup-simplify]: Simplify PI into PI
12.342 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
12.342 * [taylor]: Taking taylor expansion of 2.0 in n
12.342 * [backup-simplify]: Simplify 2.0 into 2.0
12.342 * [taylor]: Taking taylor expansion of (* n PI) in n
12.342 * [taylor]: Taking taylor expansion of n in n
12.342 * [backup-simplify]: Simplify 0 into 0
12.342 * [backup-simplify]: Simplify 1 into 1
12.342 * [taylor]: Taking taylor expansion of PI in n
12.342 * [backup-simplify]: Simplify PI into PI
12.342 * [backup-simplify]: Simplify (* 0 PI) into 0
12.343 * [backup-simplify]: Simplify (* 2.0 0) into 0
12.343 * [backup-simplify]: Simplify 0 into 0
12.343 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.344 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
12.345 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.345 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.346 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
12.346 * [backup-simplify]: Simplify 0 into 0
12.347 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.348 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.348 * [backup-simplify]: Simplify 0 into 0
12.349 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.349 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.349 * [backup-simplify]: Simplify 0 into 0
12.350 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.351 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
12.351 * [backup-simplify]: Simplify 0 into 0
12.352 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.353 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
12.353 * [backup-simplify]: Simplify 0 into 0
12.354 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
12.355 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
12.355 * [backup-simplify]: Simplify 0 into 0
12.355 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
12.356 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
12.356 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
12.356 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.356 * [taylor]: Taking taylor expansion of 2.0 in n
12.356 * [backup-simplify]: Simplify 2.0 into 2.0
12.356 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.356 * [taylor]: Taking taylor expansion of PI in n
12.356 * [backup-simplify]: Simplify PI into PI
12.356 * [taylor]: Taking taylor expansion of n in n
12.356 * [backup-simplify]: Simplify 0 into 0
12.356 * [backup-simplify]: Simplify 1 into 1
12.356 * [backup-simplify]: Simplify (/ PI 1) into PI
12.356 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.356 * [taylor]: Taking taylor expansion of 2.0 in n
12.356 * [backup-simplify]: Simplify 2.0 into 2.0
12.356 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.356 * [taylor]: Taking taylor expansion of PI in n
12.356 * [backup-simplify]: Simplify PI into PI
12.356 * [taylor]: Taking taylor expansion of n in n
12.356 * [backup-simplify]: Simplify 0 into 0
12.356 * [backup-simplify]: Simplify 1 into 1
12.357 * [backup-simplify]: Simplify (/ PI 1) into PI
12.357 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.357 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.358 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.358 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.358 * [backup-simplify]: Simplify 0 into 0
12.359 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.360 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.360 * [backup-simplify]: Simplify 0 into 0
12.360 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.361 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.361 * [backup-simplify]: Simplify 0 into 0
12.362 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.363 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.363 * [backup-simplify]: Simplify 0 into 0
12.363 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.364 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.364 * [backup-simplify]: Simplify 0 into 0
12.365 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.366 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.366 * [backup-simplify]: Simplify 0 into 0
12.366 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
12.366 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
12.366 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
12.366 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.366 * [taylor]: Taking taylor expansion of -2.0 in n
12.366 * [backup-simplify]: Simplify -2.0 into -2.0
12.366 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.367 * [taylor]: Taking taylor expansion of PI in n
12.367 * [backup-simplify]: Simplify PI into PI
12.367 * [taylor]: Taking taylor expansion of n in n
12.367 * [backup-simplify]: Simplify 0 into 0
12.367 * [backup-simplify]: Simplify 1 into 1
12.367 * [backup-simplify]: Simplify (/ PI 1) into PI
12.367 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.367 * [taylor]: Taking taylor expansion of -2.0 in n
12.367 * [backup-simplify]: Simplify -2.0 into -2.0
12.367 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.367 * [taylor]: Taking taylor expansion of PI in n
12.367 * [backup-simplify]: Simplify PI into PI
12.367 * [taylor]: Taking taylor expansion of n in n
12.367 * [backup-simplify]: Simplify 0 into 0
12.367 * [backup-simplify]: Simplify 1 into 1
12.367 * [backup-simplify]: Simplify (/ PI 1) into PI
12.368 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.368 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.368 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.369 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
12.369 * [backup-simplify]: Simplify 0 into 0
12.370 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.371 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.371 * [backup-simplify]: Simplify 0 into 0
12.372 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.373 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.373 * [backup-simplify]: Simplify 0 into 0
12.374 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.376 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.376 * [backup-simplify]: Simplify 0 into 0
12.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.378 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.378 * [backup-simplify]: Simplify 0 into 0
12.379 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.381 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.381 * [backup-simplify]: Simplify 0 into 0
12.382 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
12.382 * * * * [progress]: [ 3 / 4 ] generating series at (2)
12.384 * [backup-simplify]: Simplify (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) into (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k)))
12.384 * [approximate]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in (n k) around 0
12.384 * [taylor]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in k
12.384 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in k
12.384 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
12.384 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
12.384 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
12.384 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
12.384 * [taylor]: Taking taylor expansion of 0.5 in k
12.384 * [backup-simplify]: Simplify 0.5 into 0.5
12.384 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
12.384 * [taylor]: Taking taylor expansion of 1.0 in k
12.384 * [backup-simplify]: Simplify 1.0 into 1.0
12.384 * [taylor]: Taking taylor expansion of k in k
12.384 * [backup-simplify]: Simplify 0 into 0
12.384 * [backup-simplify]: Simplify 1 into 1
12.384 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
12.384 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
12.384 * [taylor]: Taking taylor expansion of 2.0 in k
12.384 * [backup-simplify]: Simplify 2.0 into 2.0
12.384 * [taylor]: Taking taylor expansion of (* n PI) in k
12.384 * [taylor]: Taking taylor expansion of n in k
12.384 * [backup-simplify]: Simplify n into n
12.384 * [taylor]: Taking taylor expansion of PI in k
12.384 * [backup-simplify]: Simplify PI into PI
12.384 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.384 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
12.385 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
12.385 * [backup-simplify]: Simplify (- 0) into 0
12.385 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
12.386 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
12.386 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
12.386 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
12.386 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
12.386 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
12.386 * [taylor]: Taking taylor expansion of 1.0 in k
12.386 * [backup-simplify]: Simplify 1.0 into 1.0
12.387 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.387 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.387 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.387 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.387 * [taylor]: Taking taylor expansion of k in k
12.387 * [backup-simplify]: Simplify 0 into 0
12.387 * [backup-simplify]: Simplify 1 into 1
12.388 * [backup-simplify]: Simplify (/ 1 1) into 1
12.388 * [backup-simplify]: Simplify (sqrt 0) into 0
12.390 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.390 * [taylor]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in n
12.390 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n
12.390 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
12.390 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
12.390 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
12.390 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
12.390 * [taylor]: Taking taylor expansion of 0.5 in n
12.390 * [backup-simplify]: Simplify 0.5 into 0.5
12.390 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
12.390 * [taylor]: Taking taylor expansion of 1.0 in n
12.390 * [backup-simplify]: Simplify 1.0 into 1.0
12.390 * [taylor]: Taking taylor expansion of k in n
12.390 * [backup-simplify]: Simplify k into k
12.390 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
12.390 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
12.390 * [taylor]: Taking taylor expansion of 2.0 in n
12.390 * [backup-simplify]: Simplify 2.0 into 2.0
12.390 * [taylor]: Taking taylor expansion of (* n PI) in n
12.390 * [taylor]: Taking taylor expansion of n in n
12.390 * [backup-simplify]: Simplify 0 into 0
12.390 * [backup-simplify]: Simplify 1 into 1
12.390 * [taylor]: Taking taylor expansion of PI in n
12.390 * [backup-simplify]: Simplify PI into PI
12.391 * [backup-simplify]: Simplify (* 0 PI) into 0
12.391 * [backup-simplify]: Simplify (* 2.0 0) into 0
12.393 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.393 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
12.394 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.394 * [backup-simplify]: Simplify (- k) into (- k)
12.394 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
12.394 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
12.395 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.396 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
12.397 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
12.397 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
12.397 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
12.397 * [taylor]: Taking taylor expansion of 1.0 in n
12.397 * [backup-simplify]: Simplify 1.0 into 1.0
12.397 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.397 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.397 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.397 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.397 * [taylor]: Taking taylor expansion of k in n
12.397 * [backup-simplify]: Simplify k into k
12.397 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.398 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.398 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.398 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.398 * [taylor]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in n
12.398 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n
12.398 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
12.398 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
12.398 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
12.398 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
12.398 * [taylor]: Taking taylor expansion of 0.5 in n
12.398 * [backup-simplify]: Simplify 0.5 into 0.5
12.398 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
12.398 * [taylor]: Taking taylor expansion of 1.0 in n
12.398 * [backup-simplify]: Simplify 1.0 into 1.0
12.398 * [taylor]: Taking taylor expansion of k in n
12.398 * [backup-simplify]: Simplify k into k
12.398 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
12.398 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
12.398 * [taylor]: Taking taylor expansion of 2.0 in n
12.398 * [backup-simplify]: Simplify 2.0 into 2.0
12.398 * [taylor]: Taking taylor expansion of (* n PI) in n
12.398 * [taylor]: Taking taylor expansion of n in n
12.398 * [backup-simplify]: Simplify 0 into 0
12.398 * [backup-simplify]: Simplify 1 into 1
12.398 * [taylor]: Taking taylor expansion of PI in n
12.398 * [backup-simplify]: Simplify PI into PI
12.398 * [backup-simplify]: Simplify (* 0 PI) into 0
12.399 * [backup-simplify]: Simplify (* 2.0 0) into 0
12.399 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.400 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
12.401 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.401 * [backup-simplify]: Simplify (- k) into (- k)
12.401 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
12.401 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
12.402 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.403 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
12.403 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
12.404 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
12.404 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
12.404 * [taylor]: Taking taylor expansion of 1.0 in n
12.404 * [backup-simplify]: Simplify 1.0 into 1.0
12.404 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.404 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.404 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.404 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.404 * [taylor]: Taking taylor expansion of k in n
12.404 * [backup-simplify]: Simplify k into k
12.404 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.404 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.404 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.405 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.405 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.407 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))
12.408 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) (sqrt (/ 1 k))) into (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) (sqrt (/ 1 k)))
12.408 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) (sqrt (/ 1 k))) in k
12.408 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k
12.408 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
12.408 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
12.408 * [taylor]: Taking taylor expansion of 1.0 in k
12.408 * [backup-simplify]: Simplify 1.0 into 1.0
12.408 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.409 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.409 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
12.409 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
12.409 * [taylor]: Taking taylor expansion of 0.5 in k
12.409 * [backup-simplify]: Simplify 0.5 into 0.5
12.409 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
12.409 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
12.409 * [taylor]: Taking taylor expansion of 1.0 in k
12.409 * [backup-simplify]: Simplify 1.0 into 1.0
12.409 * [taylor]: Taking taylor expansion of k in k
12.409 * [backup-simplify]: Simplify 0 into 0
12.409 * [backup-simplify]: Simplify 1 into 1
12.409 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
12.409 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
12.409 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
12.409 * [taylor]: Taking taylor expansion of 2.0 in k
12.409 * [backup-simplify]: Simplify 2.0 into 2.0
12.409 * [taylor]: Taking taylor expansion of PI in k
12.409 * [backup-simplify]: Simplify PI into PI
12.413 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.414 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.414 * [taylor]: Taking taylor expansion of (log n) in k
12.414 * [taylor]: Taking taylor expansion of n in k
12.414 * [backup-simplify]: Simplify n into n
12.414 * [backup-simplify]: Simplify (log n) into (log n)
12.414 * [backup-simplify]: Simplify (- 0) into 0
12.414 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
12.415 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
12.415 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
12.416 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
12.417 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
12.417 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.417 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.417 * [taylor]: Taking taylor expansion of k in k
12.417 * [backup-simplify]: Simplify 0 into 0
12.417 * [backup-simplify]: Simplify 1 into 1
12.417 * [backup-simplify]: Simplify (/ 1 1) into 1
12.417 * [backup-simplify]: Simplify (sqrt 0) into 0
12.418 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.419 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.420 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))
12.421 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) 0) into 0
12.422 * [backup-simplify]: Simplify 0 into 0
12.422 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
12.423 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.423 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
12.424 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.424 * [backup-simplify]: Simplify (- 0) into 0
12.425 * [backup-simplify]: Simplify (+ 0 0) into 0
12.425 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
12.427 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.428 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
12.430 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.432 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (pow (sqrt 1.0) 2))) into 0
12.434 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
12.434 * [taylor]: Taking taylor expansion of 0 in k
12.434 * [backup-simplify]: Simplify 0 into 0
12.435 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.437 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.437 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.438 * [backup-simplify]: Simplify (+ 0 0) into 0
12.438 * [backup-simplify]: Simplify (- 1) into -1
12.439 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.440 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
12.443 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
12.446 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.447 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
12.452 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))
12.461 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) +nan.0) (* (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) 0)) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))
12.463 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))
12.464 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.465 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
12.466 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
12.467 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
12.468 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.469 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.473 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
12.474 * [backup-simplify]: Simplify (- 0) into 0
12.474 * [backup-simplify]: Simplify (+ 0 0) into 0
12.475 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
12.476 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.478 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
12.480 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.482 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (pow (sqrt 1.0) 2)))) into 0
12.485 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
12.485 * [taylor]: Taking taylor expansion of 0 in k
12.485 * [backup-simplify]: Simplify 0 into 0
12.485 * [backup-simplify]: Simplify 0 into 0
12.486 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.489 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.490 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.494 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
12.496 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.496 * [backup-simplify]: Simplify (+ 0 0) into 0
12.496 * [backup-simplify]: Simplify (- 0) into 0
12.497 * [backup-simplify]: Simplify (+ 0 0) into 0
12.498 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
12.501 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
12.505 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
12.506 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
12.507 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
12.518 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.125 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))
12.536 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) +nan.0) (* (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.125 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))) 0))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
12.545 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
12.545 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.548 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
12.549 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
12.550 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
12.551 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.551 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.554 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
12.555 * [backup-simplify]: Simplify (- 0) into 0
12.555 * [backup-simplify]: Simplify (+ 0 0) into 0
12.556 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
12.557 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.558 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
12.559 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.561 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (sqrt 1.0) 2))))) into 0
12.562 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
12.562 * [taylor]: Taking taylor expansion of 0 in k
12.562 * [backup-simplify]: Simplify 0 into 0
12.562 * [backup-simplify]: Simplify 0 into 0
12.562 * [backup-simplify]: Simplify 0 into 0
12.563 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.565 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.566 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.569 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
12.571 * [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
12.571 * [backup-simplify]: Simplify (+ 0 0) into 0
12.571 * [backup-simplify]: Simplify (- 0) into 0
12.572 * [backup-simplify]: Simplify (+ 0 0) into 0
12.573 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
12.575 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0
12.579 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.579 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
12.580 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
12.591 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.020833333333333332 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 3)))) (+ (* 0.0625 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))) (* 0.020833333333333332 (* (pow (log (* 2.0 PI)) 3) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
12.618 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) +nan.0) (+ (* (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.125 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))) +nan.0) (* (- (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.020833333333333332 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 3)))) (+ (* 0.0625 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))) (* 0.020833333333333332 (* (pow (log (* 2.0 PI)) 3) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) 0)))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))))))))))))
12.637 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))))))))))))
12.660 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k)))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))))))))))))))))))))))
12.662 * [backup-simplify]: Simplify (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k))))) into (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k))
12.662 * [approximate]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in (n k) around 0
12.662 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in k
12.662 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
12.662 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
12.662 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
12.662 * [taylor]: Taking taylor expansion of 1.0 in k
12.662 * [backup-simplify]: Simplify 1.0 into 1.0
12.662 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.663 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.663 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
12.663 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
12.663 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
12.663 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
12.663 * [taylor]: Taking taylor expansion of 0.5 in k
12.663 * [backup-simplify]: Simplify 0.5 into 0.5
12.663 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
12.663 * [taylor]: Taking taylor expansion of 1.0 in k
12.663 * [backup-simplify]: Simplify 1.0 into 1.0
12.663 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.663 * [taylor]: Taking taylor expansion of k in k
12.663 * [backup-simplify]: Simplify 0 into 0
12.663 * [backup-simplify]: Simplify 1 into 1
12.664 * [backup-simplify]: Simplify (/ 1 1) into 1
12.664 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
12.664 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
12.664 * [taylor]: Taking taylor expansion of 2.0 in k
12.664 * [backup-simplify]: Simplify 2.0 into 2.0
12.664 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.664 * [taylor]: Taking taylor expansion of PI in k
12.664 * [backup-simplify]: Simplify PI into PI
12.664 * [taylor]: Taking taylor expansion of n in k
12.664 * [backup-simplify]: Simplify n into n
12.664 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.664 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
12.664 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
12.664 * [backup-simplify]: Simplify (- 1) into -1
12.665 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.665 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
12.665 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
12.666 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
12.666 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.666 * [taylor]: Taking taylor expansion of k in k
12.666 * [backup-simplify]: Simplify 0 into 0
12.666 * [backup-simplify]: Simplify 1 into 1
12.666 * [backup-simplify]: Simplify (sqrt 0) into 0
12.668 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.668 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in n
12.668 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
12.668 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
12.668 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
12.668 * [taylor]: Taking taylor expansion of 1.0 in n
12.668 * [backup-simplify]: Simplify 1.0 into 1.0
12.668 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.669 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.669 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
12.669 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
12.669 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
12.669 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
12.669 * [taylor]: Taking taylor expansion of 0.5 in n
12.669 * [backup-simplify]: Simplify 0.5 into 0.5
12.669 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
12.669 * [taylor]: Taking taylor expansion of 1.0 in n
12.669 * [backup-simplify]: Simplify 1.0 into 1.0
12.669 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.669 * [taylor]: Taking taylor expansion of k in n
12.669 * [backup-simplify]: Simplify k into k
12.669 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.669 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
12.669 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.669 * [taylor]: Taking taylor expansion of 2.0 in n
12.670 * [backup-simplify]: Simplify 2.0 into 2.0
12.670 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.670 * [taylor]: Taking taylor expansion of PI in n
12.670 * [backup-simplify]: Simplify PI into PI
12.670 * [taylor]: Taking taylor expansion of n in n
12.670 * [backup-simplify]: Simplify 0 into 0
12.670 * [backup-simplify]: Simplify 1 into 1
12.670 * [backup-simplify]: Simplify (/ PI 1) into PI
12.671 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.672 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.672 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.672 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
12.672 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
12.673 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.674 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
12.676 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
12.676 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.676 * [taylor]: Taking taylor expansion of k in n
12.676 * [backup-simplify]: Simplify k into k
12.676 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.676 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.676 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in n
12.676 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
12.676 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
12.676 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
12.676 * [taylor]: Taking taylor expansion of 1.0 in n
12.676 * [backup-simplify]: Simplify 1.0 into 1.0
12.677 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.677 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.677 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
12.677 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
12.677 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
12.677 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
12.677 * [taylor]: Taking taylor expansion of 0.5 in n
12.677 * [backup-simplify]: Simplify 0.5 into 0.5
12.677 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
12.677 * [taylor]: Taking taylor expansion of 1.0 in n
12.677 * [backup-simplify]: Simplify 1.0 into 1.0
12.677 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.677 * [taylor]: Taking taylor expansion of k in n
12.677 * [backup-simplify]: Simplify k into k
12.677 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.677 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
12.677 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.677 * [taylor]: Taking taylor expansion of 2.0 in n
12.677 * [backup-simplify]: Simplify 2.0 into 2.0
12.677 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.677 * [taylor]: Taking taylor expansion of PI in n
12.677 * [backup-simplify]: Simplify PI into PI
12.677 * [taylor]: Taking taylor expansion of n in n
12.677 * [backup-simplify]: Simplify 0 into 0
12.677 * [backup-simplify]: Simplify 1 into 1
12.678 * [backup-simplify]: Simplify (/ PI 1) into PI
12.678 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.679 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.679 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.679 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
12.679 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
12.680 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.680 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
12.681 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
12.681 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.681 * [taylor]: Taking taylor expansion of k in n
12.681 * [backup-simplify]: Simplify k into k
12.681 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.681 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.682 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.683 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
12.685 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) (sqrt k)) into (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) (sqrt k))
12.685 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) (sqrt k)) in k
12.685 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) in k
12.685 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
12.685 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
12.685 * [taylor]: Taking taylor expansion of 1.0 in k
12.685 * [backup-simplify]: Simplify 1.0 into 1.0
12.685 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.685 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.685 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
12.685 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
12.686 * [taylor]: Taking taylor expansion of 0.5 in k
12.686 * [backup-simplify]: Simplify 0.5 into 0.5
12.686 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
12.686 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
12.686 * [taylor]: Taking taylor expansion of 1.0 in k
12.686 * [backup-simplify]: Simplify 1.0 into 1.0
12.686 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.686 * [taylor]: Taking taylor expansion of k in k
12.686 * [backup-simplify]: Simplify 0 into 0
12.686 * [backup-simplify]: Simplify 1 into 1
12.686 * [backup-simplify]: Simplify (/ 1 1) into 1
12.686 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
12.686 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
12.686 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
12.686 * [taylor]: Taking taylor expansion of 2.0 in k
12.686 * [backup-simplify]: Simplify 2.0 into 2.0
12.686 * [taylor]: Taking taylor expansion of PI in k
12.686 * [backup-simplify]: Simplify PI into PI
12.686 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.687 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.687 * [taylor]: Taking taylor expansion of (log n) in k
12.687 * [taylor]: Taking taylor expansion of n in k
12.687 * [backup-simplify]: Simplify n into n
12.687 * [backup-simplify]: Simplify (log n) into (log n)
12.687 * [backup-simplify]: Simplify (- 1) into -1
12.687 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.688 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.688 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
12.689 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
12.690 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
12.690 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
12.690 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.690 * [taylor]: Taking taylor expansion of k in k
12.690 * [backup-simplify]: Simplify 0 into 0
12.690 * [backup-simplify]: Simplify 1 into 1
12.691 * [backup-simplify]: Simplify (sqrt 0) into 0
12.692 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.692 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.694 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
12.695 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) into 0
12.695 * [backup-simplify]: Simplify 0 into 0
12.696 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.696 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.697 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.697 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.697 * [backup-simplify]: Simplify (- 0) into 0
12.697 * [backup-simplify]: Simplify (+ 0 0) into 0
12.698 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
12.699 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.699 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
12.701 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.701 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
12.702 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0
12.703 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) (* 0 (sqrt k))) into 0
12.704 * [taylor]: Taking taylor expansion of 0 in k
12.704 * [backup-simplify]: Simplify 0 into 0
12.704 * [backup-simplify]: Simplify 0 into 0
12.704 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
12.706 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0
12.708 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
12.710 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
12.711 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
12.713 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.714 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.717 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
12.717 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.718 * [backup-simplify]: Simplify (- 0) into 0
12.718 * [backup-simplify]: Simplify (+ 0 0) into 0
12.719 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
12.720 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.722 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
12.724 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.725 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
12.726 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
12.728 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into 0
12.731 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
12.731 * [taylor]: Taking taylor expansion of 0 in k
12.731 * [backup-simplify]: Simplify 0 into 0
12.731 * [backup-simplify]: Simplify 0 into 0
12.731 * [backup-simplify]: Simplify 0 into 0
12.734 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.735 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
12.736 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
12.739 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into 0
12.742 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
12.744 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
12.745 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
12.746 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.747 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.755 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
12.756 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.756 * [backup-simplify]: Simplify (- 0) into 0
12.756 * [backup-simplify]: Simplify (+ 0 0) into 0
12.757 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
12.758 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.759 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
12.761 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.761 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
12.762 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
12.764 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))) into 0
12.765 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
12.765 * [taylor]: Taking taylor expansion of 0 in k
12.765 * [backup-simplify]: Simplify 0 into 0
12.765 * [backup-simplify]: Simplify 0 into 0
12.766 * [backup-simplify]: Simplify 0 into 0
12.766 * [backup-simplify]: Simplify 0 into 0
12.768 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.769 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
12.769 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
12.771 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))) into 0
12.773 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
12.775 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
12.779 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n))))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
12.781 * [backup-simplify]: Simplify (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k))))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k)))))) into (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
12.781 * [approximate]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in (n k) around 0
12.781 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
12.781 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k
12.781 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
12.781 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
12.781 * [taylor]: Taking taylor expansion of 1.0 in k
12.781 * [backup-simplify]: Simplify 1.0 into 1.0
12.781 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.782 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.782 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
12.782 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
12.782 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
12.782 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
12.782 * [taylor]: Taking taylor expansion of 0.5 in k
12.782 * [backup-simplify]: Simplify 0.5 into 0.5
12.782 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
12.782 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.782 * [taylor]: Taking taylor expansion of k in k
12.782 * [backup-simplify]: Simplify 0 into 0
12.782 * [backup-simplify]: Simplify 1 into 1
12.782 * [backup-simplify]: Simplify (/ 1 1) into 1
12.782 * [taylor]: Taking taylor expansion of 1.0 in k
12.782 * [backup-simplify]: Simplify 1.0 into 1.0
12.782 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
12.782 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
12.782 * [taylor]: Taking taylor expansion of -2.0 in k
12.782 * [backup-simplify]: Simplify -2.0 into -2.0
12.782 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.782 * [taylor]: Taking taylor expansion of PI in k
12.782 * [backup-simplify]: Simplify PI into PI
12.782 * [taylor]: Taking taylor expansion of n in k
12.782 * [backup-simplify]: Simplify n into n
12.782 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.782 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
12.782 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
12.783 * [backup-simplify]: Simplify (+ 1 0) into 1
12.783 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
12.783 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
12.783 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
12.783 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.783 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.783 * [taylor]: Taking taylor expansion of -1 in k
12.783 * [backup-simplify]: Simplify -1 into -1
12.783 * [taylor]: Taking taylor expansion of k in k
12.783 * [backup-simplify]: Simplify 0 into 0
12.783 * [backup-simplify]: Simplify 1 into 1
12.784 * [backup-simplify]: Simplify (/ -1 1) into -1
12.784 * [backup-simplify]: Simplify (sqrt 0) into 0
12.785 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.785 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.786 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
12.787 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) +nan.0) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
12.787 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in n
12.787 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
12.787 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
12.787 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
12.787 * [taylor]: Taking taylor expansion of 1.0 in n
12.787 * [backup-simplify]: Simplify 1.0 into 1.0
12.787 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.788 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.788 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
12.788 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
12.788 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
12.788 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
12.788 * [taylor]: Taking taylor expansion of 0.5 in n
12.788 * [backup-simplify]: Simplify 0.5 into 0.5
12.788 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
12.788 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.788 * [taylor]: Taking taylor expansion of k in n
12.788 * [backup-simplify]: Simplify k into k
12.788 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.788 * [taylor]: Taking taylor expansion of 1.0 in n
12.788 * [backup-simplify]: Simplify 1.0 into 1.0
12.788 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
12.788 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.788 * [taylor]: Taking taylor expansion of -2.0 in n
12.788 * [backup-simplify]: Simplify -2.0 into -2.0
12.788 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.788 * [taylor]: Taking taylor expansion of PI in n
12.788 * [backup-simplify]: Simplify PI into PI
12.788 * [taylor]: Taking taylor expansion of n in n
12.788 * [backup-simplify]: Simplify 0 into 0
12.788 * [backup-simplify]: Simplify 1 into 1
12.788 * [backup-simplify]: Simplify (/ PI 1) into PI
12.789 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.790 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.790 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
12.790 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
12.792 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.793 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
12.794 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
12.794 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.794 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.794 * [taylor]: Taking taylor expansion of -1 in n
12.794 * [backup-simplify]: Simplify -1 into -1
12.794 * [taylor]: Taking taylor expansion of k in n
12.795 * [backup-simplify]: Simplify k into k
12.795 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.795 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.795 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.795 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.796 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.798 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
12.800 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) into (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k)))
12.801 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in n
12.801 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
12.801 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
12.801 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
12.801 * [taylor]: Taking taylor expansion of 1.0 in n
12.801 * [backup-simplify]: Simplify 1.0 into 1.0
12.801 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.802 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.802 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
12.802 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
12.802 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
12.802 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
12.802 * [taylor]: Taking taylor expansion of 0.5 in n
12.802 * [backup-simplify]: Simplify 0.5 into 0.5
12.802 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
12.802 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.802 * [taylor]: Taking taylor expansion of k in n
12.802 * [backup-simplify]: Simplify k into k
12.802 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.802 * [taylor]: Taking taylor expansion of 1.0 in n
12.802 * [backup-simplify]: Simplify 1.0 into 1.0
12.802 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
12.802 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.802 * [taylor]: Taking taylor expansion of -2.0 in n
12.802 * [backup-simplify]: Simplify -2.0 into -2.0
12.802 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.802 * [taylor]: Taking taylor expansion of PI in n
12.802 * [backup-simplify]: Simplify PI into PI
12.802 * [taylor]: Taking taylor expansion of n in n
12.802 * [backup-simplify]: Simplify 0 into 0
12.803 * [backup-simplify]: Simplify 1 into 1
12.803 * [backup-simplify]: Simplify (/ PI 1) into PI
12.803 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.804 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.805 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
12.805 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
12.806 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.807 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
12.809 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
12.809 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.809 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.809 * [taylor]: Taking taylor expansion of -1 in n
12.809 * [backup-simplify]: Simplify -1 into -1
12.809 * [taylor]: Taking taylor expansion of k in n
12.809 * [backup-simplify]: Simplify k into k
12.809 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.809 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.809 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.809 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.810 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.812 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
12.815 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) into (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k)))
12.815 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) in k
12.815 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) in k
12.815 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
12.815 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
12.815 * [taylor]: Taking taylor expansion of 1.0 in k
12.815 * [backup-simplify]: Simplify 1.0 into 1.0
12.815 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.816 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.816 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
12.816 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
12.816 * [taylor]: Taking taylor expansion of 0.5 in k
12.816 * [backup-simplify]: Simplify 0.5 into 0.5
12.816 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
12.816 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
12.816 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
12.816 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
12.816 * [taylor]: Taking taylor expansion of -2.0 in k
12.816 * [backup-simplify]: Simplify -2.0 into -2.0
12.816 * [taylor]: Taking taylor expansion of PI in k
12.816 * [backup-simplify]: Simplify PI into PI
12.817 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.817 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.817 * [taylor]: Taking taylor expansion of (log n) in k
12.817 * [taylor]: Taking taylor expansion of n in k
12.817 * [backup-simplify]: Simplify n into n
12.818 * [backup-simplify]: Simplify (log n) into (log n)
12.818 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
12.818 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.818 * [taylor]: Taking taylor expansion of k in k
12.818 * [backup-simplify]: Simplify 0 into 0
12.818 * [backup-simplify]: Simplify 1 into 1
12.818 * [backup-simplify]: Simplify (/ 1 1) into 1
12.818 * [taylor]: Taking taylor expansion of 1.0 in k
12.818 * [backup-simplify]: Simplify 1.0 into 1.0
12.818 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.819 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
12.819 * [backup-simplify]: Simplify (+ 1 0) into 1
12.820 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
12.820 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
12.821 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
12.821 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.821 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.821 * [taylor]: Taking taylor expansion of -1 in k
12.821 * [backup-simplify]: Simplify -1 into -1
12.821 * [taylor]: Taking taylor expansion of k in k
12.821 * [backup-simplify]: Simplify 0 into 0
12.821 * [backup-simplify]: Simplify 1 into 1
12.822 * [backup-simplify]: Simplify (/ -1 1) into -1
12.822 * [backup-simplify]: Simplify (sqrt 0) into 0
12.823 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.823 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.825 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
12.826 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) +nan.0) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
12.827 * [backup-simplify]: Simplify (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
12.828 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.828 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
12.829 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
12.829 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.830 * [backup-simplify]: Simplify (+ 0 0) into 0
12.830 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
12.831 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.832 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
12.833 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.833 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
12.835 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0
12.836 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
12.836 * [taylor]: Taking taylor expansion of 0 in k
12.836 * [backup-simplify]: Simplify 0 into 0
12.836 * [backup-simplify]: Simplify 0 into 0
12.837 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
12.838 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0
12.838 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
12.840 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.842 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
12.844 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
12.844 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.845 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.848 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
12.849 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.849 * [backup-simplify]: Simplify (+ 0 0) into 0
12.850 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
12.852 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.853 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
12.856 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.857 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
12.858 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
12.863 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into 0
12.863 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.863 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
12.865 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
12.865 * [taylor]: Taking taylor expansion of 0 in k
12.865 * [backup-simplify]: Simplify 0 into 0
12.865 * [backup-simplify]: Simplify 0 into 0
12.865 * [backup-simplify]: Simplify 0 into 0
12.865 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
12.866 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
12.867 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into 0
12.868 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.870 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.874 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
12.875 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
12.880 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))))) into (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (+ (* +nan.0 (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2))) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
12.880 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1)
12.880 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))))
12.880 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (n k) around 0
12.881 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
12.881 * [taylor]: Taking taylor expansion of 1.0 in k
12.881 * [backup-simplify]: Simplify 1.0 into 1.0
12.881 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
12.881 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
12.881 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
12.881 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
12.881 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
12.881 * [taylor]: Taking taylor expansion of 0.5 in k
12.881 * [backup-simplify]: Simplify 0.5 into 0.5
12.881 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
12.881 * [taylor]: Taking taylor expansion of 1.0 in k
12.881 * [backup-simplify]: Simplify 1.0 into 1.0
12.881 * [taylor]: Taking taylor expansion of k in k
12.881 * [backup-simplify]: Simplify 0 into 0
12.881 * [backup-simplify]: Simplify 1 into 1
12.881 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
12.881 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
12.881 * [taylor]: Taking taylor expansion of 2.0 in k
12.881 * [backup-simplify]: Simplify 2.0 into 2.0
12.881 * [taylor]: Taking taylor expansion of (* n PI) in k
12.881 * [taylor]: Taking taylor expansion of n in k
12.881 * [backup-simplify]: Simplify n into n
12.881 * [taylor]: Taking taylor expansion of PI in k
12.881 * [backup-simplify]: Simplify PI into PI
12.881 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.881 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
12.881 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
12.881 * [backup-simplify]: Simplify (- 0) into 0
12.882 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
12.882 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
12.882 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
12.882 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
12.882 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.882 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.882 * [taylor]: Taking taylor expansion of k in k
12.882 * [backup-simplify]: Simplify 0 into 0
12.882 * [backup-simplify]: Simplify 1 into 1
12.882 * [backup-simplify]: Simplify (/ 1 1) into 1
12.883 * [backup-simplify]: Simplify (sqrt 0) into 0
12.883 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.883 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
12.883 * [taylor]: Taking taylor expansion of 1.0 in n
12.883 * [backup-simplify]: Simplify 1.0 into 1.0
12.883 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
12.883 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
12.883 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
12.883 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
12.883 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
12.883 * [taylor]: Taking taylor expansion of 0.5 in n
12.883 * [backup-simplify]: Simplify 0.5 into 0.5
12.883 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
12.884 * [taylor]: Taking taylor expansion of 1.0 in n
12.884 * [backup-simplify]: Simplify 1.0 into 1.0
12.884 * [taylor]: Taking taylor expansion of k in n
12.884 * [backup-simplify]: Simplify k into k
12.884 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
12.884 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
12.884 * [taylor]: Taking taylor expansion of 2.0 in n
12.884 * [backup-simplify]: Simplify 2.0 into 2.0
12.884 * [taylor]: Taking taylor expansion of (* n PI) in n
12.884 * [taylor]: Taking taylor expansion of n in n
12.884 * [backup-simplify]: Simplify 0 into 0
12.884 * [backup-simplify]: Simplify 1 into 1
12.884 * [taylor]: Taking taylor expansion of PI in n
12.884 * [backup-simplify]: Simplify PI into PI
12.884 * [backup-simplify]: Simplify (* 0 PI) into 0
12.884 * [backup-simplify]: Simplify (* 2.0 0) into 0
12.885 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.886 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
12.887 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.887 * [backup-simplify]: Simplify (- k) into (- k)
12.887 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
12.887 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
12.888 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.888 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
12.890 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
12.890 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.890 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.890 * [taylor]: Taking taylor expansion of k in n
12.890 * [backup-simplify]: Simplify k into k
12.890 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.890 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.890 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.890 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.890 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
12.890 * [taylor]: Taking taylor expansion of 1.0 in n
12.890 * [backup-simplify]: Simplify 1.0 into 1.0
12.890 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
12.890 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
12.890 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
12.890 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
12.890 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
12.890 * [taylor]: Taking taylor expansion of 0.5 in n
12.890 * [backup-simplify]: Simplify 0.5 into 0.5
12.890 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
12.890 * [taylor]: Taking taylor expansion of 1.0 in n
12.890 * [backup-simplify]: Simplify 1.0 into 1.0
12.890 * [taylor]: Taking taylor expansion of k in n
12.890 * [backup-simplify]: Simplify k into k
12.890 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
12.890 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
12.891 * [taylor]: Taking taylor expansion of 2.0 in n
12.891 * [backup-simplify]: Simplify 2.0 into 2.0
12.891 * [taylor]: Taking taylor expansion of (* n PI) in n
12.891 * [taylor]: Taking taylor expansion of n in n
12.891 * [backup-simplify]: Simplify 0 into 0
12.891 * [backup-simplify]: Simplify 1 into 1
12.891 * [taylor]: Taking taylor expansion of PI in n
12.891 * [backup-simplify]: Simplify PI into PI
12.891 * [backup-simplify]: Simplify (* 0 PI) into 0
12.891 * [backup-simplify]: Simplify (* 2.0 0) into 0
12.893 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.895 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
12.896 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.896 * [backup-simplify]: Simplify (- k) into (- k)
12.896 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
12.896 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
12.897 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.899 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
12.900 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
12.900 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.900 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.900 * [taylor]: Taking taylor expansion of k in n
12.900 * [backup-simplify]: Simplify k into k
12.900 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.900 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.900 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.900 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.902 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))
12.903 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))
12.903 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k
12.903 * [taylor]: Taking taylor expansion of 1.0 in k
12.903 * [backup-simplify]: Simplify 1.0 into 1.0
12.903 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k
12.903 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
12.903 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
12.903 * [taylor]: Taking taylor expansion of 0.5 in k
12.903 * [backup-simplify]: Simplify 0.5 into 0.5
12.903 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
12.903 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
12.903 * [taylor]: Taking taylor expansion of 1.0 in k
12.903 * [backup-simplify]: Simplify 1.0 into 1.0
12.903 * [taylor]: Taking taylor expansion of k in k
12.903 * [backup-simplify]: Simplify 0 into 0
12.903 * [backup-simplify]: Simplify 1 into 1
12.903 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
12.903 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
12.903 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
12.903 * [taylor]: Taking taylor expansion of 2.0 in k
12.903 * [backup-simplify]: Simplify 2.0 into 2.0
12.904 * [taylor]: Taking taylor expansion of PI in k
12.904 * [backup-simplify]: Simplify PI into PI
12.904 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.905 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.905 * [taylor]: Taking taylor expansion of (log n) in k
12.905 * [taylor]: Taking taylor expansion of n in k
12.905 * [backup-simplify]: Simplify n into n
12.905 * [backup-simplify]: Simplify (log n) into (log n)
12.906 * [backup-simplify]: Simplify (- 0) into 0
12.906 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
12.907 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
12.908 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
12.909 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
12.910 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
12.910 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.910 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.910 * [taylor]: Taking taylor expansion of k in k
12.910 * [backup-simplify]: Simplify 0 into 0
12.910 * [backup-simplify]: Simplify 1 into 1
12.911 * [backup-simplify]: Simplify (/ 1 1) into 1
12.911 * [backup-simplify]: Simplify (sqrt 0) into 0
12.913 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.914 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0
12.914 * [backup-simplify]: Simplify (* 1.0 0) into 0
12.914 * [backup-simplify]: Simplify 0 into 0
12.915 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.916 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
12.918 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.919 * [backup-simplify]: Simplify (- 0) into 0
12.919 * [backup-simplify]: Simplify (+ 0 0) into 0
12.919 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
12.921 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.922 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
12.924 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.925 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
12.927 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0
12.927 * [taylor]: Taking taylor expansion of 0 in k
12.927 * [backup-simplify]: Simplify 0 into 0
12.928 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.930 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.931 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.931 * [backup-simplify]: Simplify (+ 0 0) into 0
12.931 * [backup-simplify]: Simplify (- 1) into -1
12.932 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.933 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
12.935 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
12.939 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.943 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.945 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.946 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.946 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.947 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
12.948 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.950 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.953 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
12.953 * [backup-simplify]: Simplify (- 0) into 0
12.954 * [backup-simplify]: Simplify (+ 0 0) into 0
12.955 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
12.956 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.958 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
12.960 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.962 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
12.964 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))))) into 0
12.964 * [taylor]: Taking taylor expansion of 0 in k
12.964 * [backup-simplify]: Simplify 0 into 0
12.964 * [backup-simplify]: Simplify 0 into 0
12.965 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.968 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.969 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.972 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
12.974 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.974 * [backup-simplify]: Simplify (+ 0 0) into 0
12.975 * [backup-simplify]: Simplify (- 0) into 0
12.975 * [backup-simplify]: Simplify (+ 0 0) into 0
12.977 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
12.980 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
12.984 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
12.997 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
13.003 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
13.008 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
13.009 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.009 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
13.011 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.012 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.016 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
13.016 * [backup-simplify]: Simplify (- 0) into 0
13.016 * [backup-simplify]: Simplify (+ 0 0) into 0
13.017 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
13.018 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.019 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.020 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.022 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
13.023 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))))) into 0
13.023 * [taylor]: Taking taylor expansion of 0 in k
13.023 * [backup-simplify]: Simplify 0 into 0
13.023 * [backup-simplify]: Simplify 0 into 0
13.023 * [backup-simplify]: Simplify 0 into 0
13.024 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.026 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.027 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.030 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
13.031 * [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
13.032 * [backup-simplify]: Simplify (+ 0 0) into 0
13.032 * [backup-simplify]: Simplify (- 0) into 0
13.032 * [backup-simplify]: Simplify (+ 0 0) into 0
13.033 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.035 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0
13.039 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
13.050 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
13.062 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
13.071 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
13.097 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))))))))))))))))))
13.097 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)))
13.097 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (n k) around 0
13.097 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
13.097 * [taylor]: Taking taylor expansion of 1.0 in k
13.097 * [backup-simplify]: Simplify 1.0 into 1.0
13.097 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
13.097 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
13.097 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
13.098 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
13.098 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
13.098 * [taylor]: Taking taylor expansion of 0.5 in k
13.098 * [backup-simplify]: Simplify 0.5 into 0.5
13.098 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.098 * [taylor]: Taking taylor expansion of 1.0 in k
13.098 * [backup-simplify]: Simplify 1.0 into 1.0
13.098 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.098 * [taylor]: Taking taylor expansion of k in k
13.098 * [backup-simplify]: Simplify 0 into 0
13.098 * [backup-simplify]: Simplify 1 into 1
13.098 * [backup-simplify]: Simplify (/ 1 1) into 1
13.098 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
13.098 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
13.098 * [taylor]: Taking taylor expansion of 2.0 in k
13.098 * [backup-simplify]: Simplify 2.0 into 2.0
13.098 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.098 * [taylor]: Taking taylor expansion of PI in k
13.098 * [backup-simplify]: Simplify PI into PI
13.098 * [taylor]: Taking taylor expansion of n in k
13.098 * [backup-simplify]: Simplify n into n
13.098 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.098 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
13.098 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
13.098 * [backup-simplify]: Simplify (- 1) into -1
13.099 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.099 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
13.099 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
13.099 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
13.099 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.099 * [taylor]: Taking taylor expansion of k in k
13.099 * [backup-simplify]: Simplify 0 into 0
13.099 * [backup-simplify]: Simplify 1 into 1
13.099 * [backup-simplify]: Simplify (sqrt 0) into 0
13.100 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.100 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
13.100 * [taylor]: Taking taylor expansion of 1.0 in n
13.100 * [backup-simplify]: Simplify 1.0 into 1.0
13.100 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
13.100 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.100 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.101 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.101 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.101 * [taylor]: Taking taylor expansion of 0.5 in n
13.101 * [backup-simplify]: Simplify 0.5 into 0.5
13.101 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.101 * [taylor]: Taking taylor expansion of 1.0 in n
13.101 * [backup-simplify]: Simplify 1.0 into 1.0
13.101 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.101 * [taylor]: Taking taylor expansion of k in n
13.101 * [backup-simplify]: Simplify k into k
13.101 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.101 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.101 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.101 * [taylor]: Taking taylor expansion of 2.0 in n
13.101 * [backup-simplify]: Simplify 2.0 into 2.0
13.101 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.101 * [taylor]: Taking taylor expansion of PI in n
13.101 * [backup-simplify]: Simplify PI into PI
13.101 * [taylor]: Taking taylor expansion of n in n
13.101 * [backup-simplify]: Simplify 0 into 0
13.101 * [backup-simplify]: Simplify 1 into 1
13.101 * [backup-simplify]: Simplify (/ PI 1) into PI
13.101 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.102 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.102 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.102 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.102 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.103 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.104 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
13.105 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
13.105 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.105 * [taylor]: Taking taylor expansion of k in n
13.105 * [backup-simplify]: Simplify k into k
13.105 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.105 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.105 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
13.105 * [taylor]: Taking taylor expansion of 1.0 in n
13.105 * [backup-simplify]: Simplify 1.0 into 1.0
13.105 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
13.105 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.105 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.105 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.105 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.105 * [taylor]: Taking taylor expansion of 0.5 in n
13.105 * [backup-simplify]: Simplify 0.5 into 0.5
13.105 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.105 * [taylor]: Taking taylor expansion of 1.0 in n
13.105 * [backup-simplify]: Simplify 1.0 into 1.0
13.105 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.105 * [taylor]: Taking taylor expansion of k in n
13.105 * [backup-simplify]: Simplify k into k
13.105 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.105 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.105 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.105 * [taylor]: Taking taylor expansion of 2.0 in n
13.105 * [backup-simplify]: Simplify 2.0 into 2.0
13.105 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.105 * [taylor]: Taking taylor expansion of PI in n
13.105 * [backup-simplify]: Simplify PI into PI
13.105 * [taylor]: Taking taylor expansion of n in n
13.105 * [backup-simplify]: Simplify 0 into 0
13.105 * [backup-simplify]: Simplify 1 into 1
13.106 * [backup-simplify]: Simplify (/ PI 1) into PI
13.106 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.107 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.107 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.107 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.107 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.108 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.108 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
13.109 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
13.109 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.109 * [taylor]: Taking taylor expansion of k in n
13.109 * [backup-simplify]: Simplify k into k
13.109 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.109 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.110 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))
13.111 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))
13.111 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k
13.111 * [taylor]: Taking taylor expansion of 1.0 in k
13.111 * [backup-simplify]: Simplify 1.0 into 1.0
13.111 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k
13.111 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
13.111 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
13.111 * [taylor]: Taking taylor expansion of 0.5 in k
13.111 * [backup-simplify]: Simplify 0.5 into 0.5
13.111 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
13.111 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.111 * [taylor]: Taking taylor expansion of 1.0 in k
13.111 * [backup-simplify]: Simplify 1.0 into 1.0
13.111 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.111 * [taylor]: Taking taylor expansion of k in k
13.111 * [backup-simplify]: Simplify 0 into 0
13.111 * [backup-simplify]: Simplify 1 into 1
13.111 * [backup-simplify]: Simplify (/ 1 1) into 1
13.111 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
13.111 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.111 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.111 * [taylor]: Taking taylor expansion of 2.0 in k
13.111 * [backup-simplify]: Simplify 2.0 into 2.0
13.111 * [taylor]: Taking taylor expansion of PI in k
13.111 * [backup-simplify]: Simplify PI into PI
13.112 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.112 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.112 * [taylor]: Taking taylor expansion of (log n) in k
13.112 * [taylor]: Taking taylor expansion of n in k
13.112 * [backup-simplify]: Simplify n into n
13.112 * [backup-simplify]: Simplify (log n) into (log n)
13.113 * [backup-simplify]: Simplify (- 1) into -1
13.113 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.113 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.114 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
13.114 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
13.115 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
13.116 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
13.116 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.116 * [taylor]: Taking taylor expansion of k in k
13.116 * [backup-simplify]: Simplify 0 into 0
13.116 * [backup-simplify]: Simplify 1 into 1
13.116 * [backup-simplify]: Simplify (sqrt 0) into 0
13.117 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.118 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0
13.118 * [backup-simplify]: Simplify (* 1.0 0) into 0
13.118 * [backup-simplify]: Simplify 0 into 0
13.119 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.119 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.120 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.120 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.121 * [backup-simplify]: Simplify (- 0) into 0
13.121 * [backup-simplify]: Simplify (+ 0 0) into 0
13.121 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
13.122 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.123 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
13.124 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.125 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
13.126 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0
13.126 * [taylor]: Taking taylor expansion of 0 in k
13.126 * [backup-simplify]: Simplify 0 into 0
13.126 * [backup-simplify]: Simplify 0 into 0
13.127 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
13.128 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
13.129 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
13.129 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
13.130 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.130 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.132 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
13.132 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.133 * [backup-simplify]: Simplify (- 0) into 0
13.133 * [backup-simplify]: Simplify (+ 0 0) into 0
13.133 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
13.134 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.135 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
13.137 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.138 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
13.139 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))))) into 0
13.139 * [taylor]: Taking taylor expansion of 0 in k
13.139 * [backup-simplify]: Simplify 0 into 0
13.139 * [backup-simplify]: Simplify 0 into 0
13.139 * [backup-simplify]: Simplify 0 into 0
13.141 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.142 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
13.144 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
13.144 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
13.145 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
13.145 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.146 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.149 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
13.149 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.150 * [backup-simplify]: Simplify (- 0) into 0
13.150 * [backup-simplify]: Simplify (+ 0 0) into 0
13.151 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
13.151 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.153 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
13.154 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.156 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
13.157 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))))) into 0
13.157 * [taylor]: Taking taylor expansion of 0 in k
13.157 * [backup-simplify]: Simplify 0 into 0
13.157 * [backup-simplify]: Simplify 0 into 0
13.157 * [backup-simplify]: Simplify 0 into 0
13.157 * [backup-simplify]: Simplify 0 into 0
13.159 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.161 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
13.163 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
13.164 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
13.168 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
13.169 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k)))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))))
13.169 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (n k) around 0
13.169 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
13.169 * [taylor]: Taking taylor expansion of 1.0 in k
13.169 * [backup-simplify]: Simplify 1.0 into 1.0
13.169 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
13.169 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
13.169 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
13.170 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
13.170 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
13.170 * [taylor]: Taking taylor expansion of 0.5 in k
13.170 * [backup-simplify]: Simplify 0.5 into 0.5
13.170 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.170 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.170 * [taylor]: Taking taylor expansion of k in k
13.170 * [backup-simplify]: Simplify 0 into 0
13.170 * [backup-simplify]: Simplify 1 into 1
13.170 * [backup-simplify]: Simplify (/ 1 1) into 1
13.170 * [taylor]: Taking taylor expansion of 1.0 in k
13.170 * [backup-simplify]: Simplify 1.0 into 1.0
13.170 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
13.170 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
13.170 * [taylor]: Taking taylor expansion of -2.0 in k
13.170 * [backup-simplify]: Simplify -2.0 into -2.0
13.170 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.170 * [taylor]: Taking taylor expansion of PI in k
13.170 * [backup-simplify]: Simplify PI into PI
13.170 * [taylor]: Taking taylor expansion of n in k
13.170 * [backup-simplify]: Simplify n into n
13.171 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.171 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
13.171 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
13.171 * [backup-simplify]: Simplify (+ 1 0) into 1
13.172 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
13.172 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
13.172 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
13.172 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.172 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.172 * [taylor]: Taking taylor expansion of -1 in k
13.172 * [backup-simplify]: Simplify -1 into -1
13.172 * [taylor]: Taking taylor expansion of k in k
13.172 * [backup-simplify]: Simplify 0 into 0
13.172 * [backup-simplify]: Simplify 1 into 1
13.173 * [backup-simplify]: Simplify (/ -1 1) into -1
13.173 * [backup-simplify]: Simplify (sqrt 0) into 0
13.174 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.175 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
13.175 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
13.175 * [taylor]: Taking taylor expansion of 1.0 in n
13.175 * [backup-simplify]: Simplify 1.0 into 1.0
13.175 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
13.175 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.175 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.175 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.175 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.175 * [taylor]: Taking taylor expansion of 0.5 in n
13.175 * [backup-simplify]: Simplify 0.5 into 0.5
13.175 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.175 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.175 * [taylor]: Taking taylor expansion of k in n
13.175 * [backup-simplify]: Simplify k into k
13.175 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.175 * [taylor]: Taking taylor expansion of 1.0 in n
13.175 * [backup-simplify]: Simplify 1.0 into 1.0
13.175 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.175 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.175 * [taylor]: Taking taylor expansion of -2.0 in n
13.175 * [backup-simplify]: Simplify -2.0 into -2.0
13.175 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.176 * [taylor]: Taking taylor expansion of PI in n
13.176 * [backup-simplify]: Simplify PI into PI
13.176 * [taylor]: Taking taylor expansion of n in n
13.176 * [backup-simplify]: Simplify 0 into 0
13.176 * [backup-simplify]: Simplify 1 into 1
13.176 * [backup-simplify]: Simplify (/ PI 1) into PI
13.177 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.178 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.178 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.178 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.179 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.180 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
13.182 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
13.182 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
13.182 * [taylor]: Taking taylor expansion of (/ -1 k) in n
13.182 * [taylor]: Taking taylor expansion of -1 in n
13.182 * [backup-simplify]: Simplify -1 into -1
13.182 * [taylor]: Taking taylor expansion of k in n
13.182 * [backup-simplify]: Simplify k into k
13.182 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
13.182 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
13.182 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
13.182 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
13.183 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
13.184 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
13.184 * [taylor]: Taking taylor expansion of 1.0 in n
13.184 * [backup-simplify]: Simplify 1.0 into 1.0
13.184 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
13.184 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.184 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.184 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.184 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.184 * [taylor]: Taking taylor expansion of 0.5 in n
13.184 * [backup-simplify]: Simplify 0.5 into 0.5
13.184 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.184 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.184 * [taylor]: Taking taylor expansion of k in n
13.184 * [backup-simplify]: Simplify k into k
13.184 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.184 * [taylor]: Taking taylor expansion of 1.0 in n
13.184 * [backup-simplify]: Simplify 1.0 into 1.0
13.184 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.184 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.184 * [taylor]: Taking taylor expansion of -2.0 in n
13.184 * [backup-simplify]: Simplify -2.0 into -2.0
13.184 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.184 * [taylor]: Taking taylor expansion of PI in n
13.184 * [backup-simplify]: Simplify PI into PI
13.184 * [taylor]: Taking taylor expansion of n in n
13.184 * [backup-simplify]: Simplify 0 into 0
13.184 * [backup-simplify]: Simplify 1 into 1
13.185 * [backup-simplify]: Simplify (/ PI 1) into PI
13.185 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.187 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.187 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.187 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.192 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.193 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
13.195 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
13.195 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
13.195 * [taylor]: Taking taylor expansion of (/ -1 k) in n
13.195 * [taylor]: Taking taylor expansion of -1 in n
13.195 * [backup-simplify]: Simplify -1 into -1
13.195 * [taylor]: Taking taylor expansion of k in n
13.195 * [backup-simplify]: Simplify k into k
13.195 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
13.195 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
13.195 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
13.195 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
13.196 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
13.198 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))
13.198 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) in k
13.198 * [taylor]: Taking taylor expansion of 1.0 in k
13.198 * [backup-simplify]: Simplify 1.0 into 1.0
13.198 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
13.198 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
13.198 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
13.198 * [taylor]: Taking taylor expansion of 0.5 in k
13.198 * [backup-simplify]: Simplify 0.5 into 0.5
13.198 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
13.198 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
13.198 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
13.198 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
13.198 * [taylor]: Taking taylor expansion of -2.0 in k
13.198 * [backup-simplify]: Simplify -2.0 into -2.0
13.198 * [taylor]: Taking taylor expansion of PI in k
13.198 * [backup-simplify]: Simplify PI into PI
13.199 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.200 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.200 * [taylor]: Taking taylor expansion of (log n) in k
13.200 * [taylor]: Taking taylor expansion of n in k
13.200 * [backup-simplify]: Simplify n into n
13.200 * [backup-simplify]: Simplify (log n) into (log n)
13.200 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.200 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.200 * [taylor]: Taking taylor expansion of k in k
13.200 * [backup-simplify]: Simplify 0 into 0
13.200 * [backup-simplify]: Simplify 1 into 1
13.201 * [backup-simplify]: Simplify (/ 1 1) into 1
13.201 * [taylor]: Taking taylor expansion of 1.0 in k
13.201 * [backup-simplify]: Simplify 1.0 into 1.0
13.201 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.202 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
13.202 * [backup-simplify]: Simplify (+ 1 0) into 1
13.203 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
13.205 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
13.206 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
13.206 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.206 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.206 * [taylor]: Taking taylor expansion of -1 in k
13.206 * [backup-simplify]: Simplify -1 into -1
13.206 * [taylor]: Taking taylor expansion of k in k
13.206 * [backup-simplify]: Simplify 0 into 0
13.206 * [backup-simplify]: Simplify 1 into 1
13.207 * [backup-simplify]: Simplify (/ -1 1) into -1
13.207 * [backup-simplify]: Simplify (sqrt 0) into 0
13.208 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.210 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
13.211 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
13.212 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
13.213 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.214 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
13.216 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
13.216 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.216 * [backup-simplify]: Simplify (+ 0 0) into 0
13.217 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
13.218 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.219 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
13.222 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
13.223 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
13.225 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))) into 0
13.225 * [taylor]: Taking taylor expansion of 0 in k
13.225 * [backup-simplify]: Simplify 0 into 0
13.225 * [backup-simplify]: Simplify 0 into 0
13.226 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
13.229 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.231 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
13.233 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
13.235 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
13.236 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.237 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.240 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
13.241 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.241 * [backup-simplify]: Simplify (+ 0 0) into 0
13.242 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
13.243 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.245 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
13.247 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.248 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.248 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
13.250 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
13.252 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))))) into 0
13.252 * [taylor]: Taking taylor expansion of 0 in k
13.252 * [backup-simplify]: Simplify 0 into 0
13.252 * [backup-simplify]: Simplify 0 into 0
13.252 * [backup-simplify]: Simplify 0 into 0
13.253 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.257 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.261 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
13.264 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
13.266 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
13.270 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
13.271 * * * [progress]: simplifying candidates
13.275 * [simplify]: Simplifying:
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (+ 1/2 1/2)
  (+ 1/2 (/ 1 2))
  (+ 1 1)
  (+ (/ 1 2) 1/2)
  (+ (/ 1 2) (/ 1 2))
  (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (+ 1 1)
  (+ (log (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (log (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (log (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (exp (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (cbrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))) (cbrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))))
  (cbrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (sqrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (sqrt k)) (sqrt (sqrt k)))
  (* (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))) (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))))
  (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))) (sqrt (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))))
  (* (sqrt (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt 1))) (sqrt (/ 1.0 (sqrt 1))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 1)) (sqrt (/ 1.0 1)))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))))
  (* (sqrt 1) (sqrt 1))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* 1 1)
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* 2 1/2)
  (* 2 1)
  (* 2 (/ 1 2))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt 1))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) 1)
  (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (- (+ (log 1.0) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (- (log (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (exp (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (/ (* (* (* 1.0 1.0) 1.0) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (/ (* (* (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1)
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k)))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (+ (* +nan.0 (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2))) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
  (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
13.284 * * [simplify]: iteration 0: 340 enodes
13.399 * * [simplify]: iteration 1: 904 enodes
13.834 * * [simplify]: iteration 2: 3139 enodes
14.863 * * [simplify]: iteration complete: 5003 enodes
14.863 * * [simplify]: Extracting #0: cost 62 inf + 0
14.864 * * [simplify]: Extracting #1: cost 452 inf + 3
14.867 * * [simplify]: Extracting #2: cost 794 inf + 2339
14.880 * * [simplify]: Extracting #3: cost 1066 inf + 20833
14.892 * * [simplify]: Extracting #4: cost 1117 inf + 52368
14.915 * * [simplify]: Extracting #5: cost 942 inf + 136492
14.988 * * [simplify]: Extracting #6: cost 548 inf + 364614
15.130 * * [simplify]: Extracting #7: cost 199 inf + 579982
15.338 * * [simplify]: Extracting #8: cost 64 inf + 663660
15.556 * * [simplify]: Extracting #9: cost 8 inf + 693654
15.774 * * [simplify]: Extracting #10: cost 0 inf + 699197
16.018 * [simplify]: Simplified to:
  (* PI (* n 2.0))
  (* PI (* n 2.0))
  (log (* PI (* n 2.0)))
  (log (* PI (* n 2.0)))
  (log (* PI (* n 2.0)))
  (exp (* PI (* n 2.0)))
  (* (* (* (* n 2.0) PI) (* (* n 2.0) PI)) (* PI (* n 2.0)))
  (* (* (* (* n 2.0) PI) (* (* n 2.0) PI)) (* PI (* n 2.0)))
  (* (cbrt (* PI (* n 2.0))) (cbrt (* PI (* n 2.0))))
  (cbrt (* PI (* n 2.0)))
  (* (* (* (* n 2.0) PI) (* (* n 2.0) PI)) (* PI (* n 2.0)))
  (sqrt (* PI (* n 2.0)))
  (sqrt (* PI (* n 2.0)))
  (* (* (cbrt n) (cbrt n)) (* 2.0 PI))
  (* (* 2.0 PI) (sqrt n))
  (* 2.0 PI)
  (* n PI)
  (* PI (* n 2.0))
  (* PI (* n 2.0))
  (log (* PI (* n 2.0)))
  (log (* PI (* n 2.0)))
  (log (* PI (* n 2.0)))
  (exp (* PI (* n 2.0)))
  (* (* (* (* n 2.0) PI) (* (* n 2.0) PI)) (* PI (* n 2.0)))
  (* (* (* (* n 2.0) PI) (* (* n 2.0) PI)) (* PI (* n 2.0)))
  (* (cbrt (* PI (* n 2.0))) (cbrt (* PI (* n 2.0))))
  (cbrt (* PI (* n 2.0)))
  (* (* (* (* n 2.0) PI) (* (* n 2.0) PI)) (* PI (* n 2.0)))
  (sqrt (* PI (* n 2.0)))
  (sqrt (* PI (* n 2.0)))
  (* (* (cbrt n) (cbrt n)) (* 2.0 PI))
  (* (* 2.0 PI) (sqrt n))
  (* 2.0 PI)
  (* n PI)
  1
  1
  2
  1
  1
  (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))
  (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  2
  (+ (* (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k))))
  (+ (* (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k))))
  (exp (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (cbrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (cbrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (cbrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0)
  (sqrt k)
  (* (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (cbrt (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (cbrt (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (cbrt (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (cbrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (cbrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (cbrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt k))
  1
  (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))
  (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0)
  (/ 1 (sqrt k))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  1
  (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  1
  2
  1
  (* (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (* (cbrt (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (cbrt (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))))
  (* (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (fabs (cbrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))))
  (* (sqrt (/ 1.0 (fabs (cbrt k)))) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt 1.0))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt 1.0))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (sqrt (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0)) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (cbrt (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (cbrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))))
  (* (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))
  (* (sqrt (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0)) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0)) (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (+ (* (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k))))
  (+ (* (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k))))
  (+ (* (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k))))
  (+ (* (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k))))
  (+ (* (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k))))
  (+ (* (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k))))
  (+ (* (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k))))
  (exp (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (cbrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (cbrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (cbrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (* (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (- (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) 1.0)
  (- (sqrt k))
  (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (/ (sqrt k) 1.0) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ 1.0 (fabs (cbrt k))) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0)
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0)
  (/ (sqrt k) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* PI (* n 2.0)) (/ k 2.0)))
  (* PI (* n 2.0))
  (* PI (* n 2.0))
  (* PI (* n 2.0))
  (* PI (* n 2.0))
  (* PI (* n 2.0))
  (* PI (* n 2.0))
  (- (- (* (* 1.0 +nan.0) (* (exp (* (log (* PI (* n 2.0))) 0.5)) (* k (log n)))) (+ (- (* (* (* 1.0 +nan.0) k) (exp (* (log (* PI (* n 2.0))) 0.5))) (* (* (* (* +nan.0 (log (* 2.0 PI))) k) (exp (* (log (* PI (* n 2.0))) 0.5))) 1.0)) (- (* (* +nan.0 (log (* 2.0 PI))) (* (* 1.0 (* k k)) (exp (* (log (* PI (* n 2.0))) 0.5)))) (+ (+ (* (* 1.0 +nan.0) (* (exp (* (log (* PI (* n 2.0))) 0.5)) (* k k))) (* (* (- (log (* 2.0 PI))) (* (* +nan.0 (* (log n) (* k k))) (exp (* (log (* PI (* n 2.0))) 0.5)))) 1.0)) (+ (* (* (* 1.0 +nan.0) (* (* k (log n)) (* k (log n)))) (exp (* (log (* PI (* n 2.0))) 0.5))) (+ (* (* 1.0 +nan.0) (- (exp (* (log (* PI (* n 2.0))) 0.5)))) (- (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) (* (* 1.0 +nan.0) (* (exp (* (log (* PI (* n 2.0))) 0.5)) (* k k)))) (* 1.0 (* (* +nan.0 (* (log n) (* k k))) (exp (* (log (* PI (* n 2.0))) 0.5))))))))))))
  (- (- (/ (/ (* (* +nan.0 1.0) (exp (* (* (log (* PI (* n 2.0))) 0.5) (- 1.0 k)))) (* k k)) k) (- (/ (* (* +nan.0 1.0) (exp (* (* (log (* PI (* n 2.0))) 0.5) (- 1.0 k)))) k) (/ (* (* +nan.0 1.0) (exp (* (* (log (* PI (* n 2.0))) 0.5) (- 1.0 k)))) (* k k)))))
  (- (- (/ (* (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) +nan.0) (/ k 1.0)) (- (* (* +nan.0 1.0) (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k))))) (/ (* (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) +nan.0) (/ (* k k) 1.0)))))
  (- (+ (- (* (* (* +nan.0 (* (log n) (* k k))) (exp (* (log (* PI (* n 2.0))) 0.5))) (log (* 2.0 PI))) (* +nan.0 (exp (* (log (* PI (* n 2.0))) 0.5)))) (+ (- (* (* (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) (* k k)) (exp (* (log (* PI (* n 2.0))) 0.5))) +nan.0) (* (exp (* (log (* PI (* n 2.0))) 0.5)) (* (* k k) +nan.0))) (+ (- (* (* (* k (log n)) (* k (log n))) (* +nan.0 (exp (* (log (* PI (* n 2.0))) 0.5)))) (* (* +nan.0 (* (log n) (* k k))) (exp (* (log (* PI (* n 2.0))) 0.5)))) (+ (- (* (* (exp (* (log (* PI (* n 2.0))) 0.5)) (* k k)) (* (log (* 2.0 PI)) +nan.0)) (* (* (* +nan.0 (exp (* (log (* PI (* n 2.0))) 0.5))) (log n)) k)) (* (* k (exp (* (log (* PI (* n 2.0))) 0.5))) (- (* +nan.0 (log (* 2.0 PI))) +nan.0)))))))
  (+ (* +nan.0 (- (/ (exp (* (* (log (* PI (* n 2.0))) 0.5) (- 1.0 k))) (* k k)))) (* +nan.0 (- (/ (exp (* (* (log (* PI (* n 2.0))) 0.5) (- 1.0 k))) k) (/ (exp (* (* (log (* PI (* n 2.0))) 0.5) (- 1.0 k))) (* (* k k) k)))))
  (+ (* +nan.0 (- (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))))) (* +nan.0 (- (/ (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) k) (/ (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) (* k k)))))
16.035 * * * [progress]: adding candidates to table
17.160 * * [progress]: iteration 4 / 4
17.160 * * * [progress]: picking best candidate
17.219 * * * * [pick]: Picked  #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
17.219 * * * [progress]: localizing error
17.267 * * * [progress]: generating rewritten candidates
17.267 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1)
17.328 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 1)
17.333 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1)
17.339 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1)
17.364 * * * [progress]: generating series expansions
17.364 * * * * [progress]: [ 1 / 4 ] generating series at (2 1)
17.364 * [backup-simplify]: Simplify (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) into (* (pow (sqrt 1.0) 2) (sqrt (/ 1 k)))
17.364 * [approximate]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt (/ 1 k))) in (k) around 0
17.364 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt (/ 1 k))) in k
17.364 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
17.364 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
17.364 * [taylor]: Taking taylor expansion of 1.0 in k
17.364 * [backup-simplify]: Simplify 1.0 into 1.0
17.365 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.365 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.365 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
17.365 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.365 * [taylor]: Taking taylor expansion of k in k
17.365 * [backup-simplify]: Simplify 0 into 0
17.365 * [backup-simplify]: Simplify 1 into 1
17.366 * [backup-simplify]: Simplify (/ 1 1) into 1
17.366 * [backup-simplify]: Simplify (sqrt 0) into 0
17.367 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.367 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt (/ 1 k))) in k
17.367 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
17.367 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
17.367 * [taylor]: Taking taylor expansion of 1.0 in k
17.367 * [backup-simplify]: Simplify 1.0 into 1.0
17.367 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.368 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.368 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
17.368 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.368 * [taylor]: Taking taylor expansion of k in k
17.368 * [backup-simplify]: Simplify 0 into 0
17.368 * [backup-simplify]: Simplify 1 into 1
17.368 * [backup-simplify]: Simplify (/ 1 1) into 1
17.368 * [backup-simplify]: Simplify (sqrt 0) into 0
17.369 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.370 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
17.371 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) 0) into 0
17.371 * [backup-simplify]: Simplify 0 into 0
17.371 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
17.373 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (* 0 0)) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.375 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.375 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
17.377 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.378 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
17.378 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
17.381 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.382 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.383 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.385 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.386 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
17.386 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
17.389 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.390 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.395 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow k 2)) (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) k) (- (* +nan.0 (pow (sqrt 1.0) 2))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (* +nan.0 (* (pow (sqrt 1.0) 2) k)))))))
17.395 * [backup-simplify]: Simplify (* (sqrt (/ 1.0 (sqrt (/ 1 k)))) (sqrt (/ 1.0 (sqrt (/ 1 k))))) into (* (pow (sqrt 1.0) 2) (sqrt k))
17.395 * [approximate]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt k)) in (k) around 0
17.395 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt k)) in k
17.395 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
17.395 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
17.395 * [taylor]: Taking taylor expansion of 1.0 in k
17.395 * [backup-simplify]: Simplify 1.0 into 1.0
17.396 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.396 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.396 * [taylor]: Taking taylor expansion of (sqrt k) in k
17.396 * [taylor]: Taking taylor expansion of k in k
17.396 * [backup-simplify]: Simplify 0 into 0
17.396 * [backup-simplify]: Simplify 1 into 1
17.396 * [backup-simplify]: Simplify (sqrt 0) into 0
17.397 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.398 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt k)) in k
17.398 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
17.398 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
17.398 * [taylor]: Taking taylor expansion of 1.0 in k
17.398 * [backup-simplify]: Simplify 1.0 into 1.0
17.398 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.399 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.399 * [taylor]: Taking taylor expansion of (sqrt k) in k
17.399 * [taylor]: Taking taylor expansion of k in k
17.399 * [backup-simplify]: Simplify 0 into 0
17.399 * [backup-simplify]: Simplify 1 into 1
17.399 * [backup-simplify]: Simplify (sqrt 0) into 0
17.401 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.402 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
17.403 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) 0) into 0
17.403 * [backup-simplify]: Simplify 0 into 0
17.404 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
17.407 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (* 0 0)) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.410 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.414 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.415 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
17.416 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
17.421 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.423 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.428 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.429 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
17.430 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
17.438 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.440 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.445 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 3))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k)))))))
17.445 * [backup-simplify]: Simplify (* (sqrt (/ 1.0 (sqrt (/ 1 (- k))))) (sqrt (/ 1.0 (sqrt (/ 1 (- k)))))) into (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k)))
17.445 * [approximate]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) in (k) around 0
17.445 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) in k
17.445 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
17.445 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
17.445 * [taylor]: Taking taylor expansion of 1.0 in k
17.445 * [backup-simplify]: Simplify 1.0 into 1.0
17.445 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.446 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.446 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
17.446 * [taylor]: Taking taylor expansion of (/ -1 k) in k
17.446 * [taylor]: Taking taylor expansion of -1 in k
17.446 * [backup-simplify]: Simplify -1 into -1
17.446 * [taylor]: Taking taylor expansion of k in k
17.446 * [backup-simplify]: Simplify 0 into 0
17.446 * [backup-simplify]: Simplify 1 into 1
17.446 * [backup-simplify]: Simplify (/ -1 1) into -1
17.446 * [backup-simplify]: Simplify (sqrt 0) into 0
17.447 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
17.448 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
17.449 * [backup-simplify]: Simplify (/ (pow (sqrt 1.0) 2) +nan.0) into (* +nan.0 (pow (sqrt 1.0) 2))
17.449 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) in k
17.449 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
17.449 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
17.449 * [taylor]: Taking taylor expansion of 1.0 in k
17.449 * [backup-simplify]: Simplify 1.0 into 1.0
17.449 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.450 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.450 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
17.450 * [taylor]: Taking taylor expansion of (/ -1 k) in k
17.450 * [taylor]: Taking taylor expansion of -1 in k
17.450 * [backup-simplify]: Simplify -1 into -1
17.450 * [taylor]: Taking taylor expansion of k in k
17.450 * [backup-simplify]: Simplify 0 into 0
17.450 * [backup-simplify]: Simplify 1 into 1
17.450 * [backup-simplify]: Simplify (/ -1 1) into -1
17.450 * [backup-simplify]: Simplify (sqrt 0) into 0
17.451 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
17.452 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
17.453 * [backup-simplify]: Simplify (/ (pow (sqrt 1.0) 2) +nan.0) into (* +nan.0 (pow (sqrt 1.0) 2))
17.454 * [backup-simplify]: Simplify (* +nan.0 (pow (sqrt 1.0) 2)) into (* +nan.0 (pow (sqrt 1.0) 2))
17.454 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
17.455 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
17.456 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.460 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (sqrt 1.0) 2)) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.461 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.462 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
17.463 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
17.463 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.465 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.472 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (sqrt 1.0) 2)) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.473 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
17.477 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (/ 1 (- k))) (* +nan.0 (pow (sqrt 1.0) 2)))) into (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k)))))))
17.477 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 1)
17.477 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
17.477 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
17.477 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
17.477 * [taylor]: Taking taylor expansion of 1.0 in k
17.477 * [backup-simplify]: Simplify 1.0 into 1.0
17.477 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
17.477 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.477 * [taylor]: Taking taylor expansion of k in k
17.477 * [backup-simplify]: Simplify 0 into 0
17.477 * [backup-simplify]: Simplify 1 into 1
17.478 * [backup-simplify]: Simplify (/ 1 1) into 1
17.478 * [backup-simplify]: Simplify (sqrt 0) into 0
17.479 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.479 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
17.479 * [taylor]: Taking taylor expansion of 1.0 in k
17.479 * [backup-simplify]: Simplify 1.0 into 1.0
17.479 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
17.479 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.479 * [taylor]: Taking taylor expansion of k in k
17.479 * [backup-simplify]: Simplify 0 into 0
17.479 * [backup-simplify]: Simplify 1 into 1
17.479 * [backup-simplify]: Simplify (/ 1 1) into 1
17.479 * [backup-simplify]: Simplify (sqrt 0) into 0
17.480 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.480 * [backup-simplify]: Simplify (* 1.0 0) into 0
17.480 * [backup-simplify]: Simplify 0 into 0
17.481 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
17.482 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.482 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
17.484 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.485 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
17.485 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.486 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.488 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.489 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
17.489 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.490 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
17.490 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
17.490 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
17.490 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
17.490 * [taylor]: Taking taylor expansion of 1.0 in k
17.490 * [backup-simplify]: Simplify 1.0 into 1.0
17.490 * [taylor]: Taking taylor expansion of (sqrt k) in k
17.490 * [taylor]: Taking taylor expansion of k in k
17.490 * [backup-simplify]: Simplify 0 into 0
17.490 * [backup-simplify]: Simplify 1 into 1
17.491 * [backup-simplify]: Simplify (sqrt 0) into 0
17.491 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.492 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
17.492 * [taylor]: Taking taylor expansion of 1.0 in k
17.492 * [backup-simplify]: Simplify 1.0 into 1.0
17.492 * [taylor]: Taking taylor expansion of (sqrt k) in k
17.492 * [taylor]: Taking taylor expansion of k in k
17.492 * [backup-simplify]: Simplify 0 into 0
17.492 * [backup-simplify]: Simplify 1 into 1
17.492 * [backup-simplify]: Simplify (sqrt 0) into 0
17.493 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.493 * [backup-simplify]: Simplify (* 1.0 0) into 0
17.493 * [backup-simplify]: Simplify 0 into 0
17.494 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
17.494 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.496 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.497 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
17.497 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.499 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.501 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
17.501 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.502 * [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))))))))
17.502 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
17.502 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
17.502 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
17.502 * [taylor]: Taking taylor expansion of 1.0 in k
17.502 * [backup-simplify]: Simplify 1.0 into 1.0
17.502 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
17.502 * [taylor]: Taking taylor expansion of (/ -1 k) in k
17.502 * [taylor]: Taking taylor expansion of -1 in k
17.502 * [backup-simplify]: Simplify -1 into -1
17.502 * [taylor]: Taking taylor expansion of k in k
17.502 * [backup-simplify]: Simplify 0 into 0
17.502 * [backup-simplify]: Simplify 1 into 1
17.502 * [backup-simplify]: Simplify (/ -1 1) into -1
17.503 * [backup-simplify]: Simplify (sqrt 0) into 0
17.503 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
17.504 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
17.504 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
17.504 * [taylor]: Taking taylor expansion of 1.0 in k
17.504 * [backup-simplify]: Simplify 1.0 into 1.0
17.504 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
17.504 * [taylor]: Taking taylor expansion of (/ -1 k) in k
17.504 * [taylor]: Taking taylor expansion of -1 in k
17.504 * [backup-simplify]: Simplify -1 into -1
17.504 * [taylor]: Taking taylor expansion of k in k
17.504 * [backup-simplify]: Simplify 0 into 0
17.504 * [backup-simplify]: Simplify 1 into 1
17.504 * [backup-simplify]: Simplify (/ -1 1) into -1
17.505 * [backup-simplify]: Simplify (sqrt 0) into 0
17.505 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
17.506 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
17.506 * [backup-simplify]: Simplify +nan.0 into +nan.0
17.506 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
17.508 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.510 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
17.510 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.510 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.513 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.517 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
17.518 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.519 * [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)))))
17.519 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1)
17.519 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
17.519 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
17.519 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
17.519 * [taylor]: Taking taylor expansion of 1.0 in k
17.519 * [backup-simplify]: Simplify 1.0 into 1.0
17.519 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
17.519 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.519 * [taylor]: Taking taylor expansion of k in k
17.519 * [backup-simplify]: Simplify 0 into 0
17.519 * [backup-simplify]: Simplify 1 into 1
17.519 * [backup-simplify]: Simplify (/ 1 1) into 1
17.520 * [backup-simplify]: Simplify (sqrt 0) into 0
17.521 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.521 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
17.521 * [taylor]: Taking taylor expansion of 1.0 in k
17.522 * [backup-simplify]: Simplify 1.0 into 1.0
17.522 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
17.522 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.522 * [taylor]: Taking taylor expansion of k in k
17.522 * [backup-simplify]: Simplify 0 into 0
17.522 * [backup-simplify]: Simplify 1 into 1
17.522 * [backup-simplify]: Simplify (/ 1 1) into 1
17.522 * [backup-simplify]: Simplify (sqrt 0) into 0
17.529 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.529 * [backup-simplify]: Simplify (* 1.0 0) into 0
17.529 * [backup-simplify]: Simplify 0 into 0
17.531 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
17.531 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.532 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
17.535 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.537 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
17.537 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.538 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.542 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.544 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
17.544 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.546 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
17.546 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
17.546 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
17.546 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
17.546 * [taylor]: Taking taylor expansion of 1.0 in k
17.546 * [backup-simplify]: Simplify 1.0 into 1.0
17.546 * [taylor]: Taking taylor expansion of (sqrt k) in k
17.546 * [taylor]: Taking taylor expansion of k in k
17.546 * [backup-simplify]: Simplify 0 into 0
17.546 * [backup-simplify]: Simplify 1 into 1
17.546 * [backup-simplify]: Simplify (sqrt 0) into 0
17.548 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.548 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
17.548 * [taylor]: Taking taylor expansion of 1.0 in k
17.548 * [backup-simplify]: Simplify 1.0 into 1.0
17.548 * [taylor]: Taking taylor expansion of (sqrt k) in k
17.548 * [taylor]: Taking taylor expansion of k in k
17.548 * [backup-simplify]: Simplify 0 into 0
17.548 * [backup-simplify]: Simplify 1 into 1
17.548 * [backup-simplify]: Simplify (sqrt 0) into 0
17.550 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.550 * [backup-simplify]: Simplify (* 1.0 0) into 0
17.550 * [backup-simplify]: Simplify 0 into 0
17.551 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
17.552 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.555 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.557 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
17.557 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.561 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.563 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
17.564 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.565 * [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))))))))
17.565 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
17.565 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
17.565 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
17.565 * [taylor]: Taking taylor expansion of 1.0 in k
17.565 * [backup-simplify]: Simplify 1.0 into 1.0
17.565 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
17.565 * [taylor]: Taking taylor expansion of (/ -1 k) in k
17.566 * [taylor]: Taking taylor expansion of -1 in k
17.566 * [backup-simplify]: Simplify -1 into -1
17.566 * [taylor]: Taking taylor expansion of k in k
17.566 * [backup-simplify]: Simplify 0 into 0
17.566 * [backup-simplify]: Simplify 1 into 1
17.566 * [backup-simplify]: Simplify (/ -1 1) into -1
17.566 * [backup-simplify]: Simplify (sqrt 0) into 0
17.568 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
17.568 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
17.568 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
17.568 * [taylor]: Taking taylor expansion of 1.0 in k
17.568 * [backup-simplify]: Simplify 1.0 into 1.0
17.568 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
17.568 * [taylor]: Taking taylor expansion of (/ -1 k) in k
17.568 * [taylor]: Taking taylor expansion of -1 in k
17.568 * [backup-simplify]: Simplify -1 into -1
17.568 * [taylor]: Taking taylor expansion of k in k
17.568 * [backup-simplify]: Simplify 0 into 0
17.568 * [backup-simplify]: Simplify 1 into 1
17.569 * [backup-simplify]: Simplify (/ -1 1) into -1
17.569 * [backup-simplify]: Simplify (sqrt 0) into 0
17.570 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
17.571 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
17.571 * [backup-simplify]: Simplify +nan.0 into +nan.0
17.573 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
17.576 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.578 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
17.579 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.580 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.584 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.588 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
17.588 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
17.589 * [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)))))
17.589 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1)
17.590 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
17.590 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
17.590 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
17.590 * [taylor]: Taking taylor expansion of 2.0 in n
17.590 * [backup-simplify]: Simplify 2.0 into 2.0
17.590 * [taylor]: Taking taylor expansion of (* n PI) in n
17.590 * [taylor]: Taking taylor expansion of n in n
17.590 * [backup-simplify]: Simplify 0 into 0
17.590 * [backup-simplify]: Simplify 1 into 1
17.590 * [taylor]: Taking taylor expansion of PI in n
17.590 * [backup-simplify]: Simplify PI into PI
17.590 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
17.590 * [taylor]: Taking taylor expansion of 2.0 in n
17.590 * [backup-simplify]: Simplify 2.0 into 2.0
17.590 * [taylor]: Taking taylor expansion of (* n PI) in n
17.590 * [taylor]: Taking taylor expansion of n in n
17.590 * [backup-simplify]: Simplify 0 into 0
17.590 * [backup-simplify]: Simplify 1 into 1
17.590 * [taylor]: Taking taylor expansion of PI in n
17.590 * [backup-simplify]: Simplify PI into PI
17.591 * [backup-simplify]: Simplify (* 0 PI) into 0
17.591 * [backup-simplify]: Simplify (* 2.0 0) into 0
17.591 * [backup-simplify]: Simplify 0 into 0
17.593 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.595 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
17.595 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
17.596 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
17.597 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
17.597 * [backup-simplify]: Simplify 0 into 0
17.599 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
17.600 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
17.600 * [backup-simplify]: Simplify 0 into 0
17.602 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.604 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
17.604 * [backup-simplify]: Simplify 0 into 0
17.606 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.608 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
17.608 * [backup-simplify]: Simplify 0 into 0
17.609 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.611 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
17.611 * [backup-simplify]: Simplify 0 into 0
17.614 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
17.616 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
17.616 * [backup-simplify]: Simplify 0 into 0
17.616 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
17.617 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
17.617 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
17.617 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
17.617 * [taylor]: Taking taylor expansion of 2.0 in n
17.617 * [backup-simplify]: Simplify 2.0 into 2.0
17.617 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.617 * [taylor]: Taking taylor expansion of PI in n
17.617 * [backup-simplify]: Simplify PI into PI
17.617 * [taylor]: Taking taylor expansion of n in n
17.617 * [backup-simplify]: Simplify 0 into 0
17.617 * [backup-simplify]: Simplify 1 into 1
17.618 * [backup-simplify]: Simplify (/ PI 1) into PI
17.618 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
17.618 * [taylor]: Taking taylor expansion of 2.0 in n
17.618 * [backup-simplify]: Simplify 2.0 into 2.0
17.618 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.618 * [taylor]: Taking taylor expansion of PI in n
17.618 * [backup-simplify]: Simplify PI into PI
17.618 * [taylor]: Taking taylor expansion of n in n
17.618 * [backup-simplify]: Simplify 0 into 0
17.618 * [backup-simplify]: Simplify 1 into 1
17.618 * [backup-simplify]: Simplify (/ PI 1) into PI
17.619 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
17.619 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
17.620 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.621 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
17.621 * [backup-simplify]: Simplify 0 into 0
17.622 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.623 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
17.623 * [backup-simplify]: Simplify 0 into 0
17.625 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.627 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.627 * [backup-simplify]: Simplify 0 into 0
17.628 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.629 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.629 * [backup-simplify]: Simplify 0 into 0
17.631 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.633 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.633 * [backup-simplify]: Simplify 0 into 0
17.634 * [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
17.636 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.636 * [backup-simplify]: Simplify 0 into 0
17.636 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
17.637 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
17.637 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
17.637 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
17.637 * [taylor]: Taking taylor expansion of -2.0 in n
17.637 * [backup-simplify]: Simplify -2.0 into -2.0
17.637 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.637 * [taylor]: Taking taylor expansion of PI in n
17.637 * [backup-simplify]: Simplify PI into PI
17.637 * [taylor]: Taking taylor expansion of n in n
17.637 * [backup-simplify]: Simplify 0 into 0
17.637 * [backup-simplify]: Simplify 1 into 1
17.638 * [backup-simplify]: Simplify (/ PI 1) into PI
17.638 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
17.638 * [taylor]: Taking taylor expansion of -2.0 in n
17.638 * [backup-simplify]: Simplify -2.0 into -2.0
17.638 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.638 * [taylor]: Taking taylor expansion of PI in n
17.638 * [backup-simplify]: Simplify PI into PI
17.638 * [taylor]: Taking taylor expansion of n in n
17.638 * [backup-simplify]: Simplify 0 into 0
17.638 * [backup-simplify]: Simplify 1 into 1
17.639 * [backup-simplify]: Simplify (/ PI 1) into PI
17.639 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
17.640 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
17.641 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.641 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
17.642 * [backup-simplify]: Simplify 0 into 0
17.643 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.644 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
17.644 * [backup-simplify]: Simplify 0 into 0
17.645 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.645 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.646 * [backup-simplify]: Simplify 0 into 0
17.646 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.647 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.647 * [backup-simplify]: Simplify 0 into 0
17.648 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.649 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.649 * [backup-simplify]: Simplify 0 into 0
17.649 * [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
17.650 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.650 * [backup-simplify]: Simplify 0 into 0
17.651 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
17.651 * * * [progress]: simplifying candidates
17.654 * [simplify]: Simplifying:
  (+ 1/2 1/2)
  (+ 1/2 (/ 1 2))
  (+ 1 1)
  (+ (/ 1 2) 1/2)
  (+ (/ 1 2) (/ 1 2))
  (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))
  (+ 1 1)
  (+ (log (sqrt (/ 1.0 (sqrt k)))) (log (sqrt (/ 1.0 (sqrt k)))))
  (log (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (exp (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (* (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k)))) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k)))))
  (* (cbrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (cbrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))))
  (cbrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (* (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))
  (sqrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (sqrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt 1.0) (sqrt 1.0))
  (* (sqrt (sqrt k)) (sqrt (sqrt k)))
  (* (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k))))) (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k))))))
  (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))) (sqrt (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))))
  (* (sqrt (cbrt (/ 1.0 (sqrt k)))) (sqrt (cbrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (cbrt 1.0) (cbrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (cbrt (sqrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (cbrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (cbrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))))
  (* (sqrt (/ (cbrt 1.0) (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt k))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) 1)) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) 1)))
  (* (sqrt (/ (cbrt 1.0) (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (sqrt 1.0) (cbrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (cbrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt 1))) (sqrt (/ (sqrt 1.0) (sqrt 1))))
  (* (sqrt (/ (sqrt 1.0) (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) 1)) (sqrt (/ (sqrt 1.0) 1)))
  (* (sqrt (/ (sqrt 1.0) (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt k))))
  (* (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ 1.0 (cbrt (sqrt k)))) (sqrt (/ 1.0 (cbrt (sqrt k)))))
  (* (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ 1.0 (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt (cbrt k)))))
  (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ 1 (sqrt 1))) (sqrt (/ 1 (sqrt 1))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ 1 1)) (sqrt (/ 1 1)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt 1) (sqrt 1))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt 1.0) (sqrt 1.0))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* 1 1)
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* 2 1/2)
  (* 2 1)
  (* 2 (/ 1 2))
  (* (sqrt (/ 1.0 (sqrt k))) (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) 1)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt 1))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) 1)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt 1))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 1)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt 1))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt 1.0))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) 1)
  (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (cbrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (cbrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (cbrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (cbrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt 1.0))
  (* (sqrt 1.0) (sqrt (/ 1.0 (sqrt k))))
  (- (log 1.0) (log (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) 1)
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt 1))
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (- (log 1.0) (log (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) 1)
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt 1))
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (* +nan.0 (* (pow (sqrt 1.0) 2) k)))))))
  (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 3))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k)))))))
  (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k)))))))
  (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (- (+ (* +nan.0 (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)))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
17.658 * * [simplify]: iteration 0: 285 enodes
17.743 * * [simplify]: iteration 1: 578 enodes
18.009 * * [simplify]: iteration 2: 1485 enodes
18.861 * * [simplify]: iteration 3: 4291 enodes
19.891 * * [simplify]: iteration complete: 5006 enodes
19.891 * * [simplify]: Extracting #0: cost 88 inf + 0
19.893 * * [simplify]: Extracting #1: cost 678 inf + 3
19.904 * * [simplify]: Extracting #2: cost 1381 inf + 11184
19.941 * * [simplify]: Extracting #3: cost 866 inf + 102855
20.000 * * [simplify]: Extracting #4: cost 325 inf + 186510
20.088 * * [simplify]: Extracting #5: cost 111 inf + 240962
20.187 * * [simplify]: Extracting #6: cost 18 inf + 272414
20.290 * * [simplify]: Extracting #7: cost 0 inf + 279778
20.359 * [simplify]: Simplified to:
  1
  1
  2
  1
  1
  (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))
  (/ 1.0 (sqrt k))
  (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))
  2
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))))
  (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  1.0
  (sqrt k)
  (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k)))))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (fabs (cbrt k)))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  1
  (/ 1.0 (sqrt k))
  1.0
  (/ 1 (sqrt k))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  1
  2
  1
  (* (sqrt (/ 1.0 (sqrt k))) (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k))))))
  (* (fabs (cbrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (fabs (/ (cbrt 1.0) (cbrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (fabs (cbrt 1.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (fabs (cbrt 1.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt 1.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt 1.0)))
  (* (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (fabs (cbrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (sqrt (/ 1.0 (sqrt k)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (* (sqrt 1.0) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (sqrt (/ 1.0 (sqrt k)))
  (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (cbrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (cbrt 1.0) (cbrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (cbrt 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (cbrt 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (cbrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (cbrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (/ 1.0 (sqrt k))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (/ 1.0 (sqrt k))
  (/ 1.0 (sqrt k))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (/ 1.0 (sqrt k))
  (* (sqrt 1.0) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt 1.0) (sqrt (/ 1.0 (sqrt k))))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (fabs (cbrt k)))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (fabs (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1.0
  (/ 1.0 (sqrt (sqrt k)))
  1.0
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (fabs (cbrt k)))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (fabs (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1.0
  (/ 1.0 (sqrt (sqrt k)))
  1.0
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (* 2.0 (* PI n))
  (* 2.0 (* PI n))
  (log (* 2.0 (* PI n)))
  (log (* 2.0 (* PI n)))
  (log (* 2.0 (* PI n)))
  (exp (* 2.0 (* PI n)))
  (* n (* (* PI 2.0) (* (* n (* PI 2.0)) (* n (* PI 2.0)))))
  (* n (* (* PI 2.0) (* (* n (* PI 2.0)) (* n (* PI 2.0)))))
  (* (cbrt (* 2.0 (* PI n))) (cbrt (* 2.0 (* PI n))))
  (cbrt (* 2.0 (* PI n)))
  (* n (* (* PI 2.0) (* (* n (* PI 2.0)) (* n (* PI 2.0)))))
  (sqrt (* 2.0 (* PI n)))
  (sqrt (* 2.0 (* PI n)))
  (* (* (cbrt n) (cbrt n)) (* PI 2.0))
  (* (sqrt n) (* PI 2.0))
  (* PI 2.0)
  (* n PI)
  (- (+ (* (- +nan.0) (* (* k k) 1.0)) (* +nan.0 1.0)) (* (* +nan.0 1.0) k))
  (- (+ (* +nan.0 (- (/ 1.0 (* k k)) (/ (/ 1.0 (* k k)) k))) (* (/ 1.0 k) +nan.0)))
  (+ (- (* +nan.0 1.0)) (- (* (/ +nan.0 k) (/ 1.0 k)) (* (/ 1.0 k) +nan.0)))
  (- (- (+ (* +nan.0 k) (* (* k k) +nan.0)) +nan.0))
  (+ (+ (/ (- +nan.0) (* k k)) (/ (/ (- +nan.0) k) (* k k))) (/ +nan.0 k))
  (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (* k k)))
  (- (- (+ (* +nan.0 k) (* (* k k) +nan.0)) +nan.0))
  (+ (+ (/ (- +nan.0) (* k k)) (/ (/ (- +nan.0) k) (* k k))) (/ +nan.0 k))
  (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (* k k)))
  (* 2.0 (* PI n))
  (* 2.0 (* PI n))
  (* 2.0 (* PI n))
20.385 * * * [progress]: adding candidates to table
21.818 * [progress]: [Phase 3 of 3] Extracting.
21.818 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<alt (λ (k n) (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))> #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (/ (* 1.0 (pow (pow (* 2.0 (* n PI)) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k)))>)
21.822 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k)
21.822 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (#<alt (λ (k n) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<alt (λ (k n) (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))> #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (/ (* 1.0 (pow (pow (* 2.0 (* n PI)) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k)))>)
21.901 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<alt (λ (k n) (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))> #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (/ (* 1.0 (pow (pow (* 2.0 (* n PI)) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k)))>)
21.998 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<alt (λ (k n) (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))> #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (/ (* 1.0 (pow (pow (* 2.0 (* n PI)) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k)))>)
22.105 * * * [regime]: Found split indices: #<option (#s(si 0 255))>
22.105 * [simplify]: Simplifying:
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
22.105 * * [simplify]: iteration 0: 15 enodes
22.107 * * [simplify]: iteration 1: 18 enodes
22.108 * * [simplify]: iteration complete: 18 enodes
22.108 * * [simplify]: Extracting #0: cost 1 inf + 0
22.108 * * [simplify]: Extracting #1: cost 2 inf + 0
22.108 * * [simplify]: Extracting #2: cost 3 inf + 0
22.108 * * [simplify]: Extracting #3: cost 5 inf + 0
22.108 * * [simplify]: Extracting #4: cost 8 inf + 0
22.108 * * [simplify]: Extracting #5: cost 7 inf + 43
22.108 * * [simplify]: Extracting #6: cost 11 inf + 43
22.108 * * [simplify]: Extracting #7: cost 9 inf + 87
22.108 * * [simplify]: Extracting #8: cost 4 inf + 671
22.108 * * [simplify]: Extracting #9: cost 1 inf + 2116
22.109 * * [simplify]: Extracting #10: cost 0 inf + 2691
22.109 * [simplify]: Simplified to:
  (* (sqrt (/ (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
29.244 * [regime-testing]: Baseline error score: 0.4395176143333959
29.261 * [regime-testing]: Oracle error score: 0.07037439836274606
29.284 * [regime-testing]: End program error score: 0.4395176143333959